Validation of Accident 

Models for Intersections

PUBLICATION NO. FHWA-RD-03-037 MAY 2005

Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296
FOREWORD 

The existing crash prediction models for rural intersections developed for the Interactive Highway Safety 

Design Model (IHSDM) require validation and recalibration to improve their credibility and enhance their 

applicability. This report describes the results of validation and calibration of motor vehicle crash models 

for rural intersections. Both the validation and recalibration activities were conducted in pursuit of one 

overriding research objective, which was to make marginal improvements to an existing set of statistical 

models for predicting crashes at two- and four-lane intersections, with the primary intent to be used in the 

IHSDM. 

The five types of intersection models for which conclusions are drawn and recommendations are made 

are: three-legged stop controlled intersections of two-lane roads; four-legged stop controlled intersections 

of two-lane roads; three-legged stop controlled intersections with two lanes on minor and four lanes on 

major road; and four-legged stop controlled intersections with two lanes on minor and four lanes on major 

road, and signalized intersections of two-lane roads. 

Copies of this report can be obtained from the Research and Technology Product Distribution Center, 

9701 Philadelphia Court, Unit Q, Lanham, MD 20706; telephone: 301–577–0818; fax: 301–577–1421; or 

the National Technical Information Service (NTIS), 5285 Port Royal Road, Springfield, VA 22161; 

telephone: 703–487–4650; fax: 703–321–8547. 

Michael F. Trentacoste 

Director 

Office of Safety 

 Research and Development 

Notice 

This document is disseminated under the sponsorship of the U.S. Department of Transportation in the 

interest of information exchange. The U.S. Government assumes no liability for the use of the information 

contained in this document. This report does not constitute a standard, specification, or regulation. 

The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers' names 

appear in this report only because they are considered essential to the objective of the document. 

Quality Assurance Statement 

The Federal Highway Administration (FHWA) provides high-quality information to serve Government, 

industry, and the public in a manner that promotes public understanding. Standards and policies are used 

to ensure and maximize the quality, objectivity, utility, and integrity of its information. FHWA 

periodically reviews quality issues and adjusts its programs and processes to ensure continuous quality 

improvement. 
1. Report No.

FHWA-RD-03-037 

2. Government Accession No. 3. Recipient's Catalog No.

5. Report Date 

May 2005 

4. Title and Subtitle

Validation of Accident Models for Intersections 

6. Performing Organization Code

7. Author(s) 

Simon Washington, Bhagwant Persaud, Craig Lyon, 

and Jutaek Oh 

8. Performing Organization Report No.

None 

9. Performing Organization Name and Address 10. Work Unit No. (TRAIS)

University of Arizona 

Department of Civil Engineering 

Tucson, AZ 85721--0072 

Ryerson University 

Department of Civil Engineering 

350 Victoria Street 

Toronto, ON Canada M5B 2K3 

11. Contract or Grant No. 

DTFH61-00-C-00073 

13. Type of Report and Period Covered

Research Report 

11/2000 to 12/2003 

12. Sponsoring Agency Name and Address

Department of Transportation 

Federal Highway Administration 

400 7th Street, SW Room 4110 

Washington, DC 20590-0001 14. Sponsoring Agency Code

15. Supplementary Notes

Joe Bared, HRDS-05, Contracting Officer’s Technical Representative 

16. Abstract

This report describes the results of validation and calibration of motor vehicle crash models for 

rural intersections. Both the validation and recalibration activities were conducted in pursuit of 

one overriding research objective, which was to make marginal improvements to an existing 

set of statistical models for predicting crashes at two and four lane intersections, with the 

primary intent to be used in the Interactive Highway Safety Design Module (IHSDM). 

The five types of intersection models for which conclusions are drawn and recommendations 

are made are: Three-legged stop controlled intersections of two-lane roads; four-legged stop 

controlled intersections of two-lane roads; three-legged stop controlled intersections with two 

lanes on minor and four lanes on major road; and four-legged stop controlled intersections with 

two lanes on minor and four lanes on major road, and signalized intersections of two-lane 

roads. 

17. Key Words

Accident modification factors, traffic safety, signalized 

intersections, crash models, crash model validation, 

Interactive Highway Safety Design Model 

18. Distribution Statement 

19. Security Classif. (of this report) 

Unclassified 

20. Security Classif. (of this page)

Unclassified 

21. No. of Pages

311 

22. Price
ii

SI* (MODERN METRIC) CONVERSION FACTORS 

APPROXIMATE CONVERSIONS TO SI UNITS

Symbol When You Know Multiply By To Find Symbol 

LENGTH 

in inches 25.4 millimeters mm 

ft feet 0.305 meters m 

yd yards 0.914 meters m 

mi miles 1.61 kilometers km 

AREA 

in2 square inches 645.2 square millimeters mm2

ft2 square feet 0.093 square meters m2

yd2 square yard 0.836 square meters m2

ac acres 0.405 hectares ha 

mi2 square miles 2.59 square kilometers km2

VOLUME 

fl oz fluid ounces 29.57 milliliters mL 

gal gallons 3.785 liters L 

ft3 cubic feet 0.028 cubic meters m3 

yd3 cubic yards 0.765 cubic meters m3 

NOTE: volumes greater than 1000 L shall be shown in m3

MASS 

oz ounces 28.35 grams g

lb pounds 0.454 kilograms kg

T short tons (2000 lb) 0.907 megagrams (or "metric ton") Mg (or "t") 

TEMPERATURE (exact degrees) o

F Fahrenheit 5 (F-32)/9 Celsius oC 

or (F-32)/1.8 

ILLUMINATION 

fc foot-candles 10.76 lux lx 

fl foot-Lamberts 3.426 candela/m2 cd/m2

FORCE and PRESSURE or STRESS 

lbf poundforce 4.45 newtons N 

lbf/in2 poundforce per square inch 6.89 kilopascals kPa 

APPROXIMATE CONVERSIONS FROM SI UNITS 

Symbol When You Know Multiply By To Find Symbol 

LENGTH

mm millimeters 0.039 inches in 

m meters 3.28 feet ft 

m meters 1.09 yards yd 

km kilometers 0.621 miles mi 

AREA mm2

 square millimeters 0.0016 square inches in2 

m2 square meters 10.764 square feet ft2 

m2 square meters 1.195 square yards yd2 

ha hectares 2.47 acres ac 

km2 square kilometers 0.386 square miles mi2 

VOLUME 

mL milliliters 0.034 fluid ounces fl oz 

L liters 0.264 gallons gal 

m3 cubic meters 35.314 cubic feet ft3 

m3 cubic meters 1.307 cubic yards yd3 

MASS 

g grams 0.035 ounces oz

kg kilograms 2.202 pounds lb

Mg (or "t") megagrams (or "metric ton") 1.103 short tons (2000 lb) T 

TEMPERATURE (exact degrees) o

C Celsius 1.8C+32 Fahrenheit oF 

ILLUMINATION 

lx lux 0.0929 foot-candles fc 

cd/m2 candela/m2 0.2919 foot-Lamberts fl

FORCE and PRESSURE or STRESS 

N newtons 0.225 poundforce lbf 

kPa kilopascals 0.145 poundforce per square inch lbf/in2

*SI is the symbol for th International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E e 380. 

(Revised March 2003)
iii

TABLE OF CONTENTS 

EXECUTIVE SUMMARY ...............................................................................................1

VALIDATION FINDINGS............................................................................................ 2 

RECALIBRATION FINDINGS..................................................................................... 3 

RECOMMENDATIONS................................................................................................ 3 

1. INTRODUCTION..........................................................................................................5

1.1 VARIABLE ABBREVIATIONS ............................................................................. 6 

1.1.1 Model Types ...................................................................................................... 6 

1.1.2 Accident Models ................................................................................................ 6 

1.1.3 Definitions of Variables..................................................................................... 7 

2. VALIDATION OF ACCIDENT MODELS ..............................................................11

2.1 VALIDATION APPROACH AND PRELIMINARIES ........................................ 11 

2.2 DATA SOURCES AND ISSUES .......................................................................... 13 

2.3 MODEL PERFORMANCE MEASURES ............................................................. 15 

2.4 VALIDATION ACTIVITY 1: VALIDATION USING ADDITIONAL YEARS 

OF ACCIDENT DATA .............................................................................................. 18 

2.4.1 Model I............................................................................................................. 19 

2.4.2 Model II ........................................................................................................... 26 

2.4.3 Model III .......................................................................................................... 32 

2.4.4 Model IV.......................................................................................................... 38 

2.4.5 Model V ........................................................................................................... 43 

2.5 VALIDATION ACTIVITY 2: VALIDATION WITH GEORGIA DATA ........... 51 

2.5.1 Model I............................................................................................................. 51 

2.5.2 Model II ........................................................................................................... 56 

2.5.3 Model III .......................................................................................................... 61 

2.5.4 Model IV.......................................................................................................... 71 

2.5.5 Model V ........................................................................................................... 83 

2.6 VALIDATION ACTIVITY 3: VALIDATION OF THE ACCIDENT 

PREDICTION ALGORITHM.................................................................................... 99 

2.6.1 Validation of the Base Models....................................................................... 100 

2.6.2 Validation of the Accident Prediction Algorithm.......................................... 104 

2.7 DISCUSSION OF RESULTS............................................................................... 111 

2.7.1 Model I........................................................................................................... 112 

2.7.2 Model II ......................................................................................................... 114 

2.7.3 Model III ........................................................................................................ 116 

2.7.4 Model IV........................................................................................................ 118 

2.7.5 Model V ......................................................................................................... 119 

3. RECALIBRATION ...................................................................................................123

3.1 RESEARCH APPROACH ................................................................................... 123 

3.1.1 Model Functional Forms................................................................................ 125 

3.1.2 Goodness-of-Fit Evaluation........................................................................... 125 

3.2 DESCRIPTION OF DATA .................................................................................. 127 

3.2.1 Summary of Datasets ..................................................................................... 127 

3.2.2 Type I............................................................................................................. 129 

3.2.3 Type II............................................................................................................ 131 
iv

3.2.4 Type III .......................................................................................................... 134 

3.2.5 Type IV .......................................................................................................... 139 

3.2.6 Type V ........................................................................................................... 145 

3.3 AADT MODEL ESTIMATION RESULTS ........................................................ 153 

3.3.1 Description of Base Conditions ..................................................................... 153 

3.3.2 Model Results ................................................................................................ 157 

3.4 FULLY PARAMETERIZED STATISTICAL MODEL ESTIMATION RESULTS

................................................................................................................................... 173 

3.4.1 Type I Models................................................................................................ 174 

3.4.2 Type II Models............................................................................................... 181 

3.4.3 Type III Models ............................................................................................. 186 

3.4.4 Type IV Models ............................................................................................. 188 

3.4.5 Type V Models .............................................................................................. 191 

3.5 ESTIMATION OF ACCIDENT MODIFICATION FACTORS ........................ 194 

3.5.1 AMFs Derived from Recalibration Full Models............................................ 196 

3.5.2 AMFs Derived from Regression Models....................................................... 199 

3.5.3 Summary of AMFs ........................................................................................ 204 

3.6 SENSITIVITY ANALYSIS RESULTS............................................................... 208 

3.6.1 Type I Intersections........................................................................................ 208 

3.6.2 Type II Intersections ...................................................................................... 216 

3.6.3 Type III Intersections..................................................................................... 225 

3.6.4 Type IV Intersections..................................................................................... 236 

3.6.5 Type V Intersections...................................................................................... 245 

3.7 SUMMARY, DISCUSSION, AND CONCLUSIONS......................................... 249 

3.7.1 Model Recalibration....................................................................................... 250 

3.7.2 Summary of AMFs ........................................................................................ 257 

3.7.3 Conclusions and Recommendations .............................................................. 262 

APPENDIX A: ALL MODELS IN THE REPORTS OF RELEVANCE.................265

APPENDIX B: MODELS VALIDATED.....................................................................267

APPENDIX C: DESCRIPTIVE STATISTICS FOR FULL DATASETS BY STATE 

........................................................................................................................................269

APPENDIX D: CURE PLOTS FOR TYPE I, II, III, IV, AND V AADT MODELS293

REFERENCES.............................................................................................................. 297 
v

LIST OF FIGURES 

Figure 1. Observed versus Predicted Accident Frequency: Total Accidents Type I........ 54 

Figure 2. Observed versus Predicted Accident Frequency: Injury Accidents Type I....... 56 

Figure 3. Observed versus Predicted Accident Frequency: Total Accidents Type II....... 59 

Figure 4. Observed versus Predicted Accident Frequency: Injury Accidents Type II ..... 61 

Figure 5. Observed versus Predicted Accident Frequency: TOTACC Type II ................ 64 

Figure 6. Observed versus Predicted Accident Frequency: TOTACCI Type III ............. 66 

Figure 7. Observed versus Predicted Accident Frequency: Injury Variant 1 ................... 69 

Figure 8. Observed versus Predicted Accident Frequency: Injury Variant 2 ................... 71 

Figure 9. Observed versus Predicted Accident Frequency: TOTACC............................. 76 

Figure 10. Observed versus Predicted Accident Frequency: TOTACCI.......................... 79 

Figure 11. Observed versus Predicted Accident Frequency: INJACC............................. 81 

Figure 12. Observed versus Predicted Accident Frequency: INJACCI............................ 83 

Figure 13. Observed versus Predicted Accident Frequency: TOTACC Main Model ...... 88 

Figure 14. Observed versus Predicted Accident Frequency: TOTACC Variant 1........... 90 

Figure 15. Observed versus Predicted Accident Frequency: TOTACCI Main Model..... 92 

Figure 16. Observed versus Predicted Accident Frequency: TOTACCI Variant 3.......... 95 

Figure 17. Observed versus Predicted Accident Frequency: INJACC............................. 97 

Figure 18. Observed versus Predicted Accident Frequency: INJACCI............................ 99 

Figure 19. CURE Plot for Type III TOTACC AADT Model......................................... 126 

Figure 20. CURE Plot for Type III TOTACC AADT Model Using the CURE Method: 

Alternative Model ................................................................................................... 127 

Figure 21. CURE Plot for Alternate TOTACC Type I Group A Model ........................ 177 

Figure 22. CURE Plot for TOTACC Type I Group A Model ........................................ 178 

Figure 23. CURE Plot for Type I TOTACC AADT Model ........................................... 293 

Figure 24. CURE Plot for Type II TOTACC AADT Model.......................................... 294 

Figure 25. CURE Plot for Type III TOTACC AADT Model......................................... 294 

Figure 26. CURE Plot for Type IV TOTACC AADT Model ........................................ 295 

Figure 27. CURE Plot for Type V TOTACC AADT Model.......................................... 295 
vi

LIST OF TABLES 

Table 1. Basic Statistics for the Data Sources .................................................................. 14 

Table 2. Validation Statistics from Original Report1

........................................................ 18 

Table 3. Accident Summary Statistics for Type I Sites.................................................... 20 

Table 4. Parameter Estimates for Type I Total Accident Model Using Additional Years 

of Data............................................................................................................................. 21 

Table 5. Validation Statistics for Type I Total Accident Model Using Additional Years 

of Data............................................................................................................................. 22 

Table 6. Parameter Estimates for Type I Total Accident Model Using Washington Data

......................................................................................................................................... 23 

Table 7. Validation Statistics for Type I Total Accident Model Using Washington 

Data ................................................................................................................................. 23 

Table 8. Parameter Estimates for Type I Injury Accident Model Using Additional Years 

of Data............................................................................................................................. 24 

Table 9. Validation Statistics for Type I Injury Accident Model Using Additional 

Years of Data .................................................................................................................. 25 

Table 10. Parameter Estimates for Type I Injury Accident Model Using Washington Data

......................................................................................................................................... 25 

Table 11. Validation Statistics for Type I Injury Accident Model Using Washington 

Data ................................................................................................................................. 26 

Table 12. Accident Summary Statistics for Type II Sites................................................. 26 

Table 13. Parameter Estimates for Type II Total Accident Model Using Additional 

Years of Data .................................................................................................................. 27 

Table 14. Validation Statistics for Type II Total Accident Model Using Additional 

Years of Data .................................................................................................................. 28 

Table 15. Parameter Estimates for Type II Total Accident Model Using Washington 

Data ................................................................................................................................. 29 

Table 16. Validation Statistics for Type II Total Accident Model Using Washington 

Data ................................................................................................................................. 29 

Table 17. Parameter Estimates for Type II Injury Accident Model Using Additional 

Years of Data .................................................................................................................. 30 

Table 18. Validation Statistics for Type II Injury Accident Model Using Additional 

Years of Data .................................................................................................................. 31 

Table 19. Parameter Estimates for Type II Injury Accident Model Using Washington 

Data ................................................................................................................................. 32 

Table 20. Validation Statistics for Type II Injury Accident Model Using Washington 

Data ................................................................................................................................. 32 

Table 21. Accident Summary Statistics of Type III Sites................................................. 33 

Table 22. Parameter Estimates for TOTACC Type III Model Using Additional Years 

of Data............................................................................................................................. 34 

Table 23. Validation Statistics for TOTACC Type III Model Using Additional Years 

of Data............................................................................................................................. 34 

Table 24. Parameter Estimates for TOTACCI Type III Model Using Additional Years 

of Data............................................................................................................................. 35 
vii

Table 25. Validation Statistics for TOTACCI Type III Model Using Additional Years 

of Data............................................................................................................................. 35 

Table 26. Parameter Estimates for INJACC Type III Model Using Additional Years 

of Data: Variant 1............................................................................................................ 36 

Table 27. Validation Statistics for INJACC Type III Model Using Additional Years 

of Data: Variant 1............................................................................................................ 37 

Table 28. Parameter Estimates for INJACC Type III Model Using Additional Years 

of Data: Variant 2............................................................................................................ 37 

Table 29. Validation Statistics for INJACC Type III Model Using Additional Years 

of Data: Variant 2............................................................................................................ 38 

Table 30. Accident Summary Statistics of Type IV Sites ................................................ 38 

Table 31. Parameter Estimates for TOTACC Type IV Model Using Additional Years 

of Data............................................................................................................................. 39 

Table 32. Validation Statistics for TOTACC Type IV Model Using Additional Years 

of Data............................................................................................................................. 39 

Table 33. Parameter Estimates for TOTACCI Type IV Model Using Additional Years 

of Data............................................................................................................................. 40 

Table 34. Validation Statistics for TOTACCI Type IV Model Using Additional Years 

of Data............................................................................................................................. 40 

Table 35. Parameter Estimates for INJACC Type IV Model Using Additional Years 

of Data............................................................................................................................. 41 

Table 36. Validation Statistics for INJACC Type IV Model Using Additional Years 

of Data............................................................................................................................. 42 

Table 37. Parameter Estimates for INJACCI Type IV Model Using Additional Years 

of Data............................................................................................................................. 42 

Table 38. Validation Statistics for INJACCI Type IV Model Using Additional Years 

of Data............................................................................................................................. 43 

Table 39. Accident Summary Statistics of Type V Sites.................................................. 43 

Table 40. Parameter Estimates for TOTACC Type V Model Using Additional Years 

of Data: Main Model....................................................................................................... 44 

Table 41. Validation Statistics for TOTACC Type V Model Using Additional Years 

of Data: Main Model....................................................................................................... 45 

Table 42. Parameter Estimates for TOTACC Type V Model Using Additional Years 

of Data: Variant 1............................................................................................................ 45 

Table 43. Validation Statistics for TOTACC Type V Model Using Additional Years 

of Data: Variant 1............................................................................................................ 46 

Table 44. Parameter Estimates for TOTACCI Type V Model Using Additional Years 

of Data: Main Model....................................................................................................... 47 

Table 45. Validation Statistics for TOTACCI Type V Model Using Additional Years 

of Data: Main Model....................................................................................................... 47 

Table 46. Parameter Estimates for TOTACCI Type V Model Using Additional Years 

of Data: Variant 3............................................................................................................ 48 

Table 47. Validation Statistics for TOTACCI Type V Model Using Additional Years 

of Data: Variant 3............................................................................................................ 49 

Table 48. Parameter Estimates for INJACC Type V Model Using Additional Years of 

Data ................................................................................................................................. 49 
viii

Table 49. Validation Statistics for INJACC Type V Model Using Additional Years of 

Data ................................................................................................................................. 50 

Table 50. Parameter Estimates for INJACCI Type V Model Using Additional Years of 

Data ................................................................................................................................. 50 

Table 51. Validation Statistics for INJACCI Type V Model Using Additional Years of 

Data ................................................................................................................................. 51 

Table 52. Summary of Georgia versus Minnesota Data for Type I Sites......................... 52 

Table 53. Parameter Estimates for Type I Total Accident Model Using Georgia Data ... 53 

Table 54. Validation Statistics for Type I Total Accident Model Using Georgia Data.... 53 

Table 55. Parameter Estimates for Type I lnjury Accident Model Using Georgia Data.. 55 

Table 56. Validation Statistics for Type I Injury Accident Model Using Georgia Data .. 56 

Table 57. Summary of Georgia versus Minnesota Data for Type II Sites........................ 57 

Table 58. Parameter Estimates for Type II Total Accident Model Using Georgia Data.. 58 

Table 59. Validation Statistics for Type II Total Accident Model Using Georgia Data .. 59 

Table 60. Parameter Estimates for Type II Injury Accident Model Using Georgia Data 60 

Table 61. Validation Statistics for Type II Injury Accident Model Using Georgia Data. 61 

Table 62. Summary Statistics of Georgia Data: Type III Sites......................................... 62 

Table 63. Parameter Estimates for TOTACC Type III Model Using Georgia Data ........ 63 

Table 64. Validation Statistics for TOTACC Type III Model Using Georgia Data......... 64 

Table 65. Parameter Estimates for TOTACCI Type III Model Using Georgia Data....... 65 

Table 66. Validation Statistics for TOTACCI Type III Model Using Georgia Data ....... 66 

Table 67. Parameter Estimates for INJACC Type III Model Using Georgia Data: 

Variant 1.......................................................................................................................... 67 

Table 68. Validation Statistics for INJACC Type III Model Using Georgia Data: 

Variant 1.......................................................................................................................... 68 

Table 69. Parameter Estimates for INJACC Type III Model Using Georgia Data: 

Variant 2.......................................................................................................................... 70 

Table 70. Validation Statistics for INJACC Type III Model Using Georgia Data: 

Variant 2.......................................................................................................................... 70 

Table 71. Summary Statistics of Georgia Data: Type IV ................................................. 72 

Table 72. Summary Statistics of California, Michigan, and Georgia............................... 73 

Table 73. Pearson Correlations: Original, Georgia, and California.................................. 73 

Table 74. Parameter Estimates for TOTACC Type IV Model Using Georgia Data ........ 75 

Table 75. Validation Statistics for TOTACC Type IV Model Using Georgia Data......... 76 

Table 76. Parameter Estimates for TOTACCI Type IV Model Using Georgia Data....... 77 

Table 77. Validation Statistics for TOTACCI Type IV Model Using Georgia Data ....... 78 

Table 78. Parameter Estimates for INJACC Type IV Model Using Georgia Data .......... 79 

Table 79. Validation Statistics for INJACC Type IV Model Using Georgia Data........... 80 

Table 80. Parameter Estimates for INJACCI Type IV Model Using Georgia Data......... 82 

Table 81. Validation Statistics for INJACCI Type IV Model Using Georgia Data ......... 82 

Table 82. Summary Statistics of Georgia Data: Type V .................................................. 84 

Table 83. Summary Statistics for Three States: California, Michigan, and Georgia1 ...... 85 

Table 84. Parameter Estimates for TOTACC Type V Model Using Georgia Data: 

Main Model..................................................................................................................... 86 

Table 85. Validation Statistics for TOTACC Type V Model Using Georgia Data: 

Main Model..................................................................................................................... 87 
ix

Table 86. Parameter Estimates for TOTACC Type V Model Using Georgia Data: 

Variant 1.......................................................................................................................... 88 

Table 87. Validation Statistics for TOTACC Type V Model Using Georgia Data: 

Variant 1.......................................................................................................................... 89 

Table 88. Parameter Estimates for TOTACCI Type V Model Using Georgia Data: 

Main Model..................................................................................................................... 91 

Table 89. Validation Statistics for TOTACCI Type V Model Using Georgia Data: 

Main Model..................................................................................................................... 92 

Table 90. Parameter Estimates for TOTACC Type V Model Using Georgia Data: 

Variant 3.......................................................................................................................... 93 

Table 91. Validation Statistics for TOTACCI Type V Model Using Georgia Data: 

Variant 3.......................................................................................................................... 94 

Table 92. Parameter Estimates for INJACC Type V Model Using Georgia Data ........... 96 

Table 93. Validation Statistics for INJACC Type V Model Using Georgia Data............ 96 

Table 94. Parameter Estimates for INJACCI Type V Model Using Georgia Data .......... 98 

Table 95. Validation Statistics for INJACC Type V Model Using Georgia Data............ 98 

Table 96. Summary Accident Statistics for Sites Meeting Base Conditions.................. 100 

Table 97. Validation Statistics for Type I Base Model Intersections ............................. 101 

Table 98. Summary Accident Statistics for Sites Meeting Base Conditions.................. 102 

Table 99. Validation Statistics for Type II Base Model Intersections............................ 102 

Table 100. Validation Statistics for Type V Base Model Intersections.......................... 104 

Table 101. The AMFs for Type I, II, and V Intersections.............................................. 105 

Table 102. Validation Statistics for the Accident Prediction Algorithm: Type I ........... 106 

Table 103. Validation Statistics for the Accident Prediction Algorithm: Type I Sites 

with a Major Road Turning Lane.................................................................................. 107 

Table 104. Validation Statistics for the Accident Prediction Algorithm: Type II.......... 108 

Table 105. Validation Statistics for the Accident Prediction Algorithm: Type II Sites 

with a Major Road Turning Lane.................................................................................. 109 

Table 106. Validation Statistics for the Accident Prediction Algorithm: Type V.......... 110 

Table 107. Validation Statistics for the Accident Prediction Algorithm: Type V Sites 

with a Major Road Right-Turn Lane ............................................................................ 111 

Table 108. Sources of Data............................................................................................. 128 

Table 109. Summary Statistics for Type I Sites ............................................................. 129 

Table 110. Correlation Between Crashes and Independent Variables for Type I Sites.. 130 

Table 111. Summary of Correlations for Independent Variables for Type I Sites......... 131 

Table 112. Summary Statistics for Type II Sites ............................................................ 132 

Table 113. Correlation Between Crashes and Independent Variables for Type II Sites 133 

Table 114. Summary of Correlations for Independent Variables for Type II Sites........ 134 

Table 115. Summary Statistics for Type III Sites........................................................... 135 

Table 116. Correlation Between Crashes and Independent Variables for Type III Sites137 

Table 117. Summary of Correlations for Independent Variables for Type III Sites ...... 138 

Table 118. Summary Statistics for Type IV Sites........................................................... 140 

Table 119. Correlation Between Crashes and Independent Variables for Type IV Sites143 

Table 120. Summary of Correlations for Independent Variables for Type IV Sites ...... 144 

Table 121. Summary Statistics for Type V Sites............................................................ 145 

Table 122. Correlation Between Crashes and Independent Variables for Type V Sites 149 
x

Table 123. Summary of Correlations for Independent Variables for Type V Sites ....... 150 

Table 124. Summary of AADT Models Recalibrated and Data Used............................ 153 

Table 125. Group B Base Conditions for Type I to IV AADT Models.......................... 155 

Table 126. Group A Base Conditions for Type III TOTACC AADT Models............... 156 

Table 127. Group A Base Conditions for Type III INJACC AADT Models................. 156 

Table 128. Group A Base Conditions for Type IV TOTACC AADT Models............... 156 

Table 129. Group A Base Conditions for Type IV INJACC AADT Models................. 157 

Table 130. Group A Base Conditions for Type V TOTACC AADT Models ................ 157 

Table 131. Group A Base Conditions for Type V INJACC AADT Models .................. 157 

Table 132. Number of Sites Used for Type I Main and Group B Base AADT Models. 158 

Table 133. Summary Statistics for Type I Sites: Main and Group B Base AADT 

Models..................................................................................................................... 158 

Table 134. Parameter Estimates for Recalibrated TOTACC Type I: Main and Group B 

AADT Models ........................................................................................................ 159 

Table 135. Parameter Estimates for Recalibrated INJACC Type I: Main and Group B 

AADT Models ........................................................................................................ 160 

Table 136. Number of Sites Used for Type II Main and Group B Base AADT Models 160 

Table 137. Summary Statistics for Type II Sites: Main and Group B Base AADT 

Models..................................................................................................................... 161 

Table 138. Parameter Estimates for Recalibrated TOTACC Type II: Main and Group B 

AADT Models ........................................................................................................ 162 

Table 139. Parameter Estimates for Recalibrated INJACC Type II: Main and Group B 

AADT Models ........................................................................................................ 163 

Table 140. Number of Sites Used for Type III Main and Group B Base Condition 

AADT Models ........................................................................................................ 164 

Table 141. Summary Statistics for Type III Sites: Main and Group B Base AADT 

Models..................................................................................................................... 164 

Table 142. Parameter Estimates for Recalibrated TOTACC Type III: Main and Group B 

Base AADT Models................................................................................................ 165 

Table 143. Parameter Estimates for Recalibrated INJACC Type III: Main and Group B 

Base AADT Models................................................................................................ 165 

Table 144. Summary Statistics for Type III Sites: Group A Base AADT Models......... 166 

Table 145. Parameter Estimates for Type III Group A TOTACC and INJACC Base 

Models..................................................................................................................... 166 

Table 146. Number of Sites Used for Type IV Main and Group B Base Condition 

AADT Models ........................................................................................................ 167 

Table 147. Summary Statistics for Type IV Sites: Main and Group B Base AADT 

Models..................................................................................................................... 167 

Table 148. Parameter Estimates for Recalibrated TOTACC Type IV: Main and Group B 

Base AADT Models................................................................................................ 168 

Table 149. Parameter Estimates for Recalibrated INJACC Type IV: Main and Group B 

Base AADT Models................................................................................................ 169 

Table 150. Summary Statistics for Type IV Sites: Group A Base AADT Models ........ 169 

Table 151. Parameter Estimates for Type IV Group A TOTACC and INJACC Base 

Models..................................................................................................................... 170 

Table 152. Number of Sites Used for Type V Main AADT Model ............................... 170 
xi

Table 153. Summary Statistics for Type V Sites: Main AADT Model.......................... 171 

Table 154. Parameter Estimates for Recalibrated TOTACC Type V: Main AADT 

Model ............................................................................................................................ 171 

Table 155. Parameter Estimates for Recalibrated INJACC Type V: Main AADT 

Model ............................................................................................................................ 172 

Table 156. Summary Statistics for Type V Sites: Group A Base AADT Models.......... 172 

Table 157. Parameter Estimates for Type V Group A TOTACC and INJACC Base 

Models........................................................................................................................... 173 

Table 158. Summary of Models Recalibrated and Data Used........................................ 173 

Table 159. Parameter Estimates for Recalibrated TOTACC Full Models: Type I 

Group A ........................................................................................................................ 175 

Table 160. Parameter Estimates for Recalibrated INJACC Full Models: Type I 

Group A ........................................................................................................................ 176 

Table 161. Parameter Estimates for Recalibrated TOTACC Full Models: Type I 

Group B......................................................................................................................... 179 

Table 162. Parameter Estimates for Recalibrated INJACC Full Models: Type I 

Group B......................................................................................................................... 180 

Table 163. Parameter Estimates for Recalibrated TOTACC Full Models: Type II 

Group A ........................................................................................................................ 182 

Table 164. Parameter Estimates for Recalibrated INJACC Full Models: Type II 

Group A ........................................................................................................................ 183 

Table 165. Parameter Estimates for Recalibrated TOTACC Full Models: Type II 

Group B......................................................................................................................... 184 

Table 166. Parameter Estimates for Recalibrated INJACC Full Models: Type II 

Group B......................................................................................................................... 185 

Table 167. Parameter Estimates for Recalibrated TOTACC Full Models: Type III...... 187 

Table 168. Parameter Estimates for Recalibrated INJACC Full Models: Type III........ 188 

Table 169. Parameter Estimates for Recalibrated TOTACC Full Models: Type IV...... 190 

Table 170. Parameter Estimates for Recalibrated INJACC Type IV: Full Models........ 191 

Table 171. Parameter Estimates for Recalibrated TOTACC Full Models: Type V ....... 193 

Table 172. Parameter Estimates for Recalibrated INJACC Full Models: Type V ......... 194 

Table 173. AMFs from Previous Studies........................................................................ 196 

Table 174. AMFs Derived from Type I and II Full Models ........................................... 197 

Table 175. AMFs Derived from Type III, IV, and V Full Models................................. 198 

Table 176. AMFs Estimated from Regression Procedure .............................................. 200 

Table 177. Base Conditions for Type III Sites ............................................................... 201 

Table 178. Base Model for Type III Sites....................................................................... 201 

Table 179. AMFs for Type III Sites................................................................................ 201 

Table 180. Base Conditions for Type IV Sites ............................................................... 202 

Table 181. Base Model for Type IV Sites ...................................................................... 202 

Table 182. AMFs for Type IV Sites ............................................................................... 203 

Table 183. Base Conditions for Type V Sites................................................................. 204 

Table 184. Base Model for Type V Sites........................................................................ 204 

Table 185. Comparison of Type I–II AMFs for TOTACC ............................................ 205 

Table 186. Comparison of Type III–V AMFs for TOTACC.......................................... 206 

Table 187. Comparison of AMFs for INJACC............................................................... 207 
xii

Table 188. Sensitivity of Safety to HI1 for Type I TOTAL Accidents Per Year........... 208 

Table 189. Sensitivity of Safety to RT MAJ for Type I TOTAL Accidents Per Year ... 209 

Table 190. Sensitivity of Safety to RT MIN for Type I TOTAL Accidents Per Year ... 210 

Table 191. Sensitivity of Safety to LT MAJ for Type I TOTAL Accidents Per Year ... 211 

Table 192. Sensitivity of Safety to HI1 for Type I INJURY Accidents Per Year.......... 212 

Table 193. Sensitivity of Safety to RT MAJ for Type I INJURY Accidents Per Year.. 213 

Table 194. Sensitivity of Safety to RT MIN for Type I INJURY Accidents Per Year .. 214 

Table 195. Sensitivity of Safety to LT MAJ for Type I INJURY Accidents Per Year .. 215 

Table 196. Sensitivity of Safety to DRWY1 for Type II TOTAL Accidents Per Year.. 216 

Table 197. Sensitivity of Safety to RT MAJ for Type II TOTAL Accidents Per Year.. 217 

Table 198. Sensitivity of Safety to LT MAJ for Type II TOTAL Accidents Per Year.. 218 

Table 199. Sensitivity of Safety to MEDIAN for Type II TOTAL Accidents Per Year 219 

Table 200. Sensitivity of Safety to HI1 for Type II INJURY Accidents Per Year......... 220 

Table 201. Sensitivity of Safety to DRWY1 for Type II INJURY Accidents Per Year. 221 

Table 202. Sensitivity of Safety to RT MAJ for Type II INJURY Accidents Per Year. 222 

Table 203. Sensitivity of Safety to LT MAJ for Type II INJURY Accidents Per Year. 223 

Table 204. Sensitivity of Safety to MEDIAN for Type II INJURY Accidents Per 

Year............................................................................................................................... 224 

Table 205. Sensitivity of Safety to Skew Angles for Type III TOTAL Accidents Per 

Year............................................................................................................................... 225 

Table 206. Sensitivity of Safety to Commercial Driveways on Major Road for 

Type III TOTAL Accidents Per Year ........................................................................... 226 

Table 207. Sensitivity of Safety to Vertical Curves on Major Road (VEI1) for 

Type III TOTAL Accidents Per Year ........................................................................... 227 

Table 208. Sensitivity of Safety to Median Width on Major Road (MEDWIDTH1) for 

Type III TOTAL Accidents Per Year ........................................................................... 228 

Table 209. Sensitivity of Safety to Painted Median Type on Major Road (MEDTYPE1) 

for Type III TOTAL Accidents Per Year ..................................................................... 229 

Table 210. Sensitivity of Safety to Major Road Left-Turn Lane for Type III TOTAL 

Accidents Per Year ....................................................................................................... 230 

Table 211. Sensitivity of Safety to Skew Angles for Type III INJURY Accidents Per 

Year............................................................................................................................... 231 

Table 212. Sensitivity of Safety to Commercial Driveways on Major Road for Type III 

INJURY Accidents Per Year ........................................................................................ 232 

Table 213. Sensitivity of Safety to Hazard Rating on Major Road (HAZRAT1) for 

Type III INJURY Accidents Per Year .......................................................................... 233 

Table 214. Sensitivity of Safety to Peak Truck Percentage (PKTRUCK) for Type III 

TOTAL Accidents Per Year ......................................................................................... 234 

Table 215. Sensitivity of Safety to Peak Turning Percentage (PKTURN) for Type III 

TOTAL Accidents Per Year ......................................................................................... 235 

Table 216. Sensitivity of Safety to Skew Angles for Type IV TOTAL Accidents Per 

Year............................................................................................................................... 236 

Table 217. Sensitivity of Safety to Right Sight Distance from Minor Road (SDR2) for 

Type IV TOTAL Accidents Per Year........................................................................... 237 

Table 218. Sensitivity of Safety to Peak Truck Percentage (PKTRUCK) for Type III 

TOTAL Accidents Per Year ......................................................................................... 238 
xiii

Table 219. Sensitivity of Safety to Peak Through Percentage on Minor Road 

(PKTHRU2) for Type IV TOTAL Accidents Per Year................................................ 239 

Table 220. Sensitivity of Safety to Peak Left-Turn Percentage (PKLEFT) for Type IV 

TOTAL Accidents Per Year ......................................................................................... 240 

Table 221. Sensitivity of Safety to Skew Angles for Type IV INJURY Accidents Per 

Year............................................................................................................................... 241 

Table 222. Sensitivity of Safety to Major Right-Turn Lane for Type IV INJURY 

Accidents Per Year ....................................................................................................... 242 

Table 223. Sensitivity of Safety to Peak Truck Percentage (PKTRUCK) for Type IV 

INJURY Accidents Per Year ........................................................................................ 243 

Table 224. Sensitivity of Safety to Peak Left-Turn Percentage (PKLEFT) for Type IV 

INJURY Accidents Per Year ........................................................................................ 244 

Table 225. Sensitivity of Safety to Commercial Driveways on Major Road for Type V 

TOTAL Accidents Per Year ......................................................................................... 245 

Table 226. Sensitivity of Safety to Horizontal Curve Combinations on Major and 

Minor Roads (HEICOM) for Type III TOTAL Accidents Per Year ............................ 246 

Table 227. Sensitivity of Safety to Light for Type IV TOTAL Accidents Per Year...... 247 

Table 228. Sensitivity of Safety to Horizontal Curves on Minor Road (HEI2) for 

Type IV TOTAL Accidents Per Year........................................................................... 248 

Table 229. Sensitivity of Safety to Light for Type IV TOTAL Accidents Per Year...... 249 

Table 230. Summary of Models Recalibrated and Data Used........................................ 251 

Table 231. Comparison of Type III–V AMFs for TOTACC.......................................... 258 

Table 232. Comparison of Type I–II AMFs for TOTACC ............................................ 259 

Table 233. Comparison of Type III–V AMFs for TOTACC.......................................... 260 

Table 234. Comparison of AMFs for INJACC............................................................... 261 

Table 235. AADT Models Recommended for Use in IHSDM ...................................... 262 

Table 236. Full Models Recommended for Use in Crash Prediction ............................. 263

Table 237. All Models in the Reports of Relevance........................................................265 

Table 238. Models Validated...........................................................................................267 

Table 239. Summary Statistics for Type I Sites by State ................................................269 

Table 240. Summary Statistics for Type II Sites by State ...............................................271 

Table 241. Summary Statistics for Type III Sites by State: California (CA), Michigan 

(MI), and Georgia (GA).................................................................................................273 

Table 242. Summary Statistics for Type IV Sites by State: California (CA), Michigan 

(MI), and Georgia (GA).................................................................................................278 

Table 243. Summary Statistics for Type V Sites by State: California (CA), Michigan 

(MI), and Georgia (GA).................................................................................................285 

1 

EXECUTIVE SUMMARY 

The research described in this report consists of two separate yet complimentary 

activities—validation and calibration of crash models for rural intersections. Both the 

validation and recalibration activities were conducted with one overriding research 

objective: 

Given existing database limitations, make marginal improvements to an existing set of 

statistical models for predicting crashes at two- and four-lane intersections, with the 

primary intent to provide robust predictive models for use in the Interactive Highway 

Safety Design Module (IHSDM). 

The five types of intersection models addressed in this research effort include: 

Type I: Three-legged stop controlled intersections of two-lane roads. 

Type II: Four-legged stop controlled intersections of two-lane roads. 

Type III: Three-legged stop controlled intersections with two lanes on minor and 

four lanes on major roads. 

Type IV: Four-legged stop controlled intersections with two lanes on minor and 

four lanes on major roads. 

Type V: Signalized intersections of two-lane roads. 

The models that are the focus of this research are presented in three different Federal 

Highway Administration (FHWA) reports: Vogt and Bared (Types I and II);(1) Vogt 

(Types III, IV, and V);(2) and Harwood et al. (Types I, II, and V).(3) Each report presents 

several variants of the models for each type of intersection. The first two reports include 

models for total as well as injury accidents and present what are referred to as full models. 

The Harwood et al. report presents base models for Types I, II, and V intersections.(3)

These base models included variables that were statistically significant at the 15 percent 

level and are at the backbone of an algorithm for predicting accidents at intersections that 

are different in one or more features from the specified base conditions. Specifically, 

accident modification factors (AMF) for the features of interest are applied to the base 

model prediction to estimate accidents per unit of time for a specific intersection. This 

algorithm is intended for use in the Crash Prediction Module of FHWA’s IHSDM. The 

anticipated practical application of these models has motivated research directions taken 

throughout the course of this investigation. 

The data in support of this research were derived from three sources: 

1. The original data used for the calibration of the main models for total accidents 

were obtained from the researchers who developed those models. 

2. Highway Safety Information Systems (HSIS) data were obtained for additional 

years for the same intersections used in the calibration and for injury accidents for 

the original and additional years. 

3. An independent validation data set of intersections and their relevant crash, traffic, 

and geometric data in Georgia was specially assembled for this project.(4) 
2 

The research team faced a number of challenges while conducting this research, 

including data collection, independent variable characteristics, and the models’ intended 

end-use: 

1. The observational data on which the statistical models are based suffered from 

intercorrelation. 

2. The interactions among variables had to be carefully considered in model 

estimation. 

3. The need to forecast crashes across States posed significant difficulties. 

4. The observational data limited the amount of variation in independent variables, 

reducing overall model precision. 

5. Resource and data reliability restrictions prohibited a sufficiently large, randomly 

selected, fully comprehensive data set on which to estimate statistical models. 

6. Incongruencies between data sets across States and across time periods posed 

serious challenges. 

Despite these challenges, the research team conducted a model validation and then 

recalibrated the five intersection models. 

VALIDATION FINDINGS 

The four sets of validation activities were: 

1. Re-estimation of the model coefficients using the original data. This validation 

activity was used to determine the reproducibility of the published results and to 

ensure an “equivalent” launching point for all validation and calibration activities. 

This activity represented a logical starting point for the research effort and was 

successful in that modeling results were reproduced satisfactorily. 

2. Validation of the models against additional years of accident data for the same 

intersections used in the calibration. Because the crash models were developed as 

direct inputs into the IHSDM’s Accident Analysis Module, the models will be 

used by highway agencies to estimate the safety performance of an existing or 

proposed roadway. Therefore, the models should be able to forecast crashes 

across time and space. This validation activity was used to assess the models’ 

ability to forecast crashes across time, determining the models temporal capability 

and stability. 

3. Validation of the models against Georgia data. This validation activity assessed 

the models’ ability to forecast crashes across space. This activity tested numerous 

aspects of model prediction: comparing data from different jurisdictions; 

capturing variables that describe regional and jurisdictional differences; and 

consistency of crash processes across space. 
3 

4. Validation of the Accident Prediction Algorithm. While this research’s primary 

focus was to validate crash models, validating the Accident Prediction Algorithms 

based on these models was also important. 

Two basic sets of performance tests were employed. First, the models were re-estimated 

using the same variables and functional forms as those published in the original reports; 

the parameters for the original and re-estimated models were then compared, using a 

level of alpha = 0.10 to establish statistical significance. Second, the model (or algorithm) 

was used to predict accident frequencies at individual intersections, from which the 

following summary statistics were calculated: 

• Pearson product-moment linear correlation coefficients. 

• Mean Prediction Bias (MPB); MPB/year. 

• Mean Absolute Deviation (MAD); MAD/year. 

• Mean Squared Error (MSE); MSE/year2. 

• Mean Square Prediction Error (MSPE); MSPE/year2. 

The details of validation activities 1 through 4 are presented in sections 3.4 through 3.7 

respectively, while the results are discussed in section 3.8. 

RECALIBRATION FINDINGS 

Model recalibration was focused on improving the existing set of intersection crash 

models through use of an improved and expanded database and through lessons learned 

in the validation and recalibration activities. 

For each the five intersection types, the research team developed and/or refined three 

different sets of models, described in detail in chapter 3. The first type is Annual Average 

Daily Traffic (AADT) Models, which represent base models for predicting crashes as a 

function of major and minor road AADT. The analytical results of these models can be 

found in subsequent sections of this report. The second type of model is Full Models. 

These statistical models forecast crashes as a function of a relatively large set of 

independent variables. Details of the Full Models can be found in section 3.4 of this 

report. The third type of model is AMF. These models, better described as 

countermeasure correction factors, represent our best efforts to estimate the effect of 

geometric countermeasures on safety relative to base model predictions. AMF details can 

be found in section 3.5 of this report. 

Sensitivity analyses—tables of AMFs as a function of AADT and other factors are 

provided in section 3.6. 

RECOMMENDATIONS 

The research supported the proposed IHSDM accident prediction algorithm. An updated 

set of base models for predicting crashes using only AADT are recommended (see 

Summary, Discussion, and Conclusions section and Table 235). The updated statistical 
4 

models are based on larger sample sizes and, in some cases, resulted in slightly modified 

sets of independent variables compared to the originally estimated models. AMFs should 

be selected on a case-by-case basis, and should be updated continually to improve the 

predictive ability of the crash models. Expert opinion derived AMFs should be replaced 

with the results of state-of-the-practice before-after studies as time progresses and 

research allows. If expert opinion accurately reflects safety conditions, then carefully 

conducted future studies should reveal general agreement with expert expectation. When 

expert opinions are not confirmed over time, then empirical results should replace expert 

opinion. Full regression models are recommended for crash forecasts and find logical 

applications in the Highway Safety Manual and SafetyAnalyst (see Summary, Discussion, 

and Conclusions section and Table 236). 
5 

1. INTRODUCTION 

Effective safety management of a highway system requires that engineers know the 

present safety performance of a roadway and how it will perform if contemplated actions 

are taken. In effect, a reliable method of estimating safety performance is required. To 

this end, FHWA and its contractors have developed a new approach that combines 

historical accident data, regression analysis, before-and-after studies, and expert 

judgment to make safety performance predictions that are expected to be better than those 

obtained by any of the individual approaches. A recent report documents an accident 

prediction algorithm for implementing the new approach for two-lane rural highway 

sections that include road segments and five types of intersections.(3) Ongoing efforts aim 

to produce similar documents for other types of facilities. 

The accident prediction algorithm has been developed for incorporation in the IHSDM as 

the Crash Prediction Module, but is suitable for stand-alone applications. The structure of 

the accident prediction algorithm for the five types of rural at-grade intersections is as 

follows: 

 (1) 

where 

Nint = predicted number of total intersection-related accidents per year after application of 

 AMFs; 

Nb = predicted number of total intersection-related accidents per year for base conditions; 

and 

AMF1 AMF2 ... AMFn = AMFs for various intersection features. 

Harwood et al. presented base models and AMFs for three- and four-legged intersections 

of two-lane rural roads with STOP control, and four-legged signalized intersections of 

two-lane roads.(3) These base models were the best of available accident prediction 

models developed in earlier FHWA projects and retained model variables that were 

statistically significant at the 15 percent level.(1,2) Those projects also resulted in 

regression models with additional variables indented for use as AMFs in IHSDM. The 

full models, along with several variants, are presented in two FHWA reports: Vogt and 

Bared present models for three- and four-legged intersections of two-lane roads, while 

Vogt documents models for three other types of rural intersections: three- and fourlegged stop controlled with four lanes on the major and two on the minor; and signalized 

intersections of two-lane roads. (1,2) In summary, there are five types of intersection 

accident prediction models pertaining to the research efforts described: 

Type I: Three-legged stop controlled intersections of two-lane roads. 

Type II: Four-legged stop controlled intersections of two-lane roads. 

Type III: Three-legged stop controlled intersections with two lanes on the minor 

and four lanes on the major road. 

Type IV: Four-legged stop controlled intersections with two lanes on the minor and 

four lanes on the major road. 

Nint = Nb (AMF1 AMF2 ... AMFn) 
6 

Type V: Signalized intersections of two-lane roads. 

The models were developed using data that were limited in terms of geographical 

diversity and, in the case of Types III, IV, and V, sample size. Thus, validation of these 

models across both space and time has become of paramount importance. It was also of 

interest to validate the accident prediction algorithm as a whole, given its novelty and the 

fact that it relies on expert judgment for deriving the AMFs. An additional report 

provides additional AMFs for left- and right-turn lanes for at-grade intersections at type I, 

II and V sites.(5) These AMFs are also included in the validation effort. 

A natural follow-on to model validation is model recalibration using validation data and 

findings to improve the specification of the intersection models. This report presents 

recalibration results for the five types of rural intersections that were the subject of the 

validation exercise that was undertaken in the first part of the project. This model 

recalibration effort complemented the comprehensive model validation conducted as part 

of a larger technical evaluation of crash prediction models. AADT models and fully 

parameterized models were recalibrated, and their results are discussed in the 

recalibration chapter. 

This report consists of three chapters. This first chapter provides an introduction and 

presents the description of the variables used in this research. The second chapter 

describes four different sets of activities conducted to assess the validity of prediction 

models for the five types of rural intersections. The third chapter presents the 

recalibration efforts for the five types of intersections. The model recalibration efforts 

described in this chapter complement the comprehensive model validation exercise 

presented in the previous chapter as a part of larger technical evaluation of the models. 

1.1 VARIABLE ABBREVIATIONS 

This section provides, for ease of reference, the definitions of model types, accident types, 

and variables applied in this research investigation. 

1.1.1 Model Types 

Type I: Three-legged stop controlled intersections of two-lane roads. 

Type II: Four-legged stop controlled intersections of two-lane roads. 

Type III: Three-legged stop controlled intersections with two lanes on the minor 

and four lanes on the major road. 

Type IV: Four-legged stop controlled intersections with two lanes on the minor and 

four lanes on the major road. 

Type V: Signalized intersections of two-lane roads. 

1.1.2 Accident Models 

Models I and II

Total: Total number of police-reported intersection-related accidents within 76.25 meters 

(m) (76.25 m (250 ft) (ft)) of the intersection. 

Injury: Total number of police-reported intersection-related injury accidents within 76.25 

m (250 ft) of the intersection. 
7 

Models III, IV, and V

TOTACC: Total number of accidents within 76.25 m (250 ft) of the intersection. 

TOTACCI: Only those crashes considered intersection-related and within 76.25 m (250 

ft) of the intersection. 

INJACC: Total number of injury crashes within 76.25 m (250 ft) of the intersection. 

INJACCI: Only those injury crashes considered intersection-related and within 76.25 m 

(250 ft) of the intersection. 

1.1.3 Definitions of Variables 

AADT1: Average daily traffic on major road (vehicles per day). This variable is identical 

to ADT1 in the original (published) models. This change was made after determining that 

the traffic flow variables were, in fact, estimated AADT. 

AADT2: Average daily traffic on minor roads (vehicles per day). This variable is 

identical to ADT2 in the original models. 

COMDRWY1: Commercial driveways on major roads within 76.25 m (250 ft) of the 

intersection center. This variable is identical to NODRWYC1 in the original models. 

COMDRWY2: Commercial driveways on minor roads within 76.25 m (250 ft) of the 

intersection center. This variable is identical to NODRWYC2 in the original models. 

DRWY1: Driveways on major roads within 76.25 m (250 ft) of the intersection. This 

variable is identical to ND and NODRWY1 in the original models for Type I–II and III–

V intersections, respectively. 

DRWY2: Driveways on minor roads within 76.25 m (250 ft) of the intersection. This 

variable is identical to NODRWY2 in the original models. 

GRADE1: Average absolute grade on major roads within ±244 m (±800 ft) of the 

intersection center (percent). 

GRADE2: Average absolute grade on minor road within ±244 m (±800 ft) of the 

intersection center (percent). 

HAU: Intersection angle variable defined where the angle between the major and minor 

roads is measured from the far side of the minor road: 

• Three-legged intersections: Angle minus 90 if minor road is to the right of the 

major road in the increasing direction; 90 minus angle if minor road is to the left 

of the major road in the increasing direction. 

• Four-legged intersections: (right angle - left angle)/2.

HAZRAT1: Roadside hazard rating on major road within 76.25 m (250 ft) of the 

intersection center (from 1, least hazardous case, to 7, most hazardous case).(6) This 

variable is identical to RHRI in the original models for Type I and II intersections. 

HAZRAT2: Roadside hazard rating on minor road within 76.25 m (250 ft) of the 

intersection center (from 1, least hazardous case, to 7, most hazardous case).(6)

HEI1: Sum of degree of curve in degrees per hundred feet of each horizontal curve on 

major road, any portion of which is within ±244 m (±800 ft) of the intersection center 

divided by the number of such curves. 

HEI2: Sum of degree of curve in degrees per hundred feet of each horizontal curve on 

minor road, any portion of which is within ±244 m (±800 ft) of the intersection center 

divided by the number of such curves. 

HEICOM: (1 / 2) (HEI1 + HEI2). 
8 

HI: Sum of degree of curve in degrees per hundred feet of each horizontal curve on major 

road, any portion of which is within 76.25 m (250 ft) of the intersection center divided by 

the number of such curves. 

HI1: Sum of degree of curve in degrees per hundred feet of each horizontal curve on 

major road, any portion of which is within 76.25 m (250 ft) of the intersection center 

divided by the number of such curves. This variable is identical to HI in the original 

models for Type I and II intersections. 

HI2: Sum of degree of curve in degrees per hundred feet of each horizontal curve on 

minor road, any portion of which is within 76.25 m (250 ft) of the intersection center 

divided by the number of such curves. 

HICOM: (1 / 2) (HI1 + HI2). 

L1LT (Type III-V): Left-turn lane on major roads (0 = no, 1 for one approach, and 2 for 

both approaches). This variable is identical to LTLN1 in the original models for Type 

III–V intersections. 

L1RT (Type III-V): Right-turn lane on major roads (0 = no, 1 for one approach, and 2 

for both approaches). This variable is identical to RTLN1 in the original models for Type 

III–V intersections. 

L3LT (Type III-V): Left-turn lane on minor roads (0 = no, 1 for one approach, and 2 for 

both approaches). This variable is identical to LTLN2 in the original models for Type 

III–V intersections. 

L3RT (Type III-V): Right-turn lane on minor roads (0 = no, 1 for one approach, and 2 

for both approaches). This variable is identical to RTLN2 in the original models for Type 

III–V intersections. 

LEGACC1: Acceleration lane on major roads (0 = no, 1 = yes). 

LEGACC2: Acceleration lane on minor roads (0 = no, 1 = yes). 

LIGHT: Light at intersection (0 = no, 1 = yes). 

LTLN1S (Type III-V): Left-turn lane on major roads (0 = no, 1 = yes). 

LT MAJ (Type I-II): 1 if left-turn lane exists on at least one approach of major roads, 0 

otherwise. 

LT MIN (Type I-II): 1 if left-turn lane exists on at least one approach of minor roads, 0 

otherwise. 

MEDIAN (Type I-II): 1 if median exists on major roads, 0 otherwise. 

MEDTYPE (Type III-V): Median type (0 = no median, 1 = painted, 2 = curbed, 3 = 

others). 

MEDWDTH1: Median width on major roads (feet). This variable is identical to 

MEDWIDTH1 in the original models. 

MEDWDTH2: Median width on minor roads (feet). 

PKLEFT: Peak left-turn percentage (percent). 

PKLEFT1: Peak left-turn percentage on major roads (percent). 

PKLEFT2: Peak left-turn percentage on minor roads (percent). 

PKTHRU1: Peak through percentage on major roads (percent). 

PKTHRU2: Peak through percentage on minor roads (percent). 

PKTRUCK: Peak truck percentage passing through the intersection (percent). 

PKTURN: Peak turning percentage (percent). 

PROT_LT: Protected left lane (0 = no, 1 = yes). 

RESDRWY1: Residential driveways on major roads within 76.25 m (250 ft) of the 

intersection center. This variable is identical to NODRWYR1 in the original models. 
9 

RESDRWY2: Residential driveways on minor roads within 76.25 m (250 ft) of the 

intersection center. This variable is identical to NODRWYR2 in the original models. 

RT MAJ (Type I-II): 1 if right-turn lane exists on major roads, 0 otherwise. 

RT MIN (Type I-II): 1 if right-turn lane exists on minor roads, 0 otherwise. 

SD1: Longitudinal sight distance on major roads (feet). 

SDL2: Left-side sight distance on minor roads (feet). 

SDR2: Right-side sight distance on minor roads (feet). 

SHOULDER1: Shoulder width on major roads (feet). 

SHOULDER2: Shoulder width on minor roads (feet). 

SPD1: The average posted speed on major roads in vicinity of the intersection (miles per 

hour). This variable is identical to SPDI in the original models for Type I and II 

intersections. 

SPD2: The average posted speed on minor roads in vicinity of the intersection (miles per 

hour). 

TERRAIN (Type I-II): 1 if flat, 2 if rolling, or 3 if mountainous terrain. 

TERRAIN1 (Type III-V): Terrain on major roads within 76.25 m (250 ft) of the 

intersection center (0 = flat, 1 = rolling, 2 = mountainous). 

TERRAIN2 (Type III-V): Terrain on minor roads within 76.25 m (250 ft) of the 

intersection center (0 = flat, 1 = rolling, 2 = mountainous). 

VCEI1: Sum of absolute change of grade in percent per hundred feet for each crest curve 

on major roads, any portion of which is within 800 feet of the intersection center, divided 

by the number of such curves. 

VCEI2: Sum of absolute change of grade in percent per hundred feet for each crest curve 

on minor roads, any portion of which is within 800 feet of the intersection center, divided 

by the number of such curves. 

VCI1: Sum of absolute change of grade in percent per hundred feet for each crest curve 

on major roads, any portion of which is within 76.25 m (250 ft) of the intersection center, 

divided by the number of such curves. This variable is identical to VCI in the original 

models for Type I and II intersections. 

VCI2: Sum of absolute change of grade in percent per hundred feet for each crest curve 

on minor roads, any portion of which is within 76.25 m (250 ft) of the intersection center, 

divided by the number of such curves. 

VEI1: Sum of absolute change of grade in percent per hundred feet for each curve on 

major roads, any portion of which is within ±244 m (±800 ft) of the intersection center, 

divided by the number of such curves. 

VEI2: Sum of absolute change of grade in percent per hundred feet for each curve on 

minor roads, any portion of which is within ±244 m (±800 ft) of the intersection center, 

divided by the number of such curves. 

VEICOM: (1 / 2) (VEI1 + VEI2). 

VI1: Sum of absolute change of grade in percent per hundred feet for each curve on 

major roads, any portion of which is within 76.25 m (250 ft) of the intersection center, 

divided by the number of such curves. 

VI2: Sum of absolute change of grade in percent per hundred feet for each curve on 

minor roads, any portion of which is within 76.25 m (250 ft) of the intersection center, 

divided by the number of such curves. 

VICOM (Type III-V): (1 / 2) (VI1 + VI2). 
10 
11 

2. VALIDATION OF ACCIDENT MODELS 

This chapter presents validation results for the five types of rural intersections. It first 

provides a description of the overall validation approach. Second, the data sources and 

issues are discussed. Third, the individual validation activities and their results are 

presented. Finally, a discussion of these results is provided. 

2.1 VALIDATION APPROACH AND PRELIMINARIES 

Several objectives were identified to guide the validation efforts: 

1. Determine whether the existing accident models developed by FHWA were 

“over-fit” to the estimation data, thus making elements (factors) appear to affect 

accidents when, in fact, they do not. 

2. Determine whether important variables were omitted from the models due to lack 

of representative data, insufficient sample size, lack of power, or some 

combination of thereof. 

3. Determine whether the functional forms of the models have been properly 

specified. 

4. Determine whether the models are valid at other locations (across space) and at 

the same intersections in the future (across time). 

To meet these objectives, researchers conducted two aspects of model validation: internal 

and external model validations. The first aspect of model validation consists of 

qualitative assessments of statistical models, including examining the collection of 

variables used to identify missing or irrelevant variables, inspecting the functional form 

of the models, and assessing the implications of the models regarding an underlying 

theory of the data generating process—motor vehicle crashes, in this case. External 

model validation is more quantitative and is focused on various quantitative measures of 

a statistical model’s prediction ability. Three model validation activities comprising both 

internal and external validation activities were undertaken: 

1. Validation of the models against additional years of accident data for the same 

intersections used in the calibration. Because the existing accident models were 

developed as direct inputs into the IHSDM’s Crash Prediction Module, highway 

agencies will use the models to estimate the safety performance of an existing or 

proposed roadway. Therefore, the models should be able to forecast accidents 

over time and space. This validation was used to assess the models’ ability to 

forecast accidents across time. Temporal stability of a model suggests that it will 

predict accident frequencies well across time; the effect of time, or covariates that 

are influenced by time, are either not important or, if important, are included in 

the model by some relevant explanatory variable. 

2. Validation of the models against Georgia data. This validation was used to assess 

the models’ ability to forecast accidents over space. The primary application of 

the models is to forecast the impact of design considerations and countermeasures 

in regions and jurisdictions not represented in the calibration data. Thus, this 
12 

validation exercise attempts to assess the ability of the models to capture 

differences across regions as reflected through relevant variable expressions in the 

models. 

3. Validation of the Accident Prediction Algorithm. Validation of the Accident 

Prediction Algorithm as a whole was considered to be important. This validation 

activity addresses the logical defensibility of the algorithm used for predicting 

accidents, and provides quantitative evidence of how well it is predicting 

accidents. 

The validation exercises in this chapter focus primarily on external validation—validation 

concerned with assessing performance of the models when compared to external data. 

The discussion section mentions internal validation concerns—the internal coherence, 

structure, theoretical soundness, and plausibility of the models proposed. And more focus 

is given to internal validation in the recalibration activities documentation, which follows 

the report on these validation efforts. In these validation activities, all model 

specifications were validated “as is,” that is, no changes to model specifications were 

considered or assessed. 

Throughout the report the subjective criteria of alpha (α) equal to 0.10 is applied. The 

support for this level of α is as follows. In statistical models of accident occurrence, a 

type II error can be argued to be more serious than a type I error. With a type I error, the 

analyst concludes that the null hypothesis is false, when in fact it is true with α

probability. This translation is not precise, but the precise and correct conditional 

probability interpretation is cumbersome and, for practical purposes, does not lend any 

additional insights. This means that the analyst would conclude, for example, that the 

presence of a left-turn lane reduces accidents when, in reality, it does not. As a result of 

this conclusion, one might install left-turn lanes without realizing a reduction in crashes. 

A type II error occurs with beta (β) probability. In general, choosing a larger α results in 

a smallerβ, all else being equal. Thus, continuing with the previous example, making a 

type II error results in concluding that the presence of a left-turn lane does not reduce 

crashes when in fact it does. The risk is in failing to install an effective countermeasure. 

To summarize, committing a type I error results in applying an ineffective 

countermeasure, while committing a type II error results in failing to apply an effective 

countermeasure. Computing the actual β in negative binomial models is extremely 

difficult. However, applying a liberal α equal to 0.10 suggests that this study has 

simultaneously accepted a smaller level of beta. 

Several goodness-of-fit (GOF) statistics to assess model fit to validation data were 

employed. Comparisons between models, however, are generally subjective. In the 

documentation to follow, the terms “serious,” “moderate,” and “marginal” denote 

subjective evaluations of GOF comparisons between models. Serious differences in GOF 

are suggestive of noteworthy or significant model deficiencies. Moderate differences in 

GOF suggest cases where models could be improved, but improvements might be 

difficult to obtain. Marginal differences in GOF are thought to be negligible and are 

potentially explained by random fluctuations in the observed data. 
13 

2.2 DATA SOURCES AND ISSUES 

This section presents the data sources used for the validation and some general data 

issues. The data used came from three sources: 

1. The original data used for the calibration of the main models for total accidents 

were obtained from the researchers who developed those models. 

2. HSIS data were obtained for additional years for the same intersections used in 

the calibration for the additional years available. 

3. An independent validation data set was assembled specifically for this project. 

The first validation activity employed the original datasets with the objective of 

reproducing the original models. In the second validation activity, additional years of 

accident data (1990 to 1998) from Minnesota were used to validate models I and II over 

time. The Washington data collected, but not used, for the final development of models I 

and II, plus accident data for one more year (1996) also were utilized. For models III, IV, 

and V, additional years of accident data (1996 and 1997) from California and Michigan 

were used to validate the models over time. For the third validation activity, data from 

Georgia were assembled during this project and used to further assess the models’ ability 

to predict accidents over space (in a different jurisdiction). The fourth validation activity 

assessed the “Red Book” accident prediction algorithm, including recommended base 

models.(3)

Models I and II, which were developed using Minnesota data, modeled police reported 

“intersection” or “intersection-related” accidents which occurred within 76.25 m (250 ft) 

of the intersection. Models III, IV, and V were each developed using Michigan and 

California data for two dependent variables. The first used all accidents occurring within 

76.25 m (250 ft) of the intersection. The second used only those accidents considered to 

be “intersection-related” and occurring within 76.25 m (250 ft) of the intersection. 

Special criteria were needed for the latter case because California data does not include a 

variable indicating if an accident was “intersection-related.” An accident was considered 

to be intersection related accidents if it was: 

1. Vehicle-pedestrian accident. 

2. An accident where one vehicle involved was making a left turn, right turn or Uturn before the crash. 

3. A multivehicle accident in which the accident type is either a sideswipe, rearend, 

or broadside/angle. 

Vehicle-bicyclist, head-on, and run-off-the-road crashes may could possibly be classified 

as intersection related but were not included in the analysis in order to maintain 

consistencyand comparability with previously estimated models from which this research 

was based.(2) According to discussions with FHWA, for four-leg STOP-controlled 

intersections, these crashes typically represent about 6 percent of the total crashes 

occurring within 76.25 m (250 ft) of the intersection. For three-leg STOP-controlled 

intersections, these crashes typically represent about 13 percent of the total crashed 

occurring within 76.25 m (250 ft) of the intersection. 
14 

Table 1. Basic Statistics for the Data Sources 

Basic statistics for the data 

sources (Blank cells indicate 

accident types not validated; x 

indicates accident types 

validated) Model I1

 Model II1 Model III2 Model IV2 Model V2

Original Years 389 327 84 72 49 Sample size 

Georgia Data 121 114 52 52 51 

Original years MN MN CA and MI CA and MI CA and MI 

Subsequent 

Years MN and WA MN and WA CA and MI CA and MI CA and MI States3

Georgia Data GA GA GA GA GA 

Original Years 

5 

(1985 to 1989)

5 

(1985 to 1989) 

3 

(1993 to 1995)

3 

(1993 to 1995) 

3 

(1993 to 1995)

Subsequent 

Years 

9 

(1990 to 1998 

for MN 

1993 to 1996 

for WA) 

9 

(1990 to 1998 for 

MN 

1993 to 1996 for 

WA) 

2 

(1996 to 1997)

2 

(1996 to 1997) 

2 

Years covered (1996 to 1997)

Georgia Data 

2 

(1996 to 1997)

2 

(1996 to 1997) 

2 

(1996 to 1997)

2 

(1996 to 1997) 

2 

(1996 to 1997)

Total X X 

Injury X X 

TOTACC4 X X X 

TOTACCI4 X X X 

INJACC X X X 

Accident types 

validated 

INJACCI X X X 1 Vogt and Bared 1998, (pp. 60–67)

2

 Vogt, 1999, (pp. 53–64)

3

 MN: Minnesota, WA: Washington, CA: California, MI: Michigan, GA: Georgia. 4

 TOTACC: Total number of accidents within 76.25 m (250 ft); TOTACCI: Only those crashes considered 

intersection-related and within 76.25 m (250 ft); Similar distinction between INJACC and INJACCI 

The Georgia data specially collected for this validation also do not include a variable 

coded as “intersection” or “intersection-related” by the police. As such, the above criteria 

for determining an “intersection-related” accident were used. 

To use the Georgia data to validate the original models, consistency of accident location 

definitions had to be resolved. The original models included accidents only within 76.25 

m (250 ft) from the intersection center. However, the accident data recorded in Georgia 

measures the distance of an accident from an intersection within two decimal places of a 

mile, i.e., within 8.05 m (26.4 ft). The issue was whether or not to include accidents 

within 0.06 or .08 kilometers (km) (0.04 or 0.05 miles, or 211 or 264 ft). In the end, both 

the 0.04- and 0.05-mile buffers were used in separate validation efforts, mainly to check 

the sensitivity of the results to this definition. 
15 

2.3 MODEL PERFORMANCE MEASURES 

Several GOF measures were used to assess model performance. It is important to note at 

the outset that only after an assessment of many GOF criteria is made can the 

performance of a particular model or set of models be assessed. In addition, a model must 

be internally plausible, and agree with known theory about crash causation and processes. 

The GOF measures used were: 

Pearson’s Product Moment Correlation Coefficients Between Observed and 

Predicted Crash Frequencies 

Pearson’s product moment correlation coefficient, usually denoted by r, is a measure of 

the linear association between the two variables Y1 and Y2 that have been measured on 

interval or ratio scales. A different correlation coefficient is needed when one or more 

variable is ordinal. Pearson’s product moment correlation coefficient is given as: 

 (2) 

where 

Y = the mean of the Yi observations. 

A model that predicts observed data perfectly will produce a straight line plot between 

observed (Y1) and predicted values (Y2), and will result in a correlation coefficient of 

exactly 1. Conversely, a linear correlation coefficient of 0 suggests a complete lack of a 

linear association between observed and predicted variables. The expectation during 

model validation is a high correlation coefficient. A low coefficient suggests that the 

model is not performing well and that variables influential in the calibration data are not 

as influential in the validation data. Random sampling error, which is expected, will not 

reduce the correlation coefficient significantly. 

Mean Prediction Bias (MPB) 

The MPB is the sum of predicted accident frequencies minus observed accident 

frequencies in the validation data set, divided by the number of validation data points. 

This statistic provides a measure of the magnitude and direction of the average model 

bias as compared to validation data. The smaller the average prediction bias, the better 

the model is at predicting observed data. The MPB can be positive or negative, and is 

given by: 

1

n

i i

i

Y Y

MPB

n

∧

=

⎛ ⎞ ⎜ ⎟ − ⎝ ⎠ =

∑

 (3) 

where 

n = validation data sample size; and 

1 1 22

1/2 2 2 11 2 2

( )

(

i i

i i

Y Υ )(Y - Y

r

Y Y ) (Y Y )

− =

⎡ − − ⎤ ⎣ ⎦

∑

∑ ∑
16 

Y

∧

= the fitted value Yi observation. 

A positive MPB suggests that on average the model overpredicts the observed validation 

data. Conversely, a negative value suggests systematic underprediction. The magnitude 

of MPB provides the magnitude of the average bias. 

Mean Absolute Deviation (MAD) 

MAD is the sum of the absolute value of predicted validation observations minus 

observed validation observations, divided by the number of validation observations. It 

differs from MPB in that positive and negative prediction errors will not cancel each 

other out. Unlike MPB, MAD can only be positive. 

1

n

i i

i

Y Y

MAD

n

∧

=

−

=

∑

 (4) 

where 

n = validation data sample size. 

The MAD gives a measure of the average magnitude of variability of prediction. Smaller 

values are preferred to larger values. 

Mean Squared Prediction Error (MSPE) and Mean Squared Error (MSE) 

MSPE is the sum of squared differences between observed and predicted crash 

frequencies, divided by sample size. MSPE is typically used to assess error associated 

with a validation or external data set. MSE is the sum of squared differences between 

observed and predicted crash frequencies, divided by the sample size minus the number 

of model parameters. MSE is typically a measure of model error associated with the 

calibration or estimation data, and so degrees of freedom are lost (p) as a result of 

producing Yhat, the predicted response. 

 MSE = 

2

1

1

n

i i

i

Y Y

n p

∧

=

⎛ ⎞ ⎜ ⎟ − ⎝ ⎠

−

∑

 (5)

 MPSE = 

2

1

2

n

i i

i

Y Y

n

∧

=

⎛ ⎞ ⎜ ⎟ − ⎝ ⎠ ∑

 (6)
17 

where 

n1 = estimation data sample size; and 

n2 = validation data sample size. 

A comparison of MSPE and MSE reveals potential overfitting or underfitting of the 

models to the estimation data. An MSPE that is higher than MSE may indicate that the 

models may have been overfit to the estimation data, and that some of the observed 

relationships may have been spurious instead of real. This finding could also indicate that 

important variables were omitted from the model or the model was misspecified. Finally, 

data inconsistencies could cause a relatively high value of MSPE. Values of MSPE and 

MSE that are similar in magnitude indicate that validation data fit the model similar to 

the estimation data and that deterministic and stochastic components are stable across the 

comparison being made. Typically this is the desired result. 

To normalize the GOF measures to compensate for the different numbers of years 

associated with different data sets, GOF measures were computed on a per year basis. For 

MPB and MAD per year, MPB and MAD were divided by number of years. However, 

since MSPE and MSE are the mean values of the squared errors (MPB or MAD were 

squared and divided by n or n-p), MSPE and MSE were divided by the square of number 

of years to calculate MSPE and MSE per year, resulting in a fair comparison of 

predictions based on different numbers of years. 

Overdispersion Parameter, K

The overdispersion parameter, K, in the negative binomial distribution has been reported 

in different forms by various researchers. In the model results presented in this report, K

is reported from the variance equation expressed as: 

2 Var{m} = E{m}+ K * E{m} (7)

where 

Var{m} = the estimated variance of the mean accident rate; 

E{m} = the estimated mean accident rate; and 

K = the estimated overdispersion parameter. 

Variance overdispersion in a Poisson process can lead to a negative binomial dispersion 

of errors, particularly when the Poisson means are themselves approximately gamma 

distributed, or possess gamma heterogeneity. The negative binomial distribution has been 

shown to adequately describe errors in motor vehicle crash models in many instances. 

Because the Poisson rate is overdispersed, the estimated variance term is larger than the 

same under a Poisson process. As overdispersion gets larger, so does the estimated 

variance, and consequently all of the standard errors of estimates become inflated. As a 

result, all else being equal, a model with smaller overdispersion (i.e., a smaller value of 

K) is preferred to a model with larger overdispersion. 
18 

2.4 VALIDATION ACTIVITY 1: VALIDATION USING 

ADDITIONAL YEARS OF ACCIDENT DATA

The acquisition of subsequent years of accident data allowed for the validation of the 

models across time. For the type I and II models, although data from both Minnesota and 

Washington were collected, only data from Minnesota were used for the final calibration. 

Only the models developed using Minnesota data were validated because a report by 

Vogt and Bared states that “in view of the small size of the Washington State sample ... 

the non-random and ad hoc character of the Washington intersections, the lesser quality 

of the collected Washington data ... we take the Minnesota models as fundamental.” (p. 

123)(1) However, the Washington data were still obtained to further assess the 

transferability of these models over time and across jurisdictions. The original report 

performed a similar validation exercise with Washington data but with fewer years of 

accident data. The validation undertaken for this activity included applying the original 

models to the new data and assessing various measures of GOF. It also included 

recalibrating the models using the additional years of data and comparing the parameter 

estimates with those of the original models. 

The Type I and II models were originally calibrated on accident data from 1985 to 1989. 

In the original report, 1990 to 1993 data were used to validate the models in addition to 

the Washington data. The results for the MAD are given in Table 2. 

Table 2. Validation Statistics from Original Report1

Measure Model I (90-93 

Minnesota data) 

Model II (90-93 

Minnesota data) 

Model I (93-95 

Washington data) 

Model II (93-95 

Washington data) 

MAD 1.02 1.28 1.17 2.68 

1

 Vogt and Bared, 1998, (p. 131–132) 

For the new validation of Type I and II models, accident data from 1990 to 1998 were 

obtained to expand the validation dataset. 

For the Type III, IV, and V models, the original models were developed with accident 

data that were collected between 1993 and 1995. Accident data collected between 1996 

and 1997 at the same locations were acquired to validate the models. 

Data Limitations in the Minnesota Data

Because site characteristics change over time, the original sites were examined on 

important variables to determine which ones were no longer suitable for inclusion. Also, 

any sites where any year of accident data was missing was not included. Of the 327 

original four-legged sites, 315 were retained while 367 of the original 389 three-legged 

sites were retained. The sites that were excluded typically changed from being a rural to a 

suburban environment, changed in the number of legs, and changed traffic control or had 

missing years of accident data. 

Subsequent to the analysis and draft report, it was discovered that the mile log 

information that identifies the location of an intersection for some sites had changed over 

the 1990 to 1998 period. Although errors will exist in the accident counts used at these 
19 

sites, these errors were found to be negligible. For example, for Type I sites, the average 

number of accidents per site per year in the validation data was 0.25 and 0.11 for total 

and injury data, respectively. In the corrected data, these averages are 0.26 and 0.11. 

Therefore, the conclusions drawn from the analysis are not affected and the analysis has 

not been redone. 

Data Limitations in the Michigan Data

Traffic volumes from 1993 to 1995 were not updated for this validation exercise because 

AADT information for major and minor roads for 1996 and 1997 were not available. 

One of the complexities regarding AADT acquisition is outlined in the report published 

originally by Vogt.(2) In the original data, minor road AADT from 1993 to 1995 was not 

available for Michigan intersections. Therefore in the report, major AADT plus peakhour turning movement counts were used to estimate missing years of minor road AADT. 

Subsequent to the analysis and draft report it was discovered that for type V sites from 

Michigan, the original researchers manually identified crossroad mileposts for about 40 

percent or more of these intersections (State routes) and counted accidents that occurred 

on the crossroads. At non-State route crossroads, accidents are mileposted to the mainline. 

However, the Michigan accident data for 1996 and 1997 years obtained did not include 

the crossroad accidents at intersections with a State route crossroad because the 

validation team did not have the crossroad milepost information at that time. As a result, 

the later year crossroad accident numbers at these sites should be systematically lower 

than expected. 

2.4.1 Model I 

The summary statistics shown in table 3 indicate that there are similar accident 

frequencies between the original (1985–89 data for 389 sites) and the additional (1990–

98 data for 367 sites) years. Note that the statistics compare 5 years of accident data in 

the original set to 9 years of accident data for validation over time. The latter years of 

data exhibit an increased variability amongst the sites. The Washington data shows a 

higher average accident frequency and a lower variability between sites compared to the 

original Minnesota data. 
20 

Table 3. Accident Summary Statistics for Type I Sites 

Dataset No. of Sites Mean Median Std. Deviation Min. Max. 

Minnesota Total (85-89)1 389 1.35 

(0.27/year) 0.00 2.88 0 39 

Minnesota Injury (85-89)1 389 0.59 

(0.12/year) 0.00 N/A2

 0 17 

Minnesota Total (90-98) 367 2.21 

(0.25/year) 1.00 3.89 0 32 

Minnesota Injury (90-98) 367 0.95 

(0.11/year) 0.00 1.79 0 13 

Washington Total (93-96) 181 1.43 

(0.36/year) 0.00 2.48 0 14 

Washington Injury (93-96) 181 0.66 

(0.17/year) 0.00 1.33 0 10 1 Vogt and Bared, 1998, (p. 60) 

2 N/A: not available 

Total Accident Model 

The model was recalibrated with the additional years of accident data for the original 

Minnesota sites. Recall that the intersection related variable for vertical curvature, VCI1, 

did not exactly match those statistics given in the report. The parameter estimates, their 

standard errors, and p-values are provided in table 4, which reveals differences in the 

parameter estimates of the variables between the two time periods. 

VCI1 and RT were estimated with opposite signs to the original models, although in the 

original calibration these parameter estimates had large standard errors and were not 

statistically significant. This indicates that variables with large standard errors compared 

to the parameter estimates should not be included in the model even if engineering 

“common sense” suggests that they should. The other parameters were estimated with the 

same sign as originally and in some cases similar magnitude and significance to the 

original models. The overdispersion parameter, K, was estimated with a similar 

magnitude. 
21 

Table 4. Parameter Estimates for Type I Total Accident Model Using 

Additional Years of Data 

Variable 

Original Estimates1

(s.e., p-value) 

Recalibrated Estimates 

(s.e., p-value) 

Additional Years 

Estimates (s.e., p-value) 

Constant -12.9922 -12.90 -13.48 

 (1.1511, 0.0001) (1.16, <0.001) (1.07, <0.001) 

Log of 

AADT1 

0.8052 

(0.0639, 0.0001) 

0.8051 

(0.0784, <0.001) 

0.8199 

(0.0714, <0.001) 

Log of 

AADT2 

0.5037 

(0.0708, 0.0001) 

0.4991 

(0.0660, <0.001) 

0.4808 

(0.0584, <0.001) 

HI1 0.0339 0.0339 0.0145 

 (0.0327, 0.3004) (0.0220, 0.124) (0.0206, 0.481) 

VCI1 0.2901 0.1900 -0.245 

(0.2935, 0.3229) (0.2260, 0.402) (0.269, 0.363) 

SPD1 0.0285 0.0273 0.0375 

(0.0177, 0.1072) (0.0144, 0.058) (0.0130, 0.004) 

HAZRAT1 0.1726 0.1806 0.0779 

(0.0677, 0.0108) (0.0754, 0.017) (0.0655, 0.234) 

RT MAJ 0.2671 0.2690 -0.077 

(0.1398, 0.0561) (0.1420, 0.058) (0.126, 0.539) 

HAU 0.0045 0.0043 0.00145 

 (0.0032, 0.1578) (0.0024, 0.075) (0.00222, 0.513) 

K2 0.481 0.485 0.500 1 Vogt and Bared, 1998, (p. 115) 

2 K: Overdispersion value 

GOF measure comparisons are shown in table 5. The Pearson product-moment 

correlation coefficient was marginally higher for the original data than when the model 

based on that data were used to predict the additional years of data. The MPB is higher 

for the prediction of the additional years of data. The MADs per year are similar for the 

predictions for the two time periods. The MSPE per yearsquared is lower than the MSE 

per yearsquared. 
22 

Table 5. Validation Statistics for Type I Total Accident Model Using 

Additional Years of Data 

Measure 

Recalibrated 

1985-89 Model 

Original 

1985-89 Model 

Recalibrated 

1985-89 Model 

Years used for validation 1985-89 1990-98 1990-98 

Number of sites 389 367 367 

Pearson product-moment 

correlation coefficients 0.662 0.612 0.614 

MPB -0.01 -0.050 -0.52 

MPB/yr 0.00 -0.06 -0.06 

MAD 1.03 1.84 1.84 

MAD/yr 0.21 0.20 0.20 

MSE 4.64 

MSE/yr2 0.19 

N/A1

 N/A1

MSPE 10.93 10.94 

MSPE/yr2

N/A1

0.13 0.14 1 N/A: not available 

The model was also recalibrated with the Washington data. The parameter estimates, 

their standard errors, and p-values are provided in table 6, which reveals differences in 

the parameter estimates of the variables between the two locations. 

All parameters were estimated with the same sign as the original models, and in some 

cases with similar magnitude and significance. Notable exceptions are VCI1 and 

HAZRAT1 which were estimated with the same sign but with a large difference in 

magnitude. For VCI1 both the original and newly estimated parameters had large 

standard errors. For the new Washington data HAZRAT1 had a large standard error and 

the overdispersion parameter, K, was higher than the original Minnesota model. 

A comparison of validation measures for the model recalibrated with the original data 

and the original model applied to the Washington data is shown in table 7. 

The Pearson product-moment correlation coefficient was slightly higher for the original 

data as compared to Washington data. The MPB, mean absolute deviations and mean 

squared prediction errors were similar in magnitude. 
23 

Table 6. Parameter Estimates for Type I Total Accident Model Using 

Washington Data 

Variable 

Original Estimates 

(s.e., p-value)1

Recalibrated Estimate 

(s.e., p-value) 

Washington Data Estimates 

(s.e., p-value) 

Constant -12.9922 -12.90 -12.59 

 (1.1511, 0.0001) (1.16, <0.001) (2.01, <0.001) 

Log of AADT1 0.8052 0.8051 0.8730 

 (0.0639, 0.0001) (0.0784, <0.001) (0.1750, <0.001) 

Log of AADT2 0.5037 0.4991 0.4858 

 (0.0708, 0.0001) (0.0660, <0.001) (0.0805, <0.001) 

HI1 0.0339 0.0339 0.0170 

 (0.0327, 0.3004) (0.0220, 0.124) (0.0356, 0.632) 

VCI1 0.2901 0.1900 0.6200 

(0.2935, 0.3229) (0.2260, 0.402) (0.4440, 0.162) 

SPD1 0.0285 0.0273 0.0122 

(0.0177, 0.1072) (0.0144, 0.058) (0.0179, 0.495) 

HAZRAT1 0.1726 0.1806 0.1030 

(0.0677, 0.0108) (0.0754, 0.017) (0.1010, 0.309) 

RT MAJ 0.2671 0.2690 0.2780 

(0.1398, 0.0561) (0.1420, 0.058) (0.2750, 0.311) 

HAU 0.0045 0.0043 0.0032 

 (0.0032, 0.1578) (0.0024, 0.075) (0.0127, 0.802) 

K2 0.481 0.485 0.769 1 Vogt and Bared, 1998, (p. 115) 

2 K: Overdispersion value 

Table 7. Validation Statistics for Type I Total Accident Model Using 

Washington Data 

Measure Recalibrated 1985-89 Model Original 1985-89 Model 

Years used for validation 1985-89 (Minnesota) 1993-96 (Washington) 

Number of sites 389 181 

Pearson product-moment 

correlation coefficients 0.662 0.579 

MPB -0.01 -0.30 

MPB/yr 0.00 -0.08 

MAD 1.027 1.39 

MAD/yr 0.205 0.35 

MSE 4.64 

MSE/yr2 0.19 

N/A1

MSPE 4.45 

MSPE/yr2 N/A1

0.28 1 N/A: not available 
24 

Injury Accident Model 

Table 8 shows the parameter estimates for the type I injury accident model using 

additional years of data. VCI1, RT MAJ, and HAU were estimated with opposite signs 

than the original model, but this is not surprising when the large standard errors are 

considered. The other parameters were estimated with the same direction of effect, and in 

some cases similar magnitude and significance as the original model. The overdispersion 

parameter, K, was estimated to be slightly higher than that in the original model. 

Table 8. Parameter Estimates for Type I Injury Accident Model Using Additional 

Years of Data 

Variable Original Estimates (s.e., p-value)1 Additional Years Estimates (s.e., p-value) 

Constant -13.0374 -15.41 

 (1.7908, 0.0001) (1.44, <0.001) 

Log of AADT1 0.8122 0.7774 

 (0.0973, 0.0001) (0.0932, <0.001) 

Log of AADT2 0.4551 0.5815 

 (0.0977, 0.0001) (0.0760, <0.001) 

HI1 0.0335 0.0067 

 (0.0327, 0.3047) (0.0268, 0.802) 

VCI1 0.1869 -0.359 

(0.3657, 0.6092) (0.393, 0.361) 

SPD1 0.0156 0.0514 

(0.0269, 0.5618) (0.0179, 0.004) 

HAZRAT1 0.2065 0.1618 

(0.0930, 0.0263) (0.0857, 0.059) 

RT MAJ 0.3620 -0.260 

(0.1814, 0.0460) (0.163, 0.159) 

HAU 0.0051 -0.00109 

 (0.0045, 0.2594) (0.00282, 0.699) 

DRWY1 -0.0120 -0.0008 

 (0.0714, 0.8671) (0.0541, 0.988) 

K2 0.494 0.526 1 Vogt and Bared, 1998, (p. 116) 

2 K: Overdispersion value 

Validation statistics are shown in table 9 for the additional years of injury accident data. 

Since the original injury accident counts were not obtained these measures are not 

provided for the original years. The Pearson product-moment correlation coefficient was 

lower (0.553) than that for total accidents (0.614 for the recalibrated model) and the 

MAD per year (0.106) was about one half of that for total accidents. 

The model was also recalibrated with the Washington data. The parameter estimates, 

their standard errors, and p-values are provided in table 10, which reveals differences in 

the parameter estimates of the variables between the two States. 
25 

Table 9. Validation Statistics for Type I Injury Accident Model Using Additional 

Years of Data 

Measure 

Additional Years 

1990-98 

Number of sites 367 

Pearson product-moment 

correlation coefficients 0.553 

MPB -0.219 

MPB/yr -0.024 

MAD 0.955 

MAD/yr 0.106 

MSPE 2.530 

MSPE/yr2 0.031 

Table 10. Parameter Estimates for Type I Injury Accident Model 

UsingWashington Data 

Variable Original Estimates (s.e., p-value) 1 Washington Data Estimates (s.e., p-value) 

Constant 

 

-13.0374 

(1.7908, 0.0001) 

-14.64 

(2.49, <0.001) 

Log of AADT1 

0.8122 

(0.0973, 0.0001) 

1.012 

(0.222, <0.001) 

Log of AADT2 

0.4551 

(0.0977, 0.0001) 

0.5237 

(0.0968, <0.001) 

HI1 

0.0335 

(0.0327, 0.3047) 

0.0055 

(0.0404, 0.892) 

VCI1 

0.1869 

(0.3657, 0.6092) 

0.578 

(0.526, 0.272) 

SPD1 

0.0156 

(0.0269, 0.5618) 

0.0118 

(0.0227, 0.602) 

HAZRAT1 

0.2065 

(0.0930, 0.0263) 

0.071 

(0.119, 0.552) 

RT MAJ 

0.3620 

(0.1814, 0.0460) 

0.190 

(0.305, 0.534) 

HAU 

0.0051 

(0.0045, 0.2594) 

0.0103 

(0.0163, 0.526) 

DRWY1 

-0.0120 

(0.0714, 0.8671) 

-0.0111 

(0.0695, 0.873) 

K2 0.494 0.513 1 Vogt and Bared, 1998, (p. 116) 

2 K: Overdispersion value 

The parameters were all estimated with the same sign but in several cases the difference 

in magnitude was large. The overdispersion parameter, K, was estimated with a similar 

magnitude. 

Validation measures for the Washington data are shown in table 11. The Pearson productmoment correlation coefficient was lower (0.505) than that for total (0.579) accidents, 

and the MADs per year are about one half that for total accidents. 
26 

Table 11. Validation Statistics for Type I Injury Accident Model Using 

Washington Data 

Measure 

Washington Data 

1993-96 

Number of sites 181 

Pearson product-moment 

correlation coefficients 0.505 

MPB -0.084 

MPB/yr -0.021 

MAD 0.712 

MAD/yr 0.178 

MSPE 1.343 

MSPE/yr2 0.08 

2.4.2 Model II 

The summary statistics shown in table 12 indicate that there is little difference in the 

mean accident frequencies between original (1985–89) and additional (1990–98) years 

for the Minnesota sites, although there is more variation in the latter data. The 

Washington sites exhibit a large increase in the mean accident frequency and a larger 

variability between sites. 

Total Accident Model 

The model was recalibrated with the additional years of accident data for the Minnesota 

sites. Recall that the intersection related variables did not exactly match those statistics 

given in the report. The parameter estimates, their standard errors, and p-values are 

provided in table 13, which reveals differences in the parameter estimates of the variables 

between the two time periods. 

Table 12. Accident Summary Statistics for Type II Sites 

Dataset No. of 

Sites Mean Median Std. 

Deviation Minimum Maximum 

Minnesota Total (85-89)1 327 1.51 

(0.30/year) 1.00 2.36 0 16 

Minnesota Injury (85-89)1 327 0.77 

(0.15/year) 0.00 N/A2

 0 9 

Minnesota Total (90-98) 315 2.83 

(0.31/year) 2.00 5.17 0 67 

Minnesota Injury (90-98) 315 1.50 

(0.17/year) 1.00 2.95 0 36 

Washington Total (93-96) 90 3.97 

(0.99/year) 1.00 5.07 0 20 

Washington Injury (93-96) 90 2.46 

(0.62/year) 1.00 3.38 0 14 

1 Vogt and Bared, 1998, (p. 64) 

2 N/A: not available 

The parameters were estimated with the same sign as the original model and in several 

cases with similar magnitude and significance. VCI1 and HAU were estimated with a 
27 

large difference in magnitude. The overdispersion parameter, K, was almost twice as 

large as the original model. 

Table 13. Parameter Estimates for Type II Total Accident Model Using Additional 

 Years of Data 

Variable Original Estimates (s.e., p-value) 1 Additional Years Estimates (s.e., p-value) 

Constant -10.4260 -10.74 

 (1.3167, 0.0001) (1.08, <0.001) 

Log of AADT1 0.6026 0.6673 

 (0.0836, 0.0001) (0.0768, <0.001) 

Log of AADT2 0.6091 0.6135 

 (0.0694, 0.0001) (0.0622, <0.001) 

HI1 0.0449 0.0702 

 (0.0473, 0.3431) (0.0456, 0.123) 

VCI1 0.2885 0.066 

(0.2576, 0.2628) (0.199, 0.741) 

SPD1 0.0187 0.0130 

(0.0176, 0.2875) (0.0159, 0.415) 

DRWY1 0.1235 0.0988 

(0.0519, 0.0173) (0.0417, 0.018) 

HAU -0.0049 -0.00006 

 (0.0033, 0.1341) (0.00141, 0.967) 

K2 0.205 0.385 1 Vogt and Bared, 1998, (p. 115) 

2 K: Overdispersion value 

A comparison of validation measures for the original data additional years is shown in 

table 14. 

The Pearson product-moment correlation coefficient was higher for the original data than 

for the original model applied to the additional years. The MADs per year are similar. For 

the additional years model, the MSPE per yearsquared is higher than the MSE per year

squared, indicating that the model is not performing as well on the additional years of 

data. 
28 

Table 14. Validation Statistics for Type II Total Accident Model Using Additional 

 Years of Data 

Measure 

Original Data 

1985-89 

Additional Years 

1990-98 

Number of sites 327 315 

Pearson product-moment 

correlation coefficients 0.760 0.668 

MPB -0.017 -0.392 

MPB/yr -0.003 -0.043 

MAD 1.034 2.060 

MAD/yr 0.207 0.229 

MSE 2.364 

MSE/yr2 0.095 

N/A1

MSPE 15.000 

MSPE/yr2 N/A1

0.185 1 N/A: not available 

The model was also recalibrated with the Washington data. The parameter estimates, 

their standard errors, and p-values are provided in table 15, which reveals differences in 

the parameter estimates of the variables between the two States. 

HI1, VCI1, and HAU were estimated with opposite signs, which might be expected on 

the basis of the large standard errors both in the original model and the model estimated 

using Washington data. Again, this would seem to indicate that variables with large 

standard errors in the parameter estimates should not be included in the model even if 

engineering common sense suggests they should. The other parameters were estimated 

with the same sign but with generally large differences in magnitude. The overdispersion 

parameter, K, was estimated to be over three times as large as that for the original model. 
29 

Table 15. Parameter Estimates for Type II Total Accident Model Using 

Washington Data 

Variable Original Estimates (s.e., p-value)1 Washington Data Estimates (s.e., p-value) 

Constant 

-10.4260 

(1.3167, 0.0001) 

-8.64 

(2.06, <0.001) 

Log of AADT1 

0.6026 

(0.0836, 0.0001) 

0.3680 

(0.2030, 0.071) 

Log of AADT2 

0.6091 

(0.0694, 0.0001) 

0.7340 

(0.1080, <0.001) 

HI1 

0.0449 

(0.0473, 0.3431) 

-0.1646 

(0.0766, 0.032) 

VCI1 

0.2885 

(0.2576, 0.2628) 

-0.0140 

(0.2230, 0.950) 

SPD1 

0.0187 

(0.0176, 0.2875) 

0.0139 

(0.0185, 0.454) 

ND 

0.1235 

(0.0519, 0.0173) 

0.0118 

(0.0815, 0.884) 

HAU 

-0.0049 

(0.0033, 0.1341) 

0.0251 

(0.0129, 0.051) 

K2 0.205 0.667 1 Vogt and Bared, 1998, (p. 115) 

2 K: Overdispersion value

A comparison of validation measures for the original data and the original model applied 

to the Washington data is shown in table 16. The Pearson product-moment correlation 

coefficient was higher for the original data as compared to the Washington data. The 

MAD per year is much higher for the Washington data, indicating that the model is not 

performing well on these data. 

Table 16. Validation Statistics for Type II Total Accident Model Using 

Washington Data 

Measure 

Original Data 

1985-89 

Washington Data 

1993-96 

Number of sites 327 90 

Pearson product-moment 

correlation coefficients 0.760 0.517 

MPB -0.017 -0.42 

MPB/yr -0.003 -0.11 

MAD 1.034 3.19 

MAD/yr 0.207 0.80 

MSE 2.364 

MSE/year2 0.095 

N/A1

MSPE 20.15 

MSPE/yr2 N/A1

1.26 1 N/A: not available 
30 

Injury Accident Model 

For the injury accident model, the parameter estimates, their standard errors, and p-values 

are provided in table 17. HAU was estimated with the opposite sign to the original model 

and with a large standard error. The other variables were estimated with the same sign as 

the original model, but in some cases with large differences in magnitude. The 

overdispersion parameter, K, was estimated to be more than twice that of the original 

model. 

Table 17. Parameter Estimates for Type II Injury Accident Model Using Additional 

Years of Data 

Variable Original Estimates (s.e., p-value)1 Additional Years Estimates (s.e., p-value) 

Constant 

-10.7829 

(1.7656, 0.0001) 

-12.19 

(1.39, <0.001) 

Log of AADT1 

0.6339 

(0.1055, 0.0001) 

0.6497 

(0.0948, <0.001) 

Log of AADT2 

0.6229 

(0.0870, 0.0001) 

0.6727 

(0.0815, <0.001) 

HI1 

0.0729 

(0.0635, 0.2513) 

0.0935 

(0.0549, 0.089) 

VCI1 

0.2789 

(0.4623, 0.5464) 

0.109 

(0.240, 0.650) 

SPD1 

0.0112 

(0.0251, 0.6567) 

0.0287 

(0.0204, 0.159) 

HAZRAT1 

-0.1225 

(0.0720, 0.0889) 

-0.1313 

(0.0749, 0.080) 

RT MAJ 

0.0451 

(0.1665, 0.7865) 

0.014 

(0.148, 0.924) 

HAU 

-0.0043 

(0.0044, 0.3258) 

0.00105 

(0.00176, 0.552) 

ND 

0.0857 

(0.0639, 0.1799) 

0.0791 

(0.0513, 0.123) 

K2 0.1811 0.435 

 1 Vogt and Bared, 1998, (p. 117) 

 2 K: Overdispersion value 

Validation measures for the additional years of data are provided in table 18. Because the 

original injury accident counts were not obtained these measures are not provided for the 

original years. The Pearson product-moment correlation coefficient was lower (0.671) 

than that for total accidents (0.668), and the MAD per year is about twice that for total 

accidents. 
31 

Table 18. Validation Statistics for Type II Injury Accident Model Using 

Additional Years of Data 

Measure Additional Years 1990-98 

Number of sites 315 

Pearson product-moment 

correlation coefficients 0.641 

MPB -0.152 

MPB/yr -0.170 

MAD 1.230 

MAD/yr 0.137 

MSPE 5.130 

MSPE/yr2 0.063 

The model was also recalibrated with the Washington data. The parameter estimates, 

their standard errors, and p-values are provided in table 19, which reveals differences in 

the parameter estimates of the variables between the two States. 

HI1, RT MAJ, and HAU were estimated with opposite signs and large differences in 

magnitude compared to the original estimates. The other variables were estimated with 

the same sign but with generally large differences in magnitude. The overdispersion 

parameter, K, was estimated to be more than three times that of the original model. 

Table 20 shows the validation statistics for the original injury accident model applied to 

the Washington data. The Pearson product-moment correlation coefficient was lower 

(0.482) than that for total accidents (0.517) and the MADs per year are about sixty 

percent of that for total accidents. 
32 

Table 19. Parameter Estimates for Type II Injury Accident Model Using 

 Washington Data 

Variable Original Estimates (s.e., p-value)1 Washington Data Estimates (s.e., p-value) 

Constant 

-10.7829 

(1.7656, 0.0001) 

-11.62 

(2.39, <0.001) 

Log of AADT1 

0.6339 

(0.1055, 0.0001) 

0.504 

(0.223, 0.024) 

Log of AADT2 

0.6229 

(0.0870, 0.0001) 

0.845 

(0.135, <0.001) 

HI1 

0.0729 

(0.0635, 0.2513) 

-0.1740 

(0.0992, 0.080) 

VCI1 

0.2789 

(0.4623, 0.5464) 

0.025 

(0.223, 0.911) 

SPD1 

0.0112 

(0.0251, 0.6567) 

0.0463 

(0.0207, 0.025) 

HAZRAT1 

-0.1225 

(0.0720, 0.0889) 

-0.299 

(0.130, 0.022) 

RT MAJ 

0.0451 

(0.1665, 0.7865) 

-0.775 

(0.292, 0.008) 

HAU 

-0.0043 

(0.0044, 0.3258) 

0.0220 

(0.0136, 0.105) 

ND 

0.0857 

(0.0639, 0.1799) 

0.0589 

(0.0845, 0.486) 

K2 0.181 0.556 1 Vogt and Bared, 1998, (p. 117) 

2 K: Overdispersion value 

Table 20. Validation Statistics for Type II Injury Accident Model 

Using Washington Data 

Measure 

Washington Data 

1993-96 

Number of sites 90 

Pearson product-moment correlation coefficient 0.482 

MPB 0.345 

MPB/yr 0.086 

MAD 2.071 

MAD/yr 0.518 

MSPE 8.86 

MSPE/yr2 0.55 

2.4.3 Model III 

The summary statistics shown in table 21 indicate that there are differences in the 

accident frequencies between the original (1993–95) and additional (1996–97) years. 

Note that the statistics compare 3 years of accident data in the original data to 2 years of 

accident data for validation using the additional years of data. For example, the means per 

year of TOTACC and TOTACCI for 1993–95 are 1.29 and 0.87, respectively. The means 
33 

per year of TOTACC and TOTACCI for 1996–97 are 0.75 and 0.62, respectively. Note 

that the 1993–95 data for the original INJACC and INJACCI models could not be 

obtained. 

Table 21. Accident Summary Statistics of Type III Sites 

Dataset Mean Median Std. Deviation Minimum Maximum 

TOTACC (93-95)1

3.88 

(1.29/year) 2 4.33 0 19 

TOTACC (96-97) 

1.50 

(0.75/year) 1 2.42 0 12 

TOTACCI (93-95)1

2.62 

(0.87/year) 1 3.36 0 13 

TOTACCI (96-97) 

1.23 

(0.62/year) 0 2.09 0 10 

INJACC (96-97) 

0.55 

(0.28/year) 0 1.19 0 7 

INJACCI (96-97) 

0.46 

(0.23/year) 0 1.02 0 7 1

 Vogt, 1999, (p. 53) 

Total Accident Model (TOTACC) 

The models were recalibrated with the additional years of accident data. The parameter 

estimates, their standard errors, and p-values are provided in table 22. All of the variables 

were estimated with the same sign as in the original model, but the constant term and 

AADT2 were estimated with larger differences in magnitude than the other parameters. 

MEDWDTH1 and DRWY1 became insignificant for the recalibration with the additional 

years of data, and the overdispersion parameter, K, was almost twice as large as for the 

original model (for a discussion of K, see section 2.3). 

Table 23 shows a comparison of GOF measures between the original main models in the 

Vogt report (1999) applied to the original 1993–95 data and to the 1996–97 data. The 

Pearson product-moment correlation coefficient was higher for the original years of data 

than for the additional years of data. The MAD per year was similar, but the MPB per 

year was larger for the model for the additional years of data. The MSPE per year squared 

for the additional years was higher than the MSE per year squared for the original years, 

but the difference was not great. 
34 

Table 22. Parameter Estimates for TOTACC Type III Model Using Additional 

Years of Data 

Variable Original Estimates (s.e., p-value)1 Additional Years Estimate (s.e., p-value) 

Constant -12.2196 -14.4477 

 (2.3575, 0.0001) (3.3378, 0.00001) 

Log of AADT1 1.1479 1.1597 

 (0.2527, 0.0001) (0.3677, 0.0016) 

Log of AADT2 0.2624 0.5214 

 (0.0866, 0.0024) (0.1286, 0.00001) 

MEDWIDTH1 -0.0546 -0.0515 

 (0.0249, 0.0285) (0.0440, 0.2414) 

DRWY1 0.0391 0.0127 

 (0.0239, 0.1023) (0.0439, 0.7719) 

K2 0.3893 0.6356 1

 Vogt, 1999, (p. 111) 

2 K: Overdispersion value 

Table 23. Validation Statistics for TOTACC Type III Model Using 

Additional Years of Data 

Measure Original Data (1993-95) Additional Years (1996-98) 

Number of sites 84 84 

Pearson product-moment 

correlation coefficients 

 

0.66 

 

0.54 

MPB -0.01 1.07 

MPB/yr 0.0 0.53 

MAD 2.26 1.75 

MAD/yr 0.75 0.88 

MSE 11.01 

MSE/yr2 1.22 

N/A1

MSPE 5.57 

MSPE/yr2 N/A1

1.39 1 N/A: not available 

Intersection Related Total Accident Model (TOTACCI) 

The parameter estimates, their standard errors, and p-values are given in table 24. All of 

the variables were re-estimated with the same direction of effect as the original model, 

but the constant term and AADT2 were estimated with larger differences in magnitude. 

MEDWDTH1 and DRWY1 became statistically insignificant for the additional years data, 

and the overdispersion parameter was slightly higher than that for the original model. 
35 

Table 24. Parameter Estimates for TOTACCI Type III Model Using Additional 

Years of Data 

Variable Original Estimates (s.e., p-value)1 Additional Years Estimate (s.e., p-value) 

Constant -15.4661 -16.7738 

 (3.4685, 0.0001) (3.8495, 0.00001) 

Log of AADT1 1.4331 1.3497 

 (0.3608, 0.0001) (0.4098, 0.0010) 

Log of AADT2 0.2686 0.5439 

 (0.0988, 0.0065) (0.1434, 0.0001) 

MEDWIDTH1 -0.0612 -0.0308 

 (0.0360, 0.0888) (0.0465, 0.5074) 

DRWY1 0.0560 0.0358 

 (0.0289, 0.0525) (0.0486, 0.4608) 

K2 0.5118 0.7220 1

 Vogt, 1999, p112 

2 K: Overdispersion value 

Table 25 shows a comparison of GOF measures between the original main model in the 

Vogt report applied the original data and to the 1996–97 data.(2)

The Pearson product-moment correlation coefficient for the additional years of data was 

lower than that for the original years. The MAD per year was similar, but the MPB per 

year was slightly larger for the additional years of data. The MSPE per year squared for 

the additional years was higher than the MSE per year squared. 

Table 25. Validation Statistics for TOTACCI Type III Model Using 

Additional Years of Data 

Measure 

Original Data 

1993-95 

Additional Years 

1996-97 

Number of sites 84 84 

Pearson product-moment 

correlation coefficients 

 

0.67 

 

0.52 

MPB -0.005 0.52 

MPB/yr -0.002 0.26 

MAD 1.76 1.29 

MAD/yr 0.59 0.65 

MSE 6.50 

MSE/yr2 0.24 

N/A1

MSPE 3.54 

MSPE/yr2 N/A1

0.89 1 N/A: not available 
36 

Injury Accident Model (INJACC) 

There were two variants of the original model for injury accidents. These were validated 

separately. The original injury accident counts were not obtained. Thus, a comparison of 

prediction performance measures for the original data and additional years could not be 

accomplished. 

Variant 1

For the recalibration for the additional years of data, the parameter estimates, their 

standard errors, and p-values are given in table 26. All of the variables were estimated 

with the same sign as the original model, but that the constant term and AADT2 were 

estimated with larger differences in magnitude than the other parameters. HAU became 

insignificant for the additional years of data, and the overdispersion parameter was about 

half of that for the original model. 

Table 26. Parameter Estimates for INJACC Type III Model Using 

Additional Years of Data: Variant 1 

Variable Original Estimates (s.e., p-value)1 Additional Years Estimate (s.e., p-value) 

Constant -12.3246 -15.7264 

 (2.8076, 0.0001) (4.3853, 0.0006) 

Log of AADT1 1.1436 1.2659 

 (0.2763, 0.0001) (0.4347, 0.0036) 

Log of AADT2 0.1357 0.3883 

 (0.1029, 0.1872) (0.1574, 0.0136) 

HAU 0.0230 0.0140 

 (0.0131, 0.0790) (0.0165, 0.3969) 

K2 0.3787 0.1740 1

 Vogt, 1999, (p. 113) 

2 K: Overdispersion value

Table 27 shows the GOF measures for the original injury accident model (Variant 1) in 

the Vogt report applied to the additional years of data.(2) The Pearson product-moment 

correlation coefficient (0.37) was lower than that (0.54) for TOTACC. However, the 

MPB, MAD, and MSPE per year squared were smaller than those for TOTACC. 

Variant 2

The parameter estimates, their standard errors, and p-values are given in table 28, which 

reveals that the variables AADT1, AADT2, HAU, and ABSGRD1 were estimated with 

the same sign as for the original model, but DRWY1 was estimated with an opposite sign, 

although its estimate was statistically insignificant. HAU and ABSGRD1 were also 

statistically insignificant for the additional years. AADT2 was estimated with a higher 

magnitude and level significance than it was for the original model. The overdispersion 

parameter was much higher than that for the original model. 
37 

Table 27. Validation Statistics for INJACC Type III Model Using 

Additional Years of Data: Variant 1 

Measure Additional Years 1996-97 

Number of sites 84 

Pearson product-moment correlation coefficients 0.37 

MPB -0.15 

MPB/yr -0.07 

MAD 1.20 

MAD/yr 0.60 

MSPE 3.76 

MSPE/yr2 0.94 

Table 28. Parameter Estimates for INJACC Type III Model Using 

Additional Years of Data: Variant 2 

Variable Original Estimates (s.e., p-value)1 Additional Years Estimate (s.e., p-value) 

Constant -11.0061 -14.3764 

 (2.6937, 0.0001) (4.5820, 0.0028) 

Log of AADT1 0.9526 1.0147 

 (0.2843, 0.0008) (0.5101, 0.0467) 

Log of AADT2 0.1499 0.5327 

 (0.0916, 0.1018) (0.2667, 0.0458) 

HAU 0.0289 0.0202 

 (0.0105, 0.0061) (0.0155, 0.1936) 

DRWY1 0.0481 -0.0493 

 (0.0262, 0.0664) (0.0853, 0.5633) 

ABSGRD1 0.1838 0.2565 

(0.1130, 0.1038) (0.1987, 0.1967) 

K2 0.2588 0.9259 1

 Vogt, 1999, (p. 113) 

2 K: Overdispersion value

Table 29 shows the GOF measures for the original injury accident model (Variant 2) in 

the Vogt report applied to the additional years of data.(2) 

The Pearson product-moment correlation coefficient (0.38) was lower than that (0.54) for 

TOTACC. However, the MPB, MAD, and MSPE per year squared were smaller than 

those for TOTACC. 
38 

Table 29. Validation Statistics for INJACC Type III Model Using 

Additional Years of Data: Variant 2 

Measure Original 1993-95 Model 

Years used for validation 1996 to 1997 

Number of sites 84 

Pearson product-moment correlation coefficients 0.38 

MPB -0.16 

MPB/yr -0.08 

MAD 1.17 

MAD/yr 0.58 

MSPE 3.73 

MSPE/yr2 0.93 

2.4.4 Model IV 

The summary statistics shown in table 30 reveal that the accident frequencies were lower 

during the additional years. Mean, median, and maximum of the accident frequencies 

were almost half of those for the 1993–1995 period. Recall that the original 1993–95 

INJACC and INJACCI data were not obtained. 

Table 30. Accident Summary Statistics of Type IV Sites 

Dataset Mean Median 

Std. 

Deviation Minimum Maximum 

TOTACC (93-95)1

5.53 

(1.84/year) 3.5 6.52 0 38 

TOTACC (96-97) 

2.67 

(1.34/year) 1 3.60 0 16 

TOTACCI (93-95)1

4.13 

(1.38/year) 2 5.37 0 27 

TOTACCI (96-97) 

2.33 

(1.17/year) 1 3.21 0 13 

INJACC (96-97) 

1.43 

(0.72/year) 1 1.96 0 9 

INJACCI (96-97) 

1.26 

(0.63/year) 1 1.80 0 8 1

 Vogt, 1999, (p. 57) 

Total Accident Model (TOTACC) 

The parameter estimates, their standard errors, and p-values are shown in table 31, which 

reveals that the constant term and all of the variables were estimated with the original 

sign, but some parameters had somewhat large differences in the magnitude compared to 

the original parameter. The overdispersion parameters were similar. 
39 

Table 31. Parameter Estimates for TOTACC Type IV Model Using 

Additional Years of Data 

Variable Original Estimates (s.e., p-value)1 Additional Years Estimate (s.e., p-value) 

Constant 

 

-9.4631 

(2.5991, 0.0003) 

-9.6398 

(3.0909, 0.0038) 

Log of AADT1 

 

0.8503 

(0.2779, 0.0022 ) 

0.7258 

(0.3342, 0.0299) 

Log of AADT2 

 

0.3294 

(0.1255, 0.0087) 

0.4968 

(0.1691, 0.0033) 

PKLEFT1 

 

0.1100 

(0.0412, 0.0076) 

0.1056 

(0.0432, 0.0145) 

LTLN1S 

 

-0.4841 

(0.2311, 0.0362) 

-0.5603 

(0.2803, 0.0456) 

K2 0.4578 0.4312 1

 Vogt, 1999, (p. 116)

2

 K: Overdispersion value 

Table 32 shows a comparison of the GOF measures for the original main model in the 

Vogt report and this model applied to the additional years of data.(2) The Pearson 

product-moment correlation coefficients of the original and additional years of data are 

similar (0.56 versus 0.58). The MPB per year was slightly larger for the model based on 

additional years, while the MAD per year was similar. The MSPE per year squared was 

lower than the MSE per year squared, indicating that the model is performing fairly well 

on the additional years of data. 

Table 32. Validation Statistics for TOTACC Type IV Model Using 

Additional Years of Data 

Measure 

Original Data 

1993-95 

Additional Years 

1996-97 

Number of sites 72 72 

Pearson product-moment 

correlation coefficients 

 

0.56 

 

0.58 

MPB -0.07 -1.06 

MPB/yr -0.02 -0.53 

MAD 3.38 2.22 

MAD/yr 1.13 1.11 

MSE 30.62 

MSE/yr2 3.40 

N/A1

MSPE 9.56 

MSPE/yr2 N/A1

2.39 1 N/A: not available 
40 

Intersection Related Total Accident Model (TOTACCI) 

The parameter estimates, their standard errors, and p-values are shown in table 33, which 

reveals that the parameters were estimated with the same sign as the original model, but 

that there were some differences in magnitude. In particular, the effect of the log of 

AADT2 on accident frequency was almost twice as large as for the original model. The 

overdispersion parameter was slightly lower than that for the original model. 

Table 33. Parameter Estimates for TOTACCI Type IV Model Using 

Additional Years of Data 

Variable Original Estimate (s.e., p-value)1 Additional Years Estimate (s.e., p-value) 

Constant 

 

-11.1096 

(3.3345, 0.0008) 

-11.8796 

(3.6865, 0.0024) 

Log of AADT1 

 

0.9299 

(0.3433, 0.0067 ) 

0.7982 

(0.3764, 0.0339) 

Log of AADT2 

 

0.3536 

(0.1163, 0.0024) 

0.6624 

(0.1673, 0.0001) 

PKLEFT1 

 

0.1491 

(0.0586, 0.0110) 

0.1100 

(0.0563, 0.0509) 

K2 0.7096 0.6262 1

 Vogt, 1999, (p. 117) 

2

 K: Overdispersion value 

Table 34 shows a comparison of GOF measures between the original main model in the 

Vogt report and for this model applied to the 1996–97 data.(2) The Pearson productmoment correlation coefficient for the additional years of data was estimated as slightly 

higher than the original years. The MAD per year was similar, but the MPB per year was 

somewhat larger for the additional years of data. The MSPE per year squared was again 

lower than the MSE per year squared of the original model, indicating a good fit to the 

additional years of data. 

Table 34. Validation Statistics for TOTACCI Type IV Model Using 

Additional Years of Data 

Measure 

Original Data 

1993-95 

Additional Years 

1996-97 

Number of sites 72 72 

Pearson product-moment 

correlation coefficients 

 

0.47 

 

0.53 

MPB -0.17 -0.53 

MPB/yr -0.06 -0.27 

MAD 3.00 2.11 

MAD/yr 1.00 1.05 

MSE 24.92 

MSE/yr2 2.77 

N/A1

MSPE 8.29 

MSPE/yr2 N/A1

2.07 1 N/A: not available 
41 

Injury Accident Model (INJACC) 

Because the original injury accident counts were not obtained, a comparison of prediction 

performance measures for the original data and additional years could not be 

accomplished. 

The parameter estimates, their standard errors, and p-values are given in table 35, which 

reveals that all of the variables were estimated with the same sign as the original model, 

but that the constant term and AADT1 were estimated with somewhat larger differences 

in magnitude than the other parameters. The overdispersion parameter was slightly lower 

than that for the original model. 

Table 35. Parameter Estimates for INJACC Type IV Model Using 

Additional Years of Data 

Variable Original Estimate (s.e., p-value)1 Additional Years Estimate (s.e., p-value) 

Constant -12.5296 -8.1672 

 (2.9908, 0.0001) (3.4344, 0.0295) 

Log of AADT1 0.9505 0.3825 

 (0.3284, 0.0038 ) (0.3630, 0.2920 ) 

Log of AADT2 0.3237 0.4074 

 (0.1645, 0.0491) (0.1793, 0.0231) 

PKLEFT1 0.0994 0.1050 

 (0.0433, 0.0216) (0.0557, 0.0594) 

SPD2 0.0339 0.0402 

 (0.0179, 0.0577) (0.0220, 0.0676) 

K2 0.4308 0.3720 1

 Vogt, 1999, (p. 118) 

2

 K: Overdispersion value 

Table 36 shows the GOF measures for the original injury accident model (Variant 1) in 

the Vogt report applied to the additional years data.(2) The Pearson product-moment 

correlation coefficient (0.48) was lower than that (0.58) for the TOTACC model. 

However, the MPB, MAD, and MSPE per year squared were smaller than those for 

TOTACC. 

Intersection Related Injury Accident Model (INJACCI) 

Since the original injury accident counts were not obtained, a comparison of prediction 

performance measures for the original data and additional years could not be 

accomplished. 

The parameter estimates, their standard errors, and p-values are given in table 37, which 

reveals that the constant term and all of the variables were estimated with the same 

direction of effect as that in the original model. However, the constant term and AADT1 

were estimated with somewhat larger differences in magnitude than the other parameters. 

The overdispersion parameter for the additional years was approximately half that of the 

original years. 
42 

Table 36. Validation Statistics for INJACC Type IV Model Using 

Additional Years of Data 

Measure 

Additional Years 

1996-97 

Number of sites 84 

Pearson product-moment correlation 

coefficients 

 

0.48 

MPB -0.33 

MPB/yr -0.16 

MAD 1.32 

MAD/yr 0.66 

MSPE 3.13 

MSPE/yr2 0.78 

Table 37. Parameter Estimates for INJACCI Type IV Model Using Additional 

Years of Data 

Variable Original Estimate (s.e., p-value)1 Additional Years Estimate (s.e., p-value) 

Constant -13.5576 -9.4112 

 (3.9998, 0.0008) (3.6620, 0.0173) 

Log of AADT1 0.9918 0.4707 

 (0.4268, 0.0201) (0.3896, 0.2270 ) 

Log of AADT2 0.3310 0.4536 

 (0.1894, 0.0805) (0.1868, 0.0152) 

PKLEFT1 0.1228 0.1077 

 (0.0614, 0.0457) (0.0613, 0.0791) 

SPD2 0.0429 0.0399 

 (0.0240, 0.0740) (0.0229, 0.0815) 

K2 0.7178 0.3873 1

 Vogt, 1999, p118

2

 K: Overdispersion value

Table 38 shows the GOF measures for the original intersection related injury accident 

model (Variant 1) in the Vogt report applied to the additional years data.(2) The Pearson 

product-moment correlation coefficient was the same as that for the TOTACCI model. 

However, the MPB, MAD, and MSPE per year squared were smaller than those for the 

TOTACCI model. 
43 

Table 38. Validation Statistics for INJACCI Type IV Model Using 

Additional Years of Data 

Measure 

Additional Years 

1996-97 

Number of sites 84 

Pearson product-moment correlation coefficients 0.53 

MPB -0.03 

MPB/yr -0.014 

MAD 1.25 

MAD/yr 0.62 

MSPE 2.80 

MSPE/yr2 0.70 

2.4.5 Model V 

The summary statistics shown in table 39 indicate that fewer accidents per year occurred 

during the additional years (1996–97) than during the original years (1993–95). Again, 

note that the original years INJACC and INJACCI data were not obtained. 

Table 39. Accident Summary Statistics of Type V Sites 

Dataset Mean Median Std. Deviation Minimum Maximum 

TOTACC (93-95)1

20.76 

(6.92/year) 21 11.66 2 48 

TOTACC (96-97) 

8.65 

(4.33/year) 7 6.58 0 27 

TOTACCI (93-95)1

16.12 

(5.37/year) 17 1.27 1 37 

TOTACCI (96-97) 

7.86 

(3.93/year) 6 0.82 0 23 

INJACC (96-97) 

3.16 

(1.58/year) 2 2.87 0 10 

INJACCI (96-97) 

2.80 

(1.40/year) 2 2.58 0 9 1 Vogt, 1999, (p. 61) 

Total Accident Models (TOTACC) 

The original report contained a main model and a variant, both of which were validated. 

Main Model

The parameter estimates, their standard errors, and p-values are given in table 40, which 

reveals varying degrees of differences in magnitude and significance for the parameters 

for additional years data compared to those of the original model. VEICOM was 

estimated with an opposite sign to that of the original model, but was not statistically 

significant in the recalibration. The constant term and PKLEFT2 also became 
44 

insignificant for the additional years of data. The overdispersion parameter was almost 

twice as large as for the original model. 

Table 40. Parameter Estimates for TOTACC Type V Model Using 

Additional Years of Data: Main Model 

Variable Original Estimate (s.e., p-value)1 Recalibrated Estimate (s.e., p-value) 

Constant -6.9536 -7.7450 

 (2.7911, 0.0132) (4.7450, 0.1152) 

Log of AADT1 0.6199 0.7625 

 (0.2504, 0.0133) (0.4489, 0.0894) 

Log of AADT2 0.3948 0.3221 

 (0.1737, 0.0133) (0.1857, 0.0830) 

PROT_LT -0.6754 -0.8238 

 (0.1824, 0.0002) (0.2688, 0.0022) 

PKLEFT2 -0.0142 -0.0115 

 (0.0047, 0.0023) (0.0098, 0.2392) 

VEICOM 0.1299 -0.0625 

 (0.045, 0.0039) (0.0688, 0.3635) 

PKTRUCK 0.0315 0.0262 

 (0.0143, 0.0275) (0.0154, 0.0874) 

K2 0.1161 0.2651 1 Vogt, 1999, (p. 122) 2 K: Overdispersion value

Table 41 shows a comparison of GOF measures between the original main models in the 

Vogt report applied to the original data and the 1996–97 data.(2) 

The Pearson product-moment correlation coefficient for the additional years of data was 

significantly lower than the original years. The MPB and MAD per year were larger for 

the additional years of data. The MSPE per year squared for the additional years of 

accident data was much higher than the MSE per year squared. 
45 

Table 41. Validation Statistics for TOTACC Type V Model Using 

Additional Years of Data: Main Model 

Measure 

Original Data 

1993-95 

Additional Years 

1996-97 

Number of sites 49 49 

Pearson product-moment correlation 

coefficients 

 

0.73 

 

0.40 

MPB -0.40 -5.45 

MPB/yr -0.13 -2.73 

MAD 6.53 6.83 

MAD/yr 2.18 3.42 

MSE 77.04 

MSE/yr2 8.56 

N/A1

MSPE 84.75 

MSPE/yr2 N/A1

21.19 1 N/A: not available 

Variant 1

The parameter estimates, their standard errors, and p-values are given in table 42. The 

constant term, PKLEFT2, VEICOM, PKTRUCK became insignificant for the additional 

years of data. VEICOM was estimated with an opposite sign to that for the original model, 

but it was not statistically significant in the recalibration. The overdispersion parameter 

was almost twice as large as for the original model. 

Table 42. Parameter Estimates for TOTACC Type V Model Using 

Additional Years of Data: Variant 1 

Variable Original Estimate (s.e., p-value)1 Recalibrated Estimate (s.e., p-value) 

Constant -6.1236 -6.0566 

 (2.5973, 0.0184) (3.3474, 0.1091) 

Log of 

AADT1*AADT2 0.4643 0.4546 

 (0.1483, 0.0017) (0.1940, 0.0191) 

PROT_LT -0.6110 -0.7273 

 (0.1507, 0.0001) (0.2546, 0.0043) 

PKLEFT2 -0.0134 -0.0100 

 (0.0048, 0.0052) (0.0102, 0.3249) 

VEICOM 0.1243 -0.0692 

 (0.0507, 0.0142) (0.0681, 0.3093) 

PKTRUCK 0.0300 0.0236 

 (0.0141, 0.0331) (0.0153, 0.1245) 

K2 0.1186 0.2801 1 Vogt, 1999, (p. 122) 2 K: Overdispersion value 

Table 43 shows the GOF measures for the original accident model (Variant 1) in the Vogt 

report and the model applied to the additional years of data.(2) The Pearson product-
46 

moment correlation coefficient for the additional years of data was significantly lower 

than for the original years. The MPB and MAD per year were larger for the additional 

years of data. The MSPE per year squared was also higher than the MSE per year squared. 

Table 43. Validation Statistics for TOTACC Type V Model Using 

Additional Years of Data: Variant 1 

Measure 

Original Data 

1993-95 

Additional Years 

1996-97 

Number of sites 49 49 

Pearson product-moment 

correlation coefficients 

 

0.73 

 

0.39 

MPB -0.37 -5.43 

MPB/yr -0.12 -2.72 

MAD 6.48 6.84 

MAD/yr 2.16 3.42 

MSE 73.31 

MSE/yr2 8.15 

N/A1

MSPE 83.70 

MSPE/yr2 N/A1

20.93 1 N/A: not available 

Intersection Related Total Accident Model (TOTACCI) 

The main model and one variant were validated. Since the base model in the accident 

prediction algorithm is identical to Variant 3 of the Vogt model for TOTACCI, the 

Variant 3 model was also validated. 

Main Model

The parameter estimates, their standard errors, and p-values are given in table 44, which 

again reveals differences in magnitude and significance in the parameter estimates. The 

constant term, PKLEFT2, and VEICOM became insignificant for the additional years of 

data, while VEICOM was estimated with an opposite sign to that of the original model, 

but was not statistically significant in the recalibration. The overdispersion parameter was 

almost twice as large as for the original model. 

Table 45 shows a comparison of GOF measures between the original main model in the 

Vogt report for the original data and the original model applied to the 1996–97 data.(2)

The Pearson product-moment correlation coefficient for the additional years of data was 

significantly lower than for the original years. The MPB and MAD per year were larger 

for the additional years of data. The MSPE per yearsquared with the additional years of 

accident data was also higher than the MSE per year squared. 
47 

Table 44. Parameter Estimates for TOTACCI Type V Model Using 

Additional Years of Data: Main Model 

Variable Original Estimate (s.e., p-value)1 Recalibrated Estimate (s.e., p-value) 

Constant -6.0841 -7.3834 

 (3.3865, 0.0724) (4.2640, 0.1166) 

Log of AADT1 0.5951 0.7249 

 (0.2847, 0.0366) (0.4332, 0.0943) 

Log of AADT2 0.2935 0.3110 

 (0.1972, 0.1366) (0.1893, 0.1004) 

PROT_LT -0.4708 -0.7381 

 (0.2000, 0.0186) (0.2702, 0.0063) 

PKLEFT2 -0.0165 -0.0116 

 (0.0057, 0.0036) (0.0095, 0.2254) 

VEICOM 0.1126 -0.0740 

 (0.0365, 0.0020) (0.0685, 0.2799) 

PKTRUCK 0.0289 0.0233 

 (0.0131, 0.0276) (0.0139, 0.0937) 

K2 0.1313 0.2433 1 Vogt, 1999, p123 2 K: Overdispersion value

Table 45. Validation Statistics for TOTACCI Type V Model Using 

Additional Years of Data: Main Model 

Measure 

Original Data 

1993-95 

Additional Years 

1996-97 

Number of sites 49 49 

Pearson product-moment 

correlation coefficients 

 

0.62 

 

0.37 

MPB -0.28 -3.08 

MPB/yr -0.09 -1.54 

MAD 5.63 4.95 

MAD/yr 1.88 2.47 

MSE 58.24 

MSE/yr2 6.47 

N/A1

MSPE 44.17 

MSPE/yr2 N/A1

11.04 1 N/A: not available 

Variant 3

The parameter estimates, their standard errors, and p-values are given in table 46, which 

reveals that most of the variables showed some differences in magnitude and significance 

for the additional years. VEICOM and DRWY1 were estimated with an opposite sign to 

those for the original model, but they were not statistically significant for the recalibrated 

model. AADT2 and PKLEFT2 also became insignificant for the additional years. The 

overdispersion parameter was almost twice as large as for the original model. 
48 

Table 46. Parameter Estimates for TOTACCI Type V Model Using 

Additional Years of Data: Variant 3 

Variable Original Estimate (s.e., p-value)1 Recalibrated Estimate (s.e., p-value) 

Constant -5.4581 -7.8110 

 (3.1937, 0.0874) (4.3760, 0.1038) 

Log of AADT1 0.5995 0.7354 

 (0.2795, 0.0319) (0.4443, 0.0909) 

Log of AADT2 0.2015 0.3553 

 (0.1917, 0.2932) (0.2235, 0.1118) 

PROT_LT -0.4041 -0.7622 

 (0.1883, 0.0319) (0.2802, 0.0065) 

PKLEFT2 -0.0177 -0.0112 

 (0.0050, 0.0005) (0.0098, 0.2527) 

VEICOM 0.1114 -0.0705 

 (0.0326, 0.0006) (0.0685, 0.3031) 

PKTRUCK 0.0256 0.0247 

 (0.0117, 0.0287) (0.0144, 0.0873) 

DRWY1 0.0407 -0.0178 

(0.0246, 0.0983) (0.0463, 0.7009) 

K2 0.1145 0.2412 1

 Vogt, 1999, p123

2

 K: Overdispersion value 

A comparison of GOF measures is given in table 47, which reveals that the Pearson 

product-moment correlation coefficient for the additional years of data, is significantly 

lower than that for the original years. The MPB and MAD per year were larger for the 

models based on additional years of data. The MSPE per year squared with the additional 

years data was almost twice as high as the MSE per year squared, suggesting a general 

lack-of-fit to the additional years of data. 

Injury Accident Model (INJACC) 

The parameter estimates, their standard errors, and p-values are given in table 48, which 

reveals that the variables AADT1*AADT2 and PKLEFT2 were estimated with a similar 

degree of magnitude and significance as the original model, but that the other variables 

showed larger differences in magnitude or significance. VEICOM was estimated with an 

opposite sign to that for the original years, and PKTRUCK became statistically 

insignificant, while PRO_LT turned out to be significant in the recalibration. The 

overdispersion parameter for the additional years was higher than that for the original 

years. 
49 

Table 47. Validation Statistics for TOTACCI Type V Model Using 

Additional Years of Data: Variant 3 

Measure 

Original Data 

1993-95 

Additional Years 

1996-97 

Number of sites 49 49 

Pearson product-moment 

correlation coefficients 

 

0.67 

 

0.36 

MPB -0.31 -3.10 

MPB/yr -0.10 -1.55 

MAD 5.34 5.23 

MAD/yr 1.78 2.62 

MSE 51.57 

MSE/yr2 5.73 

N/A1

MSPE 45.75 

MSPE/yr2 N/A1

11.44 1 N/A: not available 

Table 48. Parameter Estimates for INJACC Type V Model Using 

Additional Years of Data 

Variable Original Estimate (s.e., p-value)1 Recalibrated Estimate (s.e., p-value) 

Constant -3.2562 -4.4380 

 (2.9932, 0.2767) (3.1219, 0.2303) 

Log of 

AADT1*AADT2 0.2358 0.3093 

 (0.1722, 0.1707) (0.1760, 0.0789) 

PROT_LT -0.2943 -0.4734 

 (0.1864, 0.1144) (0.2419, 0.0504) 

PKLEFT2 -0.0113 -0.0203 

 (0.0062, 0.0678) (0.0101, 0.0443) 

VEICOM 0.0822 -0.0642 

 (0.0551, 0.1358) (0.0748, 0.3907) 

PKTRUCK 0.0323 0.0319 

 (0.0146, 0.0267) (0.0217, 0.1408) 

K2 0.1630 0.2124 1 Vogt, 1999, p124 2 K: Overdispersion value 

Table 49 shows the GOF measures for the original injury accident model (Variant 1) in 

the Vogt report applied to the additional years of data.(2)

The Pearson product-moment correlation coefficient was similar to that for the TOTACC 

model. However, the MPB, MAD, and MSPE per year squared were significantly smaller 

than those for the TOTACC model. 
50 

Table 49. Validation Statistics for INJACC Type V Model Using 

Additional Years of Data 

Measure 

Additional Years 

1996-97 

Number of sites 49 

Pearson product-moment correlation coefficients 0.41 

MPB -1.84 

MPB/yr -0.92 

MAD 2.79 

MAD/yr 1.39 

MSPE 10.66 

MSPE/yr2 2.67 

Intersection Related Total Injury Accident Model (INJACCI) 

The parameter estimates, their standard errors, and p-values are given in table 50, which 

reveals that all of the variables were insignificant for the additional years. VEICOM was 

estimated with an opposite sign for the recalibration. The overdispersion parameter for 

the additional years of data was over twice as large as for the original years. 

Table 50. Parameter Estimates for INJACCI Type V Model Using Additional Years 

of Data 

Variable Original Estimate (s.e., p-value)1 Recalibrated Estimate (s.e., p-value) 

Constant -1.5475 -2.5686 

 (3.0298, 0.6095) (3.5706, 0.5994) 

Log of 

AADT1*AADT2 0.1290 0.1849 

 (0.1757, 0.4627) (0.2000, 0.3554) 

PKLEFT2 -0.0149 -0.0183 

 (0.0066, 0.0250) (0.0116, 0.1164) 

VEICOM 0.0686 -0.0548 

 (0.0692, 0.1858) (0.0827, 0.5075) 

PKTRUCK 0.0282 0.0255 

 (0.0152, 0.0628) (0.0261, 0.3280) 

K2 0.1433 0.3496 1 Vogt, 1999, (p. 124) 2 K: Overdispersion value 

Table 51 shows the GOF measures for the original intersection related injury accident 

model (Variant 1) in the Vogt report applied to the additional years of data.(2) The 

Pearson product-moment correlation coefficient was similar to that for the TOTACCI 

model. However, the MPB, MAD, and MSPE per year squared were smaller than those 

for the TOTACCI model. 
51 

Table 51. Validation Statistics for INJACCI Type V Model Using 

Additional Years of Data 

Measure 

Additional Years 

1996-97 

Number of sites 49 

Pearson product-moment correlation coefficients 0.39 

MPB -0.95 

MPB/yr -0.47 

MAD 2.45 

MAD/yr 1.23 

MSPE 7.96 

MSPE/yr2 1.99 

2.5 VALIDATION ACTIVITY 2: VALIDATION WITH GEORGIA 

DATA 

For this validation activity, the models were used to predict accidents for the Georgia 

data that also were used to re-estimate the models. Data from 1996 and 1997 in Georgia 

were used for accident related variables; Other variables used, such as roadway 

geometrics and traffic volumes, were based on the 1997 road characteristic files 

maintained by the Georgia Department of Transportation and on data collected in the 

field during the summer of 2001. Recall that for Georgia data, two sets of accidents were 

extracted—those within 0.08 km (0.05 miles) of the intersection and those within 0.06 

km (0.04 miles). 

2.5.1 Model I 

The summary statistics in the original report and for the Georgia data are given in table 

52. The summary statistics reveal that Georgia sample had more accidents per year than 

the original Minnesota data. This difference in underlying safety may be explained by the 

fact that Georgia sites, for example, had, on average, higher values for the variables 

related to horizontal curvature, vertical curvature and roadside hazard rating, all of which 

increase accident risk according to indications from the original model. 

Total Accident Model 

The model was recalibrated with both sets of the Georgia accident data. The parameter 

estimates, their standard errors, and p-values are provided in table 53, which reveals 

differences in the parameter estimates between the two States. 

HAZRAT1 was estimated with a similar degree of magnitude and significance as the 

original model. The constant term, AADT1, AADT2, VCI1, and SPD1 were estimated 

with the same sign but a larger difference in magnitude. HI1, HAU, and RT (for the 0.04 

mile limit) were estimated with opposite signs and large differences in magnitude. The 

overdispersion parameter, K, was much smaller for the Georgia data. 
52 

Table 54 shows a comparison of validation measures between the original data and the 

Georgia data. The Pearson product-moment correlation coefficient was much higher for 

the original data as compared to Georgia. The MPB and mean absolute deviations are 

also higher than for the original Minnesota data. On a per year squared basis the mean 

squared prediction errors are much higher than the MSE indicating that the model is not 

performing well on the Georgia data. 

Table 52. Summary of Georgia versus Minnesota Data for Type I Sites 

Variable and Abbreviation N Mean Median Minimum Maximum Freq. % 

Zero 

Original Data 

Total 

389 1.35 

(0.27/year) 

0.00 0 39 524 51.9 

Original Data 

Injury 

389 0.59 

(0.12/year) 

0.00 0 17 229 69.9 

Georgia Total 

(0.04 MI) 

121 1.45 

(0.73/year) 

1.00 0 7 176 33.1 

Georgia Total 

(0.05 MI) 

121 1.55 

(0.78/year) 

1.00 0 7 187 30.6 

Georgia Injury 

(0.04 MI) 

121 0.595 

(0.30/year) 

0.00 0 4 72 61.2 

No. of 

Crashes 

Georgia Injury 

(0.05 MI) 

121 0.644 

(0.32/year) 

0.00 0 4 78 60.3 

Original Data 389 1.21 0.00 0 29 N/A1 HI1 54.0 

Georgia 121 2.53 0.64 0.00 23.00 N/A1 N/A1

Original Data 389 0.12 0.00 0 4 N/A1 VCI1 53.2 

Georgia 121 1.31 0.88 0.00 14.00 N/A1 N/A1

Original Data 389 52.75 55 23 55 N/A1 N/A1 SPD1 

Georgia 121 47.11 45 25 55 N/A1 N/A1

Original Data 389 2.11 2.00 1.0 5.0 N/A1 N/A1 HAZRAT1 

Georgia 121 3.57 3.50 1.5 7.0 N/A1 N/A1

Original Data 389 1.26 1.00 0 9 N/A1 DRWY1 37.5 

Georgia 121 2.13 2.00 0 8 N/A1 27.3 

RT MAJ Original Data 389 224 (57.6%) without RT MAJ, 165 (42.4%) with RT MAJ 

Georgia 121 117 (96.7%) without RT MAJ, 4 (3.3%) with RT MAJ 

Original Data 389 -0.515 0 -90 85 N/A1 HAU 50.6 

Georgia 121 -3.09 0 -65 60 N/A1 N/A1

Original Data 389 3687 2313 201 19413 N/A1 N/A1 AADT1 on 

Major Road Georgia 121 3565 3000 420 16900 N/A1 N/A1

Original Data 389 413 240 4.53 4206 N/A1 N/A1 AADT2 on 

Minor Road Georgia 121 616 430 70 6480 N/A1 N/A1

1 N/A: not available 
53 

Table 53. Parameter Estimates for Type I Total Accident Model Using Georgia Data 

Variable 

Original Estimate1

(s.e., p-value) 

Georgia Data 0.04 Mile 

(s.e., p-value) 

Georgia Data 0.05 Mile 

(s.e., p-value) 

-12.9922 -6.99 -6.84 

Constant (1.1511, 0.0001) (1.17, <0.001) (1.14, <0.001) 

0.8052 0.484 0.497 

Log of AADT1 (0.0639, 0.0001) (0.111, <0.001) (0.108, <0.001) 

0.5037 0.272 0.239 

Log of AADT2 (0.0708, 0.0001) (0.130, 0.036) (0.127, 0.060) 

0.0339 -0.0223 -0.0209 

HI1 (0.0327, 0.3004) (0.0281, 0.427) (0.0273, 0.443) 

0.2901 0.0413 0.0294 

VCI1 (0.2935, 0.3229) (0.0480, 0.389) (0.0477, 0.537) 

0.0285 0.00995 0.00686 

SPD1 (0.0177, 0.1072) (0.00947, 0.293) (0.00894, 0.443) 

0.1726 0.1642 0.2048 

HAZRAT1 (0.0677, 0.0108) (0.0914, 0.072) (0.0890, 0.021) 

0.2671 -0.283 0.158 

RT MAJ (0.1398, 0.0561) (0.580, 0.625) (0.490, 0.748) 

0.0045 -0.00455 -0.00546 

HAU (0.0032, 0.1578) (0.00326, 0.163) (0.00320, 0.088) 

K2 0.481 0.192 0.185 1 Vogt and Bared, 1998, (p. 115) 

2 K: Overdispersion value 

Table 54. Validation Statistics for Type I Total Accident Model Using Georgia Data 

Measure Original Data 

Georgia Data 

0.04 Mile 

Georgia Data 

0.05 Mile 

Years used for the validation 1985 to 1989 1996 to 1997 1996 to 1997 

Number of sites 389 121 121 

Pearson product-moment 

correlation coefficients 0.66 0.32 0.31 

MPB -0.01 0.47 0.56 

MPB/yr 0.00 0.23 0.28 

MAD 1.03 1.21 1.28 

MAD/yr 0.21 0.60 0.64 

MSE 4.64 

MSE/yr2 0.19 

N/A1

 N/A1

MSPE 3.15 3.55 

MSPE/yr2 N/A1

0.79 0.89 1 N/A: not available 

Figure 1 depicts the prediction performance of the original model for individual sites in 

the Georgia 0.05-mile data. It is quite evident that the original model failed to account for 

higher accident frequencies in most sites in the Georgia data. 
54 

Figure 1. Observed versus Predicted Accident Frequency: Total Accidents Type I 

Injury Model 

The injury model was recalibrated with both sets of the Georgia accident data. The 

parameter estimates, their standard errors, and p-values are provided in table 55, which 

reveals differences in the parameter estimates of the variables between the two States. 

HI1, RT MAJ, HAU, and SPD1 (for the 0.05-mile buffer only) were estimated with the 

opposite sign. Aside from the AADT variables, none of the variables were estimated with 

satisfactory significance for the Georgia data. Perhaps this should not be surprising given 

that only two years of accident data were available and injury accidents are relatively few 

compared to total accidents. The overdispersion parameter, K, was estimated to be 

approximately one half of that for the original model. 

0

1

2

3

4

5

6

7

8

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121

Sites

No. of Accidents

Predicted

Accidents

Observed

A id t
55 

Table 55. Parameter Estimates for Type I lnjury Accident Model 

Using Georgia Data 

Variable 

Original Estimate1 

(s.e., p-value) 

Georgia Data 0.04 Mile 

(s.e., p-value) 

Georgia Data 0.05 Mile 

(s.e., p-value) 

-13.0374 -7.56 -7.60 

Constant (1.7908, 0.0001) (2.00, < 0.001) (1.94, < 0.001) 

0.8122 0.611 0.699 

Log of AADT1 (0.0973, 0.0001) (0.174,< 0.001) (0.171,< 0.001) 

0.4551 0.149 0.098 

Log of AADT2 (0.0977, 0.0001) (0.193, 0.439) (0.186, 0.599) 

0.0335 -0.0091 -0.0102 

HI1 (0.0327, 0.3047) (0.0418, 0.828) (0.0414, 0.806) 

0.1869 0.0233 0.0061 

VCI1 (0.3657, 0.6092) (0.0790, 0.768) (0.0778, 0.937) 

0.0156 0.0048 -0.0039 

SPD1 (0.0269, 0.5618) (0.0244, 0.842) (0.0233, 0.869) 

0.2065 0.101 0.147 

HAZRAT1 (0.0930, 0.0263) (0.138, 0.464) (0.133, 0.269) 

0.3620 -0.81 -0.087 

RT MAJ (0.1814, 0.0460) (1.07, 0.450) (0.788, 0.913) 

0.0051 -0.00189 -0.00354 

HAU (0.0045, 0.2594) (0.00492, 0.701) (0.00478, 0.459) 

-0.0120 -0.0413 -0.0632 

DRWY1 (0.0714, 0.8671) (0.0714, 0.563) (0.0694, 0.362) 

K2 0.494 0.299 0.270 1 Vogt and Bared, 1998, (p. 116) 

2 K: Overdispersion value

The validation measures for the Georgia data is shown in table 56. The Pearson productmoment correlation coefficients were quite low while the MAD was roughly half that for 

total accidents. 

Figure 2 depicts the prediction performance of the original model for individual sites in 

the Georgia 0.05-mile data. It is quite evident that the original model failed to account for 

higher accident frequencies in most sites in the Georgia data. 
56 

Table 56. Validation Statistics for Type I Injury Accident Model 

Using Georgia Data 

Measure 

Georgia Data 

0.04 Mile 

Georgia Data 

0.05 Mile 

Years used for validation 1996 to 1997 1996 to 1997 

Number of sites 116 116 

Pearson product-moment correlation coefficients 0.23 0.25 

MPB 0.24 0.29 

MPB/yr 0.12 0.14 

MAD 0.61 0.66 

MAD/yr 0.31 0.33 

MSPE 0.88 1.03 

MSPE/yr2 0.22 0.26 

Figure 2. Observed versus Predicted Accident Frequency: Injury Accidents Type I 

2.5.2 Model II 

The summary statistics in the original report and Georgia data are given provided in table 

57. The summary statistics again reveal that the Georgia sample had more accidents per 

year than the original data. 

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121

Sites

No. of Accidents

Predicted Accidents

Observed Accidents
57 

Table 57. Summary of Georgia versus Minnesota Data for Type II Sites 

Variable and Abbreviation N Mean Median Minimum Maximum Freq. % 

Zero 

Original Data 

Total 

327 1.51 

(0.30/year) 

1.00 0 16 494 39.8 

Original Data 

Injury 

327 0.77 

(0.15/year) 

0.00 0 9 253 59.9 

Georgia Total 

(0.04 MI) 

114 2.25 

(1.13/year) 

1.00 0 12 256 29.8 

Georgia Injury 

(0.04 MI) 

114 0.98 

(0.49/year) 

0.00 0 7 112 55.3 

Georgia Total 

(0.05 Mile) 

114 2.26 

(1.13/year) 

1.00 0 12 258 28.9 

No. of 

Crashes 

Georgia Injury 

(0.05 Mile) 

114 0.98 

(0.49/year) 

0.00 0 7 112 55.3 

Original Data 327 0.49 0.00 0 9 N/A1 59.9 HI1 Georgia 114 1.66 0.25 0.00 14.55 N/A1 50.0 

Original Data 327 0.13 0.02 0 2 N/A1 48.0 VCI1 Georgia 114 1.09 0.89 0.00 7.50 N/A1 45.6 

Original Data 327 53.97 55 30 55 N/A1 N/A1

SPD1 Georgia 114 48.31 47.50 30 55 N/A1 N/A1

Original Data 327 0.62 0.00 0 6 204 67.6 DRWY1 Georgia 114 1.19 1.00 0 6 136 40.4 

Original Data 327 -0.03 0 -120 150 N/A1 37.9 HAU Georgia 114 0.27 0.00 -58 50 N/A1 3.5 

Original Data 327 2238 1742 174 14611 N/A1 N/A1 AADT1 on 

Major Road Georgia 114 3073 2000 420 12300 N/A1 N/A1

Original Data 327 308 192 7 3414 N/A1 N/A1 AADT2 on 

Minor Road Georgia 114 614 430 80 7460 N/A1 N/A1

 1 N/A: not available 

Total Accident Model 

The model was recalibrated with both sets of the Georgia accident data. The parameter 

estimates, their standard errors, and p-values are provided in table 58, which reveals 

differences in the parameter estimates of the variables between the two States. 

The variables HI1, VCI1, and SPD1 were estimated with opposite signs while HAU was 

estimated to have no effect on safety for the Georgia data. The constant term and the 

other variables were estimated with the same sign but with varying differences in 

magnitude and significance. The overdispersion parameter, K, was estimated to be more 

than twice as large that of the original model. 
58 

Table 58. Parameter Estimates for Type II Total Accident Model 

Using Georgia Data 

Variable 

Original Estimate1 

(s.e., p-value) 

Georgia Data 0.04 Mile 

(s.e., p-value) 

Georgia Data 0.05 Mile 

(s.e., p-value) 

-10.4260 -7.26 -7.21 

Constant (1.3167, 0.0001) (1.32, <0.001) (1.32, <0.001) 

0.6026 0.627 0.627 

Log of AADT1 (0.0836, 0.0001) (0.134, <0.001) (0.133, <0.001) 

0.6091 0.500 0.493 

Log of AADT2 (0.0694, 0.0001) (0.154, 0.001) (0.154, 0.001) 

0.0449 -0.0158 -0.0165 

HI1 (0.0473, 0.3431) (0.0403, 0.695) (0.0402, 0.681) 

0.2885 -0.0606 -0.0438 

VCI1 (0.2576, 0.2628) (0.0794, 0.445) (0.0781, 0.575) 

0.0187 -0.0172 -0.0177 

SPD1 (0.0176, 0.2875) (0.0104, 0.097) (0.0104, 0.087) 

0.1235 0.0927 0.0940 

NODRWYS (0.0519, 0.0173) (0.0710, 0.192) (0.0707, 0.184) 

-0.0049 -0.00038 0.00000 

HAU (0.0033, 0.1341) (0.00450, 0.932) (0.00448, 1.000) 

K2 0.205 0.455 0.455 1 Vogt and Bared, 1998, (p. 115) 

2 K: Overdispersion value 

Table 59 shows a comparison of validation measures between the original data and the 

Georgia data. The Pearson product-moment correlation coefficient was much higher for 

the original data as compared to Georgia. The MPBs and MADs are also higher than for 

the original Minnesota data. The MSPEs are much higher than the MSE, indicating that 

the model is not performing well on the Georgia data. 

Figure 3 depicts the prediction performance of the original model for individual sites in 

the Georgia 0.05-mile data. It is quite evident that the original model failed to account for 

higher accident frequencies in most sites in the Georgia data. 
59 

Table 59. Validation Statistics for Type II Total Accident Model Using Georgia Data 

Measure Original Data 

Georgia Data 

0.04 Mile 

Georgia Data 

0.05 Mile 

Number of years 1985 to 1989 1996 to 1997 1996 to 1997 

Number of sites 327 114 114 

Pearson product-moment correlation coefficients 0.77 0.39 0.39 

MPB 0.004 0.70 0.72 

MPB/yr 0.00 0.35 0.36 

MAD 1.01 1.82 1.82 

MAD/yr 0.20 0.91 0.91 

MSE 2.38 

MSE/yr2 0.10 

N/A1

 N/A1

MSPE 6.94 6.94 

MSPE/yr2 N/A1

1.73 1.73 1 N/A: not available 

Figure 3. Observed versus Predicted Accident Frequency: Total Accidents Type II 

0

2

4

6

8

10

12

14

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113

Sites

No. of Accidents

Predicted Accidents

Observed Accidents
60 

Injury Accident Model 

The parameter estimates, their standard errors, and p-values are provided in table 60, 

which reveals that the variables HI1, VCI1, SPD1, HAZRAT1, and HAU were estimated 

with the opposite signs. With the exception of the AADT variables none were estimated 

to be highly significant statistically. Only one Georgia model is shown since, as indicated 

in table 57, the observed number of accidents at each of the Type II sites was equal for 

the 0.04- and 0.05-mile buffers. The overdispersion parameter, K, was estimated to be 

over twice that of the original model. 

Table 60. Parameter Estimates for Type II Injury Accident Model 

Using Georgia Data 

Variable Original Estimate (s.e., p-value)1 Georgia Data (s.e., p-value) 

Constant 

-10.7829 

(1.7656, 0.0001) 

-10.85 

(2.01, <0.001) 

Log of AADT1 

0.6339 

(0.1055, 0.0001) 

0.702 

(0.181, <0.001) 

Log of AADT2 

0.6229 

(0.0870, 0.0001) 

0.869 

(0.180, <0.001) 

HI1 

0.0729 

(0.0635, 0.2513) 

-0.0096 

(0.0529, 0.856) 

VCI1 

0.2789 

(0.4623, 0.5464) 

-0.094 

(0.111, 0.397) 

SPD1 

0.0112 

(0.0251, 0.6567) 

-0.0224 

(0.0205, 0.274) 

HAZRAT1 

-0.1225 

(0.0720, 0.0889) 

0.039 

(0.130, 0.766) 

RT MAJ 

0.0451 

(0.1665, 0.7865) 

0.070 

(0.660, 0.915) 

HAU 

-0.0043 

(0.0044, 0.3258) 

0.00603 

(0.00631, 0.339) 

DRWY1 

0.0857 

(0.0639, 0.1799) 

0.0114 

(0.0988, 0.908) 

K2 0.1811 0.392 

1 Vogt and Bared, 1998, (p. 115) 2 K: Overdispersion value 

The validation measures for the Georgia data are shown in table 61. The Pearson productmoment correlation coefficients were higher than for total accidents but still quite low. 

The MAD was roughly half that for total accidents. 

Figure 4 depicts the prediction performance of the original model for individual sites in 

the Georgia 0.05-mile data. It is quite evident that the original model failed to account for 

higher accident frequencies in most sites in the Georgia data. 
61 

Table 61. Validation Statistics for Type II Injury Accident Model 

Using Georgia Data 

Measure 

Georgia Data 

0.04 Mile 

Georgia Data 

0.05 Mile 

Years used for validation 1996 to 1997 1996 to 1997 

Number of sites 114 114 

Pearson product-moment correlation coefficients 0.44 0.44 

MPB 0.33 0.33 

MPB/yr 0.17 0.17 

MAD 0.95 0.95 

MAD/yr 0.48 0.48 

MSE 

MSE/yr2 N/A1

 N/A1

MSPE 2.00 2.00 

MSPE/yr2 0.50 0.50 1 N/A: not available 

Figure 4. Observed versus Predicted Accident Frequency: Injury Accidents Type II 

2.5.3 Model III 

The summary statistics in the original report and Georgia data are given in table 62, 

which reveals that the Georgia sample had on average fewer accidents per year than the 

0

1

2

3

4

5

6

7

8

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113

Sites

No. of Accidents

Predicted Accidents

Observed Accidents
62 

original data. This implies that either the Georgia sites were relatively more safe than the 

sites selected for the original model, or that the passage of time between the period for 

the original calibration (1993–95) and that for the validation data (1996–97) had resulted 

in an overall improvement in safety (due to many factors including improved roadway 

design, improved vehicles, emergency response services, etc.). The Georgia sites may 

also be safer because they have, on average, wider medians on major roads and fewer 

numbers of driveways than the original intersections. In addition, more than 50 percent of 

the sites in the original data had no median, while only 5 percent of sites in Georgia were 

without a median. 

Table 62. Summary Statistics of Georgia Data: Type III Sites 

Variable and Abbreviation N Mean Median Minimum Maximum Freq. % Zero 

Original 

Data 84 3.88 2 0 19 326 21.4 

Georgia 

(0.05 Mile) 52 2.4 1.5 0 12 124 21.2 

No. of Crashes 

(TOTACC) 

 Georgia 

(0.04 Mile) 52 2.2 1 0 12 116 25.0 

Original 

Data 84 2.62 1 0 13 135 34.5 

Georgia 

(0.05 Mile) 52 1.6 1 0 11 85 32.7 

Georgia 

(0.04 Mile) 52 1.5 1 0 11 80 36.5 

Georgia 

(0.05 Mile) 52 1.08 1 0 8 56 44.2 

Georgia 

(0.04 Mile) 52 1.02 1 0 8 53 48.1 

Georgia 

(0.05 Mile) 52 0.81 0 0 8 42 57.7 

No. of 

IntersectionType Crashes 

(TOTACCI) 

 

Georgia 

(0.04 Mile) 52 0.77 0 0 8 40 61.5 

Original 

Data 84 3.74 0 0 36 N/A1 53.6 

Median Width 

on Major Road 

(MEDWIDTH1) Georgia 52 27.0 20 0 63 N/A1 5.8 

Original 

Data 84 3.1 1 0 15 259 42.9 

No. of 

Driveways on 

Major Road 

(DRWY1) Georgia 52 1.5 1 0 9 77 42.3 

Original 

Data 84 12870 12050 2367 33058 N/A1 N/A

AADT1 on 1

Major Road 

 Georgia 52 13100 12200 6500 28600 N/A1 N/A1

Original 

Data 84 596 349 15 3001 N/A1 N/A

AADT2 on 1

Minor Road 

 Georgia 52 892 430 80 9490 N/A1 N/A1

1 N/A: not available 

Total Accident Models (TOTACC) 

The model was recalibrated using the Georgia data. The parameter estimates, their 

standard errors, and p-values are shown in table 63, which reveals that the constant term, 
63 

AADT1 and AADT2, were estimated with the same sign but with large differences in 

magnitude. MEDWDTH2 and DRWY1 were estimated with an opposite sign, although 

they were not statistically significant. AADT1 was also estimated as insignificant. The 

overdispersion parameters were lower than that for the original model, but the difference 

was not great. 

Table 63. Parameter Estimates for TOTACC Type III Model Using Georgia Data 

Variable 

Original Estimate1

 

(s.e., p-value) 

Georgia Data 0.04 Mile 

(s.e, p-value) 

Georgia Data 0.05 Mile 

(s.e., p-value) 

-12.2196 -8.690 -8.857 

Constant (2.3575, 0.0001) (4.945, 0.1059) (4.585, 0.0750) 

1.1479 0.536 0.580 

Log of AADT1 (0.2527, 0.0001) (0.459, 0.2434) (0.426, 0.1737) 

0.2624 0.551 0.536 

Log of AADT2 (0.0866, 0.0024) (0.179, 0.0021) (0.163, 0.0010) 

-0.0546 0.004 0.0002 

MEDWIDTH1 (0.0249, 0.0285) (0.013, 0.7748) (0.012, 0.9894) 

0.0391 -0.009 0.011 

DRWY1 (0.0239, 0.1023) (0.088, 0.9156) (0.094, 0.9101) 

K2 0.3893 0.374 0.300 1

 Vogt, 1999, (p. 111) 

2 K: Overdispersion value 

Table 64 shows the prediction performance statistics for Model III for TOTACC. Low 

Pearson product-moment correlation coefficients with the Georgia data indicate that the 

accident predictions by the original model are marginally correlated with the observed 

number of accidents in the Georgia data. Other validation statistics also suggest a poor fit 

of the original model to the Georgia data. The MPB and MAD per year were larger than 

those for the original model. The MSPE per year squared was almost twice as high as the 

MSE per year squared. 

Figure 5 depicts the prediction performance of the original model for individual sites in 

the Georgia 0.05-mile data. It is quite evident that the original model does not do a good 

job of predicting accidents at the Georgia intersections; this finding was expected on the 

basis of the low Pearson product-moment coefficients for the Georgia data. 
64 

Table 64. Validation Statistics for TOTACC Type III Model Using Georgia Data 

Georgia Data Measure Original Data 

0.04 Mile 0.05 Mile 

Years used for validation 1993 to 1995 1996 to 1997 1996 to 1997 

Number of sites 84 52 52 

Pearson product-moment 

correlation coefficients 

 

0.66 

 

0.03 

 

0.09 

MPB -0.01 -1.34 -1.49 

MPB/yr 0.00 -0.45 -0.50 

MAD 2.26 5.93 6.14 

MAD/yr 0.75 1.98 2.05 

MSE 11.01 

MSE/yr2 1.22 

N/A1

 N/A1

MSPE 9.36 9.64 

MSPE/yr2

N/A1

2.34 2.41 1 N/A: not available 

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Sites

No. of Accidents

Predicted Accidents

Observed Accidents

Figure 5. Observed versus Predicted Accident Frequency: TOTACC Type III 
65 

Intersection Related Total Accident Model (TOTACCI) 

The parameter estimates, their standard errors, and p-values are given in table 65. Similar 

to the model of TOTACC, the variables AADT1, MEDWITH1, and DRWY1 were 

estimated as statistically insignificant. The constant term and AADT1, AADT2, and 

DRWY1 were estimated with the same direction of effect but with large differences in 

magnitude. The overdispersion parameters, K, were lower than that for the original model. 

Table 65. Parameter Estimates for TOTACCI Type III Model Using Georgia Data 

Variable 

Original Estimate1

(s.e., p-value) 

Georgia Data 0.04 Mile 

(s.e, p-value) 

Georgia Data 0.05 Mile 

(s.e., p-value) 

-15.4661 -7.774 -8.163 

Constant (3.4685, 0.0001) (4.511, 0.1165) (4.097, 0.0683) 

1.4331 0.232 0.301 

Log of AADT1 (0.3608, 0.0001) (0.366, 0.5264) (0.339, 0.3747) 

0.2686 0.764 0.740 

Log of AADT2 (0.0988, 0.0065) (0.262, 0.0035) (0.229, 0.0012) 

-0.0612 0.004 0.002 

MEDWIDTH1 (0.0360, 0.0888) (0.013, 0.7719) (0.012, 0.8682) 

0.0560 0.090 0.095 

DRWY1 (0.0289, 0.0525) (0.133, 0.4980) (0.126, 0.4504) 

K2 0.5118 0.352 0.272 1 Vogt, 1999, (p. 112) 2 K: Overdispersion value 

Table 66 shows the GOF statistics for Model III for TOTACCI. Low Pearson productmoment correlation coefficients with the Georgia data indicate that the accident 

predictions by the original model are marginally correlated with the observed number of 

accidents in the Georgia data. Other validation statistics also suggest lack-of-fit to the 

Georgia data. The MPB and MAD per year were larger than those for the original model. 

The MSPE per year squared was almost twice as high as the MSE per year squared, 

indicating a general lack-of-fit to the Georgia data. 

A plot of the predicted versus actual accidents using Georgia data will help to understand 

prediction performances of the original model for the Georgia data. As shown in figure 6, 

it is quite evident that the original model does not do a good job of predicting accidents at 

the Georgia intersections; this finding was expected on the basis of the low Pearson 

product-moment coefficients for the Georgia data. 
66 

Table 66. Validation Statistics for TOTACCI Type III Model Using Georgia Data 

Georgia Data 

Measure Original Data 0.04 Mile 0.05 Mile 

Years used for validation 1993 to 1995 1996 to 1997 1996 to 1997 

Number of sites 84 52 52 

Pearson product-moment 

correlation coefficients 

 

0.67 

 

0.08 

 

0.10 

MPB -0.005 -1.03 -1.13 

MPB/yr -0.002 -0.52 -0.56 

MAD 1.76 1.95 1.95 

MAD/yr 0.59 0.97 0.97 

MSE 6.50 

MSE/yr2 0.72 

N/A1

 N/A1

MSPE 5.93 6.14 

MSPE/yr2 N/A1

1.48 1.54 1 N/A: not available 

0

2

4

6

8

10

12

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Sites

No. of Accidents

Predicted Accidents

Observed Accidents

Figure 6. Observed versus Predicted Accident Frequency: TOTACCI Type III 
67 

Injury Accident Model (INJACC) 

The two original variants for model III were validated. 

Variant 1

The parameter estimates, their standard errors, and p-values are given in table 67, which 

reveals that the constant term and all of the variables were estimated with the same sign 

as in the original model, but there were large differences in their magnitudes. The 

constant term, AADT1, and HAU became insignificant with the Georgia data. The 

overdispersion parameters, K, were higher than that for the original model. 

Table 68 shows the GOF measures for the original injury accident model (Variant 1) in 

the Vogt report applied to the Georgia data.(2)

The Pearson product-moment correlation coefficients were similar to those for the 

TOTACC model. However, the MPB, MAD, and MSPE per year squared were smaller 

than those for the TOTACC model. 

Table 67. Parameter Estimates for INJACC Type III Model Using Georgia 

Data: Variant 1 

Variable 

Report Estimate1

(s.e., p-value) 

Georgia Data 0.04 Mile 

(s.e, p-value) 

Georgia Data 0.05 Mile 

(s.e., p-value) 

-12.3246 -7.642 -6.958 

Constant (2.8076, 0.0001) (6.397, 0.2774) (5.949, 0.2923) 

1.1436 0.423 0.381 

Log of AADT1 (0.2763, 0.0001) (0.573, 0.4602) (0.531, 0.4730) 

0.1357 0.454 0.420 

Log of AADT2 (0.1029, 0.1872) (0.255, 0.0752) (0.243, 0.0838) 

0.0230 0.001 0.000 

HAU (0.0131, 0.0790) (0.010, 0.8886) (0.009, 0.9743) 

K2 0.3787 0.682 0.553 1 Vogt, 1999, (p. 113) 2 K: Overdispersion value
68 

Table 68. Validation Statistics for INJACC Type III Model Using 

Georgia Data: Variant 1 

Georgia Data 

Measure 

0.04 Mile 0.05 Mile 

Years used for validation 1996 to 1997 1996 to 1997 

Number of sites 52 52 

Pearson product-moment correlation coefficients 0.09 0.08 

MPB 0.23 0.19 

MPB/yr 0.11 0.10 

MAD 0.78 0.78 

MAD/yr 0.39 0.39 

MSPE 2.30 2.30 

MSPE/yr2 0.58 0.58 

Figure 7 depicts the prediction performance of the original model for individual sites in 

the Georgia 0.05-mile data. It is quite evident that the original model does not do a good 

job of predicting accidents at the Georgia intersections, a finding that would have been 

expected on the basis of the low Pearson product-moment coefficients for the Georgia 

data. 
69 

0

1

2

3

4

5

6

7

8

9

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Sites

No. of Accidents

Observed Injury

Predicted Injury(Variant1)

Figure 7. Observed versus Predicted Accident Frequency: Injury Variant 1 

Variant 2

The parameter estimates, their standard errors, and p-values are given in table 69, which 

reveals that the constant term and all of the variables were estimated with the same sign 

as in the original model. However, all of the variables except AADT2 became 

insignificant, and there were large differences in the magnitudes of the parameters. The 

overdispersion parameter, K, was almost twice as high as for the original model. 

Table 70 shows the GOF measures for the original injury accident model (Variant 2) in 

the Vogt report applied to the Georgia data.(2) 

The Pearson product-moment correlation coefficient was similar to that for TOTACC. 

However, the MPB, MAD, and MSPE per year squared were smaller than those for 

TOTACC. 

Figure 8 depicts the prediction performance of the original model for individual sites in 

the Georgia 0.05-mile data. It is quite evident that the original model performs poorly 

when applied to the Georgia data, a finding that would have been expected on the basis of 

the low Pearson product-moment coefficients for the Georgia data. 
70 

Table 69. Parameter Estimates for INJACC Type III Model Using 

Georgia Data: Variant 2 

Variable 

Report Estimate1

(s.e., p-value) 

Georgia Data 0.04 Mile 

(s.e, p-value) 

Georgia Data 0.05 Mile 

(s.e., p-value) 

-11.0061 -8.238 -7.786 

Constant (2.6937, 0.0001) (7.223, 0.2962) (6.571, 0.2803) 

0.9526 0.457 0.410 

Log of AADT1 (0.2843, 0.0008) (0.627, 0.4663) (0.565, 0.4678) 

0.1499 0.468 0.457 

Log of AADT2 (0.0916, 0.1018) (0.278, 0.0920) (0.258, 0.0771) 

0.0289 0.002 0.001 

HAU (0.0105, 0.0061) (0.010, 0.8764) (0.010, 0.9046) 

0.0481 0.038 0.085 

DRWY1 (0.0262, 0.0664) (0.120, 0.7488) (0.151, 0.5734) 

0.1838 0.167 0.225 

ABSGRD1 (0.1130, 0.1038) (0.439, 0.7042) (0.415, 0.5871) 

K2 0.2588 0.666 0.501 1 Vogt, 1999, (p. 113) 2 K: Overdispersion value 

Table 70. Validation Statistics for INJACC Type III Model Using 

Georgia Data: Variant 2 

Georgia Data 

Measure 

 0.04 Mile 0.05 Mile 

Years used for validation 1996 to 1997 1996 to 1997 

Number of sites 52 52 

Pearson product-moment correlation coefficients 0.05 0.04 

MPB 0.15 0.11 

MPB/yr 0.08 0.06 

MAD 0.77 0.77 

MAD/yr 0.39 0.39 

MSPE 2.61 2.61 

MSPE/yr2 0.65 0.65 
71 

0

1

2

3

4

5

6

7

8

9

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Sites

No. of Accidents

Predicted Injury(Variant1)

Observed Injury

Figure 8. Observed versus Predicted Accident Frequency: Injury Variant 2 

2.5.4 Model IV 

The summary statistics are provided in table 71. Peak left-turn percentage on major road 

was not available in the Georgia data, since this variable would be too costly to collect in 

the field. Since the variable was not present in the Georgia data, modifications to the 

validation procedure had to be performed. The variable was removed from the original 

model by dividing both sides of the model equation by the exponential value of the 

coefficient of the variable times its average effect (the average effect of PKLEFT1 is the 

average value of PKLEFT1 in the calibration data). 

The summary statistics showed that about 31 percent of the sites in the original data had 

no left-turn lane, while 17 percent in the Georgia data were without a left-turn lane. The 

summary statistics for all of the three States (California, Michigan, and Georgia) were 

also compared (refer to table 72). All of the sites in Michigan had no LTLN1S, while 

frequencies of TOTACC and TOTACCI for Georgia were higher than for the California 

data. 

Pearson correlations of the original data, Georgia, and California are given in table 73. 

The observation that the coefficients for AADT 2 and LTLN1S estimated using Georgia 

data resulted in opposite signs than the original model required further investigation. 

Pearson correlations for these variables with the response (accident frequency) were 

computed for all three States—California, Michigan, and Georgia. Recall that the Pearson 

correlation reflects the degree to which the two variables are linearly related. Unlike the 
72 

original data, AADT2 in Georgia is estimated as negative linearly related with TOTACC 

and TOTACCI, but these correlations are marginal and statistically insignificant. The 

variable LTLN1 is positively related with TOTACC and TOTACCI in Georgia and 

California (not significant), but is negative and significant for the Michigan data. 

Table 71. Summary Statistics of Georgia Data: Type IV 

Variable and Abbreviation N Mean Median Minimum Maximum Freq. 

% 

Zero 

Original 

Data 72 5.5 3.5 0 38 398 12.5 

Georgia 

No. of Crashes (0.05 Mile) 52 4.27 4.0 0 13 222 13.5 

(TOTACC) 

 

Georgia 

(0.04 Mile) 52 4.17 3.0 0 13 217 13.5 

Original 

Data 72 4.1 2 0 27 297 22.2 

Georgia 

(0.05 Mile) 52 3.08 3.0 0 11 160 26.9 

No. of 

Intersection-Type 

Crashes 

(TOTACCI) 

 

Georgia 

(0.04 Mile) 52 3.06 3.0 0 11 159 36.5 

Georgia 

(0.05 Mile) 52 2.06 2.0 0 9.0 107 32.7 

No. of Injury 

Crashes (INJACC) 

Georgia 

(0.04 Mile) 52 2.0 2.0 0 9.0 104 32.7 

Georgia 

(0.05 Mile) 52 1.67 1.0 0 9.0 87 38.5 

No. of 

Intersection-Type 

Injury Crashes 

 (INJACCI) 

Georgia 

(0.04 Mile) 52 1.67 1 0 9 87 38.5 

Original 

Data 72 0.7 1 0 1 N/A1 30.6 

Left-Turn Lanes 

on Major Road 

(LTLN1S) Georgia 52 0.8 1 0 1 N/A1 17.3 

Original 

Data 72 2.8 1.51 0 13.96 N/A1 5.6 

Peak Left-Turn 

Percentage on 

Major Road 

(PKLEFT1) Georgia N/A1

Original 

Data 72 13018 11166 3350 73000 N/A1 N/A1 AADT1 on Major 

Road 

 Georgia 52 13100 12200 6500 28600 N/A1 N/A1

Original 

Data 72 559 410 21 2018 N/A1 N/A1 AADT2 on Minor 

Road 

 Georgia 52 892 430 80 9490 N/A1 N/A1

1 N/A: not available 
73 

Table 72. Summary Statistics of California, Michigan, and Georgia 

California (N=54)1 Michigan (N=18)1

 Georgia (N=52)2

Variable Mean Median Min. Max. Mean Median Min. Max. Mean Median Min. Max. 

TOTACC 4.2 3 0 22 9.4 8.5 0 38 4.3 4 0 13

TOTACCI 3.5 2 0 21 6 4.5 0 27 3.1 3 0 11

AADT1 13788 11250 3350 73000 10707 10550 5967 19383 12631 12831 5300 25800

AADT2 441 301 21 1850 913 733 254 2018 706 463 300 2990

PKLEFT1 2.25 1 0 14 4.4 3.1 0.8 11.6 N/A N/A N/A N/A

LTLNS 0.93 1 0 1 0 0 0 0 0.9 1 0 1

1

 Summary Statistics for California and Michigan were produced using the obtained original data 

2

 Used TOTACC and TOTACCI for 0.05 mile

Table 73. Pearson Correlations: Original, Georgia, and California 

The original data (N=72)

Variable TOTACC TOTACCI AADT1 AADT2 

Pearson Correlation 1.000 0.961 0.152 0.480 

TOTACC Sig. (2-tailed) N/A1

 0.000 0.203 0.000 

Pearson Correlation 0.961 1.000 0.164 0.461 

TOTACCI Sig. (2-tailed) 0.000 N/A1

 0.168 0.000 

Pearson Correlation 0.152 0.164 1.000 -0.108 

AADT1 Sig. (2-tailed) 0.203 0.168 N/A1

 0.365 

Pearson Correlation 0.480 0.461 -0.108 1.000 

AADT2 Sig. (2-tailed) 0.000 0.000 0.365 N/A1

Pearson Correlation -0.279 -0.169 0.210 -0.219 

LTLN1 Sig. (2-tailed) 0.018 0.156 0.077 0.064 

Georgia (N= 52): 0.05 mile

Variable TOTACC TOTACCI AADT1 AADT2 

Pearson Correlation 1.000 0.934 0.294 -0.096 

TOTACC Sig. (2-tailed) N/A1

 0.000 0.035 0.501 

Pearson Correlation 0.934 1.000 0.247 -0.096 

TOTACCI Sig. (2-tailed) 0.000 N/A1

 0.077 0.499 

Pearson Correlation 0.294 0.247 1.000 -0.008 

AADT1 Sig. (2-tailed) 0.035 0.077 N/A1

 0.956 

Pearson Correlation -0.096 -0.096 -0.008 1.000 

AADT2 Sig. (2-tailed) 0.501 0.499 0.956 N/A1

Pearson Correlation 0.293 0.250 0.083 0.143 

LTLN1 Sig. (2-tailed) 0.035 0.074 0.558 0.313 1 N/A: not available 
74 

Table 73. Pearson Correlations: Original, Georgia, and California (Continued) 

California (N=54)

Variable TOTACC TOTACCI AADT1 AADT2 

Pearson Correlation 1 0.987 0.215 0.494

TOTACC Sig. (2-tailed) N/A1

 0 0.118 0 

Pearson Correlation 0.987 1 0.201 0.508

TOTACCI Sig. (2-tailed) 0 N/A1

 0.146 0 

Pearson Correlation 0.215 0.201 1 -0.035

AADT1 Sig. (2-tailed) 0.118 0.146 N/A1

 0.804

Pearson Correlation 0.494 0.508 -0.035 1 

AADT2 Sig. (2-tailed) 0 0 0.804 N/A1

Pearson Correlation 0.074 0.046 0.138 0.266

LTLN1 Sig. (2-tailed) 0.596 0.742 0.319 0.052

 1 N/A: not available 

Total Accident Models (TOTACC) 

The parameter estimates, their standard errors, and p-values are given in table 74. Since 

the variable PKLEFT1 (peak left-turn percentage on major road) is not present in the 

Georgia data, modifications to the validation procedure had to be performed as described 

earlier. In the validation, the same parameter estimates in the originally published report 

were used, and the parameter estimates were also reproduced without PKLEFT1 for the 

revised original model (“Revised Estimates” in table 74). 

In the revised original model, all of the variables were estimated with the same sign but 

with large differences in magnitude. The effect of AADT1 became smaller, while that of 

AADT2 became larger. The overdispersion values with the Georgia data were higher 

than for the original models, but the difference was not great. 

For the Georgia data, the constant term and AADT1 were estimated with the same sign as 

for the original models. However, AADT2 and LTLN1S were estimated with an opposite 

sign to the original model, although AADT2 was insignificant. The values of the 

overdispersion parameter K for the Georgia data were lower than those for the original 

data. 
75 

Table 74. Parameter Estimates for TOTACC Type IV Model Using Georgia Data 

Variable 

Original Estimates1

(s.e., p-value) 

Revised Estimates2

(s.e, p-value) 

Georgia Data 0.04 

Mile (s.e., p-value) 

Georgia Data 0.05 

Mile (s.e., p-value) 

-9.4631 -6.705 -5.599 -5.764 

Constant (2.5991, 0.0003) (2.373, 0.0181) (3.977, 0.2174) (4.110, 0.2173) 

Log of 0.8503 0.501 0.624 0.653 

AADT1 (0.2779, 0.0022 ) (0.231, 0.0301) (0.365, 0.0875) (0.380, 0.0860) 

Log of 0.3294 0.478 -0.112 -0.097 

AADT2 (0.1255, 0.0087) (0.097, 0.0000) (0.229, 0.6253) (0.241, 0.6867) 

PKLEFT1 

0.1100 

(0.0412, 0.0076) N/A4

 N/A4 N/A4

-0.4841 -0.504 1.273 1.085 

LTLN1S (0.2311, 0.0362) (0.245, 0.0393) (0.432, 0.0032) (0.377, 0.0040) 

K3 0.4578 0.553 0.382 0.417 1

 Vogt, 1999, (p. 116) 

2 Coefficient estimates of the variables were reproduced without PKLEFT1 using the original data 3

 K: Overdispersion value 

 4 N/A: not available 

Since PKLEFT1 was not available in the Georgia data, two models (original model and 

revised original model) were used for the validation activity to determine GOF measures. 

For the original model, the same parameter estimates in the report were used. For the 

revised original model, since PKLEFT1 was not available, PKLEFT1 was removed from 

the original model by dividing by the exponential value of the coefficient of this variable 

times its average effect, i.e., the average value of PKLEFT1. 

GOF measures of the revised original model, shown in table 75, indicate that it could be a 

good alternative to the original model. Pearson product-moment correlation coefficients, 

MAD per year, and MSE per year squared were similar to those for the original model. 

The MPB per year was higher than that for the original model, but the difference was not 

great. 

 

Values of 0.05 and 0.08 of the Pearson product-moment correlation coefficient indicate 

that the accidents in the Georgia data are not linearly related with the model-predicted 

values. This could be the result of a significant nonlinearity in the data and original model. 

The MPB and MAD per year for the Georgia data were larger than those for the original 

year data. The MSPEs per year squared were also higher than the MSEs per year squared. 

Figure 9 depicts the prediction performance of the original model for individual sites in 

the Georgia 0.05-mile data. It is quite evident that the original model does not fit the 

Georgia data well, a finding that would have been expected on the basis of the low 

Pearson product-moment coefficients for the Georgia data. 
76 

Table 75. Validation Statistics for TOTACC Type IV Model Using Georgia Data 

Measure 

Original 

Model1

 Revised Original 

Model2

Georgia3

(0.04 Mile) 

Georgia3

(0.05 Mile) 

Years used for validation 1993-1995 1993-1995 1996-1997 1996-1997 

Number of sites 72 72 51 51 

Pearson product-moment 

correlation coefficients 

 

0.56 

 

0.56 

 

0.05 

 

0.08 

MPB -0.07 1.41 2.25 2.27 

MPB/yr -0.02 0.47 1.12 1.13 

MAD 3.38 3.49 3.09 3.11 

MAD/yr 1.13 1.16 1.54 1.55 

MSE 30.62 32.66 

MSE/yr2 3.40 3.63 

N/A4

 N/A4

MSPE 17.86 18.51 

MSPE/yr2 N/A4

 N/A4

4.47 4.63 1

 Used the original main model in the report. This model includes PKLEFT1 

2

 Used the same coefficients in the original model, but PKLEFT1 was removed from the model by dividing 

 by the exponential value of the coefficient of this variable times its average effect 3

 Used the revised original model 

4

 N/A: not available 

0

2

4

6

8

10

12

14

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Sites

No. of Accidents

Predicted Accidents

Observed Accidents

Figure 9. Observed versus Predicted Accident Frequency: TOTACC 
77 

Intersection Related Total Accident Model (TOTACCI) 

The parameter estimates, their standard errors, and p-values are given in table 76. As 

before, the two models (original model and revised original model) were used for the 

validation. For the original model, the same parameter estimates in the report were used. 

Since the report also developed a model with AADT1 and AADT2 only, which model 

(“Revised Estimates” in table 76) was included for the validation. 

In the alternative original model the constant term and parameter estimates of AADT1 

and AADT2 were estimated with the same sign but with some difference in magnitude. 

The effect of AADT1 became smaller, while that of AADT2 became larger. The 

overdispersion value was slightly higher than for the original model. 

For the Georgia data, AADT2 was estimated with an opposite sign to that of the original 

models. However, it was statistically insignificant, and the impact of the variable on the 

accident prediction was marginal. The constant term and AADT1 were also estimated as 

insignificant for the Georgia data. The overdispersion values for the Georgia data were 

similar to that for the revised original model. 

The prediction performance measures are shown in table 77. As was the case for the 

TOTACC models, the revised model showed similar prediction performance measures to 

the original model. 

Table 76. Parameter Estimates for TOTACCI Type IV Model Using Georgia Data 

Variable 

Original Estimates1

(s.e., p-value) 

Revised Estimates2

(s.e, p-value) 

Georgia Data 

0.04 Mile 

(s.e., p-value) 

Georgia Data 

0.05 Mile 

(s.e., p-value) 

-11.1096 -7.2501 -4.604 -4.603 

Constant (3.3345, 0.0008) (2.9094, 0.0130) (5.482, 0.4755) (5.498, 0.4770) 

Log of 0.9299 0.4582 0.562 0.563 

AADT1 (0.3433, 0.0067 ) (0.2844, 0.1071) (0.495, 0.2564) (0.497, 0.2568) 

Log of 0.3536 0.5311 -0.041 -0.043 

AADT2 (0.1163, 0.0024) (0.0996, 0.0001) (0.325, 0.8996) (0.326, 0.8957) 

PKLEFT1 

0.1491 

(0.0586, 0.0110) N/A4

 N/A4 N/A4

K3 0.7096 0.8814 0.857 0.857 1

 Vogt, 1999, (p. 117) 

2 The report presents this model developed with AADT1 and AADT2 only 

3 K: Overdispersion value 

4 N/A: not available 

 
78 

Table 77. Validation Statistics for TOTACCI Type IV Model Using Georgia Data 

Measure 

Original 

Model1

 Revised Original 

Model2

Georgia3

(0.04 Mile) 

Georgia3

(0.05 Mile) 

Years used for validation 1993-1995 1993-1995 1996-1997 1996-1997 

Number of sites 72 72 51 51 

Pearson product-moment 

correlation coefficients 

 

0.47 

 

0.47 

 

0.16 

 

0.17 

MPB -0.17 1.28 1.81 1.76 

MPB/yr -0.06 0.43 0.90 0.88 

MAD 3.00 3.00 2.59 2.54 

MAD/yr 1.00 1.00 1.29 1.27 

MSE 24.92 24.85 

MSE/yr2 2.77 2.76 

N/A4

 N/A4

MSPE 12.32 12.18 

MSPE/yr2

N/A4 N/A4

3.08 3.05 1

 Used the original main model in the report. This model includes PKLEFT1 

2

 Used the same coefficients in the original model, but PKLEFT1 was removed from the model by dividing 

 by the exponential value of the coefficient of this variable times its average effect 3

 Used the revised original model 

4

 N/A: not available 

Values of 0.16 and 0.l7 of the Pearson product-moment correlation coefficients indicate 

that the accident predictions by the original models are not strongly linearly correlated 

with the observed number of accidents in the Georgia data. Again, there are several 

possible explanations for this. The MPBs and MAD per year was larger than those for the 

original models. The MSPEs per year squared were also slightly higher than the MSEs 

per year squared. 

Figure 10 depicts the prediction performance of the original model for individual sites in 

the Georgia 0.05-mile data. It is quite evident that the original model does not fit the 

Georgia data well, a finding that would have been expected on the basis of the low 

Pearson product-moment coefficients. 
79 

0

2

4

6

8

10

12

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Sites

No. of Accidents

Predicted Accidents

Observed Accidents

Figure 10. Observed versus Predicted Accident Frequency: TOTACCI 

Injury Accident Model (INJACC) 

The parameter estimates, their standard errors, and p-values are given in table 78. Again, 

all of the variables including the constant term were insignificant for the Georgia data, 

and AADT2 was estimated with an opposite sign to that of the original model. The 

overdispersion values for the Georgia data were higher than that for the original model. 

Table 78. Parameter Estimates for INJACC Type IV Model Using Georgia Data 

Variable 

Original Estimates1

(s.e., p-value) 

Georgia Data 0.04 Mile2

(s.e., p-value) 

Georgia Data 0.05 Mile2

(s.e., p-value) 

Constant 

-12.5296 

(2.9908, 0.0001) 

-4.811 

(4.912, 0.4018) 

-5.260 

(4.778, 0.3392) 

Log of AADT1 

0.9505 

(0.3284, 0.0038 ) 

0.599 

(0.467, 0.1990 ) 

0.652 

(0.457, 0.1543 ) 

Log of AADT2 

0.3237 

(0.1645, 0.0491) 

-0.191 

(0.374, 0.6100) 

-0.162 

(0.367, 0.6586) 

PKLEFT1 

0.0994 

(0.0433, 0.0216) N/A4 N/A4

SPD2 

0.0339 

(0.0179, 0.0577) 

0.010 

(0.031, 0.7379) 

0.005 

(0.031, 0.8732) 

K3 0.4308 0.649 0.645 1

 Vogt, 1999, (p. 118) 

2

 PKLEFT1 was not included in the model 

3

 K: Overdispersion value 

4 N/A: not available 

Table 79 shows the GOF measures for the original injury accident model (Variant 1) in 

the Vogt report applied to the Georgia data.(2)
80 

The Pearson product-moment correlation coefficients were higher those for the TOTACC 

models, and the MPB, MAD, and MSPE per year squared were smaller than those for the 

TOTACC models. 

Table 79. Validation Statistics for INJACC Type IV Model Using Georgia Data 

Georgia1

Measure 

 0.04 Mile 0.05 Mile 

Years used for the validation 1996-1997 1996-1997 

Number of sites 52 52 

Pearson product-moment 

correlation coefficients 

 

0.18 

 

0.18 

MPB 0.75 0.81 

MPB/yr 0.38 0.40 

MAD 1.67 1.73 

MAD/yr 0.84 0.86 

MSPE 5.02 5.23 

MSPE/yr2 1.26 1.31 1 Used Variant 1, but PKLEFT1 was removed from the model by dividing by the exponential 

 value of the coefficient of this variable times its average effect 

Figure 11 depicts the prediction performance of the original model for individual sites in 

the Georgia 0.05-mile data. It is quite evident that the original model generally does not 

fit the Georgia data well, a finding that would have been expected on the basis of the low 

Pearson product-moment coefficients. 
81 

0

1

2

3

4

5

6

7

8

9

10

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Sites

No. of Accidents

Predicted Injury(Variant1)

Observed Injury

Figure 11. Observed versus Predicted Accident Frequency: INJACC 

Intersection Related Injury Accident Model (INJACCI) 

The parameter estimates, their standard errors, and p-values are given in table 80. As was 

the case for INJACC, all of the variables were insignificant for the Georgia data. The 

variable AADT2 was estimated with an opposite sign to that for the original model. The 

overdispersion values with the Georgia data were similar to that for the original model. 

Table 81 shows the GOF measures for the original intersection related injury accident 

model (Variant 1) in the Vogt report applied to the Georgia data.(2)

 

The Pearson product-moment correlation coefficient was similar to that for the 

TOTACCI model, but the MPB, MAD, and MSPE per year squared were smaller. 
82 

Table 80. Parameter Estimates for INJACCI Type IV Model Using Georgia Data 

Variable 

Original Estimates1

(s.e., p-value) 

Georgia Data 0.04 Mile2

(s.e., p-value) 

Georgia Data 0.05 Mile2

(s.e., p-value) 

-13.5576 -4.475 -4.475 

Constant (3.9998, 0.0008) (5.357, 0.4803) (5.357, 0.4803) 

0.9918 0.564 0.564 

Log of AADT1 (0.4268, 0.0201) (0.499, 0.2590 ) (0.499, 0.2590 ) 

0.3310 -0.189 -0.189 

Log of AADT2 (0.1894, 0.0805) (0.407, 0.6430) (0.407, 0.6430) 

0.1228 

PKLEFT1 (0.0614, 0.0457) N/A4 N/A4

0.0429 0.005 0.005 

SPD2 (0.0240, 0.0740) (0.036, 0.8892) (0.036, 0.8892) 

K3 0.7178 0.789 0.789 1

 Vogt, 1999, (p. 118) 

2

 PKLEFT1 was not included in the model 

3

 K: Overdispersion value 

 4 N/A: not available 

Table 81. Validation Statistics for INJACCI Type IV Model Using Georgia Data 

Georgia Data1

Measure 

 0.04 Mile 0.05 Mile 

Years used for validation 1996-1997 1996-1997 

Number of sites 52 52 

Pearson product-moment 

correlation coefficients 

 

0.15 

 

0.15 

MPB 1.08 1.14 

MPB/yr 0.54 0.57 

MAD 1.72 1.78 

MAD/yr 0.86 0.89 

MSPE 5.59 5.86 

MSPE/yr2 1.40 1.47 1 Used Variant 1, but PKLEFT1 was removed from the model by dividing by the exponential 

 value of the coefficient of this variable times its average effect 

Figure 12 depicts the prediction performance of the original model for individual sites in 

the Georgia 0.05-mile data. It is quite evident that the original model generally does not 

fit the Georgia data well, a finding that would have been expected on the basis of the low 

Pearson product-moment coefficients. 
83 

0

1

2

3

4

5

6

7

8

9

10

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Sites

No. of Accidents

Predicted IINJACCI(Variant1)

Observed INJACCI

Figure 12. Observed versus Predicted Accident Frequency: INJACCI 

2.5.5 Model V 

The summary statistics of the variables used in this model are provided in table 82. 

PKLEFT2 and PKTRUCK were not included in the Georgia data. The summary statistics 

indicate that the Georgia intersections had fewer accidents, on average, than those in the 

original data. For example, about 10 percent of the Georgia sites did not have an accident 

during the period of 1996 and 1997, while all of the original sites experienced at least one 

accident. The majority of the Georgia sites did not have a protected left-turn lane on the 

major road (PROT_LT), while PROT_LT was present at almost a half of the sites in the 

original models. As mentioned previously, some of the data acquired did not exactly 

match the summary statistics given in the report.(2) Specifically, there was a problem 

reproducing vertical alignment related variables: VEI1, VEI2, and VEICOM. 
84 

Table 82. Summary Statistics of Georgia Data: Type V 

Variable and Abbreviation1 N Mean Median Minimum Maximum Freq. % Zero

Original Data 49 20.8 21 2 48 1017 0.0

Georgia 

(0.05 Mile) 51 9.6 7 0 53 489 11.8

No. of Crashes 

(TOTACC) 

 Georgia 

(0.04 Mile) 51 9.3 7 0 51 473 11.8

Original Data 49 16.1 17 1 37 790 0.0

Georgia 

(0.05 Mile) 51 8.7 7 0 52 445 11.8

No. of IntersectionType Crashes 

(TOTACCI) 

 Georgia 

(0.04 Mile) 51 8.5 7 0 50 433 13.7

Original Data 49 7.47 7 0 25 366 4.1

Georgia 

(0.05 Mile) 51 2.3 1 0 13 118 25.5

 No. of Injury Crashes 

(INJACC)

Georgia 

(0.04 Mile) 51 2.2 1 0 13 113 25.5

Original Data 49 6.14 6 0 21 301 4.1

Georgia 

(0.05 Mile) 51 2.2 1 0 13 110 27.5

 No. of IntersectionType Injury Crashes 

 (INJACCI) 

 Georgia 

(0.04 Mile) 51 2.1 1 0 13 106 27.5

Original Data 49 18.2 17.97 4.2 37.07 N/A2 N/A2 Peak Left-Turn 

Percentage on Minor 

Road 

(PKLEFT2) Georgia N/A2

Original Data 49 8.96 7.71 2.69 7.71 N/A2 N/A2 Peak Truck Percentage 

(PKTRUCK) Georgia N/A2

Original Data 49

0=NO 28

1=YES 21

Georgia 51

0=NO 42

Protected Left Turn 

(PROT_LT) 

 

 

 

 1=YES 9

N/A2

Original Data N/A Combined VEI1 and 2

VEI2 

(VEICOM) Georgia 51 1.69 1.60 0 4.79 N/A2

 7.8

Original Data 49 13018 11166 3350 73000 N/A2 N/A2 AADT1 on Major Road 

 Georgia 51 13100 12200 6500 28600 N/A2 N/A2

Original Data 49 559 410 21 2018 N/A2 N/A2 AADT2 on Minor Road 

 Georgia 51 892 430 80 9490 N/A2 N/A2

1

 Vogt, 1999, (p. 61-64) 

 2 N/A: not available 

Separate summary statistics for three States, shown in table 83, were examined to see if 

there were differences in the variables between States. These summary statistics indicate 

that the Michigan sites had, on average, higher accident frequencies than California. They 

also reveal that the majority of the sites in California had protected left-turn lanes 

(PROT_LT=1), while the Michigan and Georgia data had no sites with this feature 

present. 
85 

Table 83. Summary Statistics for Three States: California, Michigan, and Georgia1

California (N=18)1 Michigan (N=31)1 Georgia (N=51) 

Variable Mean Median Min. Max. Mean Median Min. Max. Mean Median Min. Max.

TOTACC 15.2 16 2 32 24 25 2 48 9.6 7 0 53

TOTACCI 13.8 15 2 30 17.5 18 1 37 8.7 7 0 52

AADT1 13048 12484 7500 25133 9007 8435 4917 17483 7798 7400 430 15200

AADT2 3630 3026 940 10067 4796 4434 1961 12478 2749 2200 420 10400

PKLEFT2 28.83 25.07 2.5 68.57 28.17 25.65 9.91 75.73 N/A2

PKTRUCK 7.36 6.43 2.69 15.45 9.89 8.37 2.97 45.43 N/A2

PROT_LT 0.94 1 0 1 0.13 0 0 1 0.18 0 0 1

VEICOM 1.91 1.08 0 8.13 1.54 1.48 0 6.75 1.69 1.6 0 4.79

 1 Summary Statistics for California and Michigan were produced using the obtained original data 

 2 N/A: not available 

Total Accident Models (TOTACC) 

Since the variables PKLEFT1 and PKTRUCK were not present in the Georgia data, 

modifications to the validation procedure had to be performed as described earlier. In the 

validation, the same parameter estimates in the originally original report were used, and 

the parameter estimates were also reproduced without PKLEFT1 and PKTRUCK for the 

revised original model. 

Two models (original model and revised original model) were used for the validation 

activity to determine GOF measures. For the original model, the same parameter 

estimates in the report were used. For the revised original model, since PKLEFT2 and 

PKTRUCK were not available in the Georgia data, these variables were removed from 

the original published model by dividing by the exponential value of their coefficients 

times their average effects, i.e., their average values. 

The validation addressed the main model and one variant. 

Main Model

The model re-estimation results are shown in table 84. For the revised original model, 

without the variables PKLEFT2 and PKTRUCK, the constant term and all of the 

variables were estimated with the same sign as the reported model, but all of them except 

PROT_LT were insignificant. The overdispersion parameter, K, was almost twice as high 

as that for the original model. 

For the Georgia data, the constant term, AADT1, AADT2, and VEICOM were estimated 

with the same sign as the reported model, but there were differences in magnitude. 

PROT_LT was estimated with an opposite sign, although it was statistically insignificant. 

AADT2 and VEICOM were also insignificant. The overdispersion parameter, K, was 

substantially higher than that for the original models. 
86 

Table 84. Parameter Estimates for TOTACC Type V Model Using Georgia 

Data: Main Model 

Variable 

Original 

Estimate1

(s.e., p-value) 

Revised 

Estimates2

 

(s.e, p-value) 

Georgia Data 

0.04 Mile 

(s.e., p-value) 

Georgia Data 0.05 

Mile 

(s.e., p-value) 

-6.9536 -4.084 -5.755 -5.430 

Constant (2.7911, 0.0132) (3.659, 0.4146) (3.432, 0.1403) (3.816, 0.2144) 

0.6199 0.272 0.606 0.575 

Log of AADT1 (0.2504, 0.0133) (0.308, 0.3761) (0.325, 0.0623) (0.354, 0.1036) 

0.3948 0.422 0.222 0.219 

Log of AADT2 (0.1737, 0.0133) (0.264, 0.1106) (0.151, 0.1412) (0.156, 0.1620) 

-0.6754 -0.462 0.589 0.604 

PROT_LT (0.1824, 0.0002) (0.222, 0.0372) (0.437, 0.1782) (0.463, 0.1922) 

-0.0142 

PKLEFT2 (0.0047, 0.0023) N/A4 N/A4 N/A4

0.1299 0.094 0.012 0.011 

VEICOM (0.045, 0.0039) (0.087, 0.2813) (0.179, 0.9484) (0.188, 0.9522) 

PKTRUCK 0.0315 

 (0.0143, 0.0275) N/A4 N/A4 N/A4

K3 0.1161 0.216 0.730 0.731 1

 Vogt, 1999, (p. 122) 

2

 Coefficient estimates of the variables were reproduced without PKLEFT2 and PKTRUCK using the 

 original data

3

 K: Overdispersion value

 4 N/A: not available 

The validation statistics are shown in table 85. The revised original model was estimated 

with the same Pearson product-moment correlation coefficient as that for the original 

model. The MPB per year was larger than that for the original model, while the MADs 

were similar. The MSE per year was slightly higher than that for the original model. 

The Pearson correlation coefficient for the Georgia data was relatively low, indicating a 

poor linear fit. A value of 0.18 of the Pearson correlation coefficient indicates that the 

accident predictions by the original model and the Georgia data are marginally correlated 

at best. The MPB and MAD per year were larger than those for the original models. The 

MSPEs per year squared were significantly higher than the MSEs per year squared, 

indicating a general lack-of-fit. 
87 

Table 85. Validation Statistics for TOTACC Type V Model Using Georgia 

Data: Main Model 

Georgia2

Measure 

Original 1993-95 

Model1 

Revised 1993-95 

Model2 0.04 Mile 0.05 Mile 

Years used for validation 1993-1995 1993-1995 1996-1997 1996-1997 

Number of sites 49 49 51 51 

Pearson product-moment 

correlation coefficients 

 

0.73 

 

0.73 

 

0.18 

 

0.18 

MPB -0.40 -3.06 -3.38 -3.06 

MPB/yr -0.13 -1.02 -1.69 -1.53 

MAD 6.53 6.82 8.50 8.59 

MAD/yr 2.18 2.27 4.25 4.30 

MSE 77.04 95.92 

MSE/yr2 8.56 10.66 

N/A3

 N/A3

MSPE 126.44 130.01 

MSPE/yr2

N/A3

 N/A3

31.61 32.50 1 The original main model in the report. This model includes PKLEFT2 and PKTRUCK 

2

 Used the same coefficients in the original model, but PKLEFT2 and PKTRUCK were removed from the 

 model by dividing by the exponential value of the coefficient of these variables times their average 

 effects 

3 N/A: not available 

Figure 13 depicts the prediction performance of the original model for individual sites in 

the Georgia 0.05-mile data. It is quite evident that the original model generally does not 

fit the Georgia data well, a finding that would have been expected on the basis of the low 

Pearson product-moment coefficients. 

Variant 1

The parameter estimates, their standard errors, and p-values are given in table 86. In the 

revised original model, without the variables PKLEFT2 and PKTRUCK, the constant 

term, AADT1*AADT2 and PROT_LT were estimated with the same sign as the reported 

model, but there were differences in magnitude. The constant term and VEICOM were 

statistically insignificant. The overdispersion parameter, K, was almost twice as high as 

that for the original model. 

For the Georgia data, the constant term, AADT1*AADT2, and VEICOM were estimated 

with the same sign as the reported model, but the constant term and VEICOM were 

insignificant. PROT_LT was estimated with an opposite sign, but with similar degree of 

magnitude. The overdispersion parameter K was significantly higher than that for the 

original models. 
88 

0

10

20

30

40

50

60

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Sites

No. of Accidents

Predicted Accidents

Observed Accidents

Figure 13. Observed versus Predicted Accident Frequency: TOTACC Main Model 

Table 86. Parameter Estimates for TOTACC Type V Model Using 

Georgia Data:Variant 1 

Variable 

Original Estimate1

(s.e., p-value) 

Revised Estimates2

(s.e, p-value) 

Georgia Data3

 

0.04 Mile 

(s.e., p-value) 

Georgia Data3 

0.05 Mile 

(s.e., p-value) 

-6.1236 -4.589 -3.891 -3.766 

Constant (2.5973, 0.0184) (3.669, 0.34125) (2.313, 0.1668) (2.386, 0.1978) 

Log of 

AADT1*AADT2 

0.4643 

(0.1483, 0.0017) 

0.373 

(0.212, 0.0792) 

0.315 

(0.141, 0.0256) 

0.309 

(0.146, 0.0343) 

PROT_LT 

-0.6110 

(0.1507, 0.0001) 

-0.501 

(0.179, 0.0051) 

0.684 

(0.405, 0.0917) 

0.682 

(0.415, 0.1008) 

PKLEFT2 

-0.0134 

(0.0048, 0.0052) N/A5 N/A5 N/A5

VEICOM 

0.1243 

(0.0507, 0.0142) 

0.097 

(0.082, 0.2365) 

0.009 

(0.174, 0.9601) 

0.008 

(0.181, 0.9648) 

PKTRUCK 

0.0300 

(0.0141, 0.0331) N/A5 N/A5 N/A5

K4 0.1186 0.217 0.766 0.763 1

 Vogt, 1999, (p. 122) 

2

 Coefficient estimates of the variables were reproduced without PKLEFT2 and PKTRUCK using the 

 original data 

3

 PKLEFT2 and PKTRUCK were not included in the model 

4

 K: Overdispersion value 

5 N/A: not available 
89 

The validation statistics are shown in table 87. For the revised original model the Pearson 

correlation coefficient was the same as that for the reported model. The MPB per year 

was larger than that for the original model, while the MADs and MSEs per year were 

similar. A value of 0.19 of the correlation coefficient indicates that the accident 

predictions by the original model and the Georgia data are marginally correlated at best. 

The MPBs and MAD per year was almost twice as large as those for the original model. 

The MSPEs per year squared were also significantly higher than the MSEs per year 

squared, indicating a general lack-of-fit. 

Table 87. Validation Statistics for TOTACC Type V Model Using 

Georgia Data: Variant 1 

Georgia data2

Measure Variant 11

Revised 

Variant 12 0.04 Mile 0.05 Mile 

Years used for validation 1993-1995 1993-1995 1996-1997 1997-1997 

Number of sites 49 49 51 51 

Pearson product-moment 

correlation coefficients 

 

0.73 

 

0.73 

 

0.19 

 

0.19 

MPB -0.37 -2.81 -3.08 -2.76 

MPB/yr -0.12 -0.94 -1.54 -1.38 

MAD 6.48 6.67 8.36 8.51 

MAD/yr 2.16 2.22 4.18 4.26 

MSE 73.31 88.12 

MSE/yr2 8.15 9.79 

N/A3

 N/A3

MSPE 123.18 126.91 

MSPE/yr2 N/A3

 N/A3

30.80 31.73 1 The Variant 1 in the report. This model includes PKLEFT2 and PKTRUCK 

2

 Used the same coefficients as Variant 1, but PKLEFT2 and PKTRUCK were removed from the model by 

 dividing by the exponential value of the coefficient of these variables times their average effects 3

 N/A: not available 

Figure 14 depicts the prediction performance of the original model for individual sites in 

the Georgia 0.05-mile data. It is quite evident that the original model generally does not 

fit the Georgia data well, a finding that would have been expected on the basis of the low 

Pearson product-moment coefficients. 
90 

0

10

20

30

40

50

60

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Sites

No. of Accidents

Predicted Accidents

Observed Accidents

Figure 14. Observed versus Predicted Accident Frequency: TOTACC Variant 1 

Intersection Related Total Accident Model (TOTACCI) 

As before, since the variables PKLEFT1 and PKTRUCK were not present in the Georgia 

data, models were re-estimated without PKLEFT1 and PKTRUCK for the revised 

original model. In addition, the estimation of GOF measures, used a revised original in 

which these variables were removed from the original published model by dividing by 

the exponential value of their coefficients times their average effects, i.e., their average 

values. 

The validation addresses the main model and one variant. 

Main Model

The parameter estimates, their standard errors, and p-values are given in table 88. In the 

revised original model all of the variables were estimated with the same direction of 

effect as for the original model, but there were sizeable differences in magnitude and 

significance. The estimates for all of the variables and the constant term were statistically 

insignificant. The overdispersion parameter, K, was somewhat higher than that for the 

original model. 
91 

Table 88. Parameter Estimates for TOTACCI Type V Model Using Georgia 

Data: Main Model 

Variable 

Original Estimate1

(s.e., p-value) 

Revised Estimates2

(s.e, p-value) 

Georgia Data3

0.04 Mile 

(s.e., p-value) 

Georgia Data3

0.05 Mile 

(s.e., p-value) 

Constant 

-6.0841 

(3.3865, 0.0724) 

-3.410 

(3.663, 0.5281) 

-6.551 

(2.968, 0.0485) 

-6.061 

(3.486, 0.1236) 

Log of AADT1 

0.5951 

(0.2847, 0.0366) 

0.245 

(0.315, 0.4373) 

0.694 

(0.286, 0.0151) 

0.644 

(0.327, 0.0487) 

Log of AADT2 

0.2935 

(0.1972, 0.1366) 

0.337 

(0.248, 0.1742) 

0.206 

(0.154, 0.1813) 

0.204 

(0.158, 0.1981) 

PROT_LT 

-0.4708 

(0.2000, 0.0186) 

-0.256 

(0.222, 0.2505) 

0.610 

(0.418, 0.1445) 

0.637 

(0.441, 0.1490) 

PKLEFT2 

-0.0165 

(0.0057, 0.0036) N/A5 N/A5 N/A5

VEICOM 

0.1126 

(0.0365, 0.0020) 

0.073 

(0.071, 0.3037) 

0.021 

(0.173, 0.9050) 

0.021 

(0.179, 0.9078) 

PKTRUCK 

0.0289 

(0.0131, 0.0276) N/A5

 N/A5 N/A5

4

K 0.1313 0.231 0.730 0.708 1

 Vogt, 1999, (p. 123) 

2

 Coefficient estimates of the variables were reproduced without PKLEFT2 and PKTRUCK using the 

 original data 

3

 PKLEFT2 and PKTRUCK were not included in the model 

4

 K: Overdispersion value

 5 N/A: not available 

For the Georgia data, the constant term, AADT1, AADT2, and VEICOM were estimated 

with the same sign as the reported model, but there were differences in the magnitude and 

significance. PROT_LT was estimated with an opposite sign, although it was statistically 

insignificant. AADT2 and VEICOM also became insignificant. The overdispersion 

parameters, K, are significantly higher than for the original models. 

The validation statistics are shown in table 89. The Pearson product-moment correlation 

coefficient of the revised original model was estimated to be the same as that for the 

original model. The MPB per year was somewhat larger, while the MAD per year was 

similar to that for the original model. The MSE per was higher than that for the original 

model, but the difference was not great. 

A value of 0.23 of the Pearson correlation coefficient indicates that the accident 

predictions by the original model are marginally linearly correlated with observed 

number of accidents in the 1996 to 1997 period. The MPB and MAD per year were larger 

than those for the original models. The MSPEs per year squared were significantly higher 

than the MSEs per year squared, indicating a general lack-of-fit. 

Figure 15 depicts the prediction performance of the original model for individual sites in 

the Georgia 0.05-mile data. It is quite evident that the original model generally does not 

fit the Georgia data well, a finding that would have been expected on the basis of the low 

Pearson product-moment coefficients. 
92 

Table 89. Validation Statistics for TOTACCI Type V Model Using Georgia 

Data: Main Model 

Georgia data2

Measure 

Original 

1993-95 Model1

Revised 

1993-95 Model2 0.04 Mile 0.05 Mile 

Years used for validation 1993-95 1993-95 1996-97 1996-97 

Number of sites 49 49 51 51 

Pearson product-moment 

correlation coefficients 

 

0.62 

 

0.61 

 

0.23 

 

0.23 

MPB -0.28 -4.04 -3.39 -3.16 

MPB/yr -0.09 -1.35 -1.70 -1.58 

MAD 5.63 6.33 7.53 7.53 

MAD/yr 1.88 2.11 3.77 3.77 

MSE 58.24 85.81 

MSE/yr2 6.47 9.53 

N/A3

 N/A3

MSPE 98.36 100.71 

MSPE/yr2

N/A3

 N/A3

24.59 25.18 1 The original main model in the report. This model includes PKLEFT2 and PKTRUCK

2

 Used the same coefficients as the original model, but PKLEFT2 and PKTRUCK were removed from the 

 model by dividing by the exponential value of the coefficient of these variables times their average 

 effects 

3

 N/A: not available 

0

10

20

30

40

50

60

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Sites

No. of Accidents

Predicted Accidents

Observed Accidents

Figure 15. Observed versus Predicted Accident Frequency: TOTACCI Main Model 
93 

Variant 3

The parameter estimates, their standard errors, and p-values are provided in table 90. 

In the revised original model all of the variables were estimated as insignificant, while 

only AADT2 was insignificant in the original model. There were also differences in the 

magnitude of the parameters. The overdispersion parameter, K, was almost twice as high 

as that for the original model. 

For the Georgia data, the constant term, AADT1, AADT2, and VEICOM were estimated 

with the same sign as the reported model, but there were slight differences in magnitude. 

PROT_LT and DRWY1 were estimated with an opposite sign to that in the original 

model, but these were insignificant. VEICOM was also insignificant. The overdispersion 

parameter K was significantly higher than that for the original model, indicating lack-offit to the Georgia data. 

Table 90. Parameter Estimates for TOTACC Type V Model Using 

Georgia Data: Variant 3 

Variable 

Original Estimate1

(s.e., p-value) 

Revised Estimates2

(s.e, p-value) 

Georgia Data3

0.04 Mile 

(s.e., p-value) 

Georgia Data3

0.05 Mile 

(s.e., p-value) 

Constant 

 

-5.4581 

(3.1937, 0.0874) 

-2.783 

(3.472, 0.6277) 

-6.475 

(2.872, 0.0441) 

-6.006 

(3.367, 0.1146) 

Log of 

AADT1 

0.5995 

(0.2795, 0.0319) 

0.265 

(0.298, 0.3732) 

0.713 

(0.289, 0.0137) 

0.663 

(0.324, 0.0405) 

Log of 

AADT2 

0.2015 

(0.1917, 0.2932) 

0.219 

(0.255, 0.3911) 

0.188 

(0.156, 0.2291) 

0.187 

(0.159, 0.2397) 

PROT_LT 

-0.4041 

(0.1883, 0.0319) 

-0.222 

(0.199, 0.2666) 

0.591 

(0.400, 0.1402) 

0.617 

(0.422, 0.1437) 

PKLEFT2 

-0.0177 

(0.0050, 0.0005) N/A5 N/A5 N/A5

VEICOM 

0.1114 

(0.0326, 0.0006) 

0.070 

(0.068, 0.3049) 

0.021 

(0.170, 0.8998) 

0.021 

(0.175, 0.9023) 

PKTRUCK 

0.0256 

(0.0117, 0.0287) N/A5 N/A5 N/A5

DRWY1

0.0407 

(0.0246, 0.0983) 

0.047 

(0.036, 0.1874) 

-0.033 

(0.064, 0.6011) 

-0.031 

(0.062, 0.6153) 

K4 0.1145 0.208 0.725 0.704 1

 Vogt, 1999, (p. 123) 

2

 Coefficient estimates of the variables were reproduced without PKLEFT2 and PKTRUCK using the 

 original data 

3

 PKLEFT2 and PKTRUCK were not included in the model 

4

 K: Overdispersion value 

 5 N/A: not available 

Table 91 shows the validation statistics. The Pearson product-moment correlation 

coefficient of the revised original model was estimated to be the same as the original 

model. The MPB and MAD per year were somewhat larger than for the original model. 

The MSE per was also higher than that for the original model. 
94 

Table 91. Validation Statistics for TOTACCI Type V Model Using 

Georgia Data: Variant 3 

Georgia2

Measure 

 Variant 31

Revised 

Variant 32 0.04 Mile 0.05 Mile 

Years used for validation 1993-95 1993-95 1996-97 1996-97 

Number of sites 49 49 51 51 

Pearson product-moment 

correlation coefficients 

 

0.67 

 

0.67 

 

0.22 

 

0.22 

MPB -0.31 -5.41 -5.49 -5.25 

MPB/yr -0.10 -1.80 -2.74 -2.63 

MAD 5.34 6.67 8.68 8.68 

MAD/yr 1.78 2.22 4.34 4.34 

MSE 51.57 98.20 

MSE/yr2 5.73 10.91 

N/A3

 N/A3

MSPE 118.60 119.85 

MSPE/yr2 N/A3

 N/A3

29.65 29.96 1

 Variant 3 in the report; this model includes PKLEFT2 and PKTRUCK 

2

 Used the same coefficients as Variant 3, but PKLEFT2 and PKTRUCK were removed from the model by 

 dividing by the exponential value of the coefficient of these variables times their average effects 

3 N/A: not available

A value of 0.22 of the Pearson correlation coefficient indicates that the accident 

predictions by the original model are marginally linearly correlated with observed 

number of accidents in the 1996 to 1997 period. The MPBs and MADs per year for the 

Georgia data were larger than those for the original models. The MSPEs were also 

significantly higher than the MSEs, which suggests lack-of-fit to the Georgia data. 

Figure 16 depicts the prediction performance of the original model for individual sites in 

the Georgia 0.05-mile data. It is quite evident that the original model generally does not 

fit the Georgia data well, a finding that would have been expected on the basis of the low 

Pearson product-moment coefficients. 
95 

0

10

20

30

40

50

60

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Sites

No. of Accidents

Predicted Accidents

Observed Accidents

Figure 16. Observed versus Predicted Accident Frequency: TOTACCI Variant 3 

Injury Accident Model (INJACC) 

The parameter estimates, their standard errors, and p-values are provided in table 92. The 

models estimated with the Georgia data generally showed differences in sign, magnitude, 

and significance of the parameter estimates. PROT_LT and VEICOM were estimated 

with an opposite sign to those in the original model, although they were insignificant. The 

constant term and AADT1*AADT2 were estimated with the same direction of effect and 

in general a similar degree of magnitude and significance to the original model. The 

overdispersion parameter K was significantly higher than that for the original model. 

Table 93 shows the GOF measures for the original injury accident model in the Vogt 

report applied to the Georgia data.(2)

The Pearson product-moment correlation coefficient was similar to that for the TOTACC 

model. However, the MPB, MAD, and MSPE per year squared were smaller. 
96 

Table 92. Parameter Estimates for INJACC Type V Model Using Georgia Data 

Variable 

Original Estimate1

(s.e., p-value) 

Georgia Data 0.04 Mile2

(s.e., p-value) 

Georgia Data 0.05 Mile2

(s.e., p-value) 

-3.2562 -3.952 -3.815 

Constant (2.9932, 0.2767) (2.455, 0.1845) (2.437, 0.2002) 

Log of 

AADT1*AADT2 

0.2358 

(0.1722, 0.1707) 

0.239 

(0.150, 0.1100) 

0.234 

(0.149, 0.1153) 

PROT_LT 

-0.2943 

(0.1864, 0.1144) 

0.439 

(0.398, 0.2700) 

0.361 

(0.397, 0.3640) 

-0.0113 

PKLEFT2 (0.0062, 0.0678) N/A4 N/A4

0.0822 -0.007 0.008 

VEICOM (0.0551, 0.1358) (0.177, 0.9683) (0.179, 0.9641) 

0.0323 

PKTRUCK (0.0146, 0.0267) N/A4 N/A4

K3 0.1630 0.647 0.662 1

 Vogt, 1999, (p. 124) 

2

 PKLEFT2 and PKTRUCK were not included in the model

3

 K: Overdispersion value 

 4 N/A: not available 

Table 93. Validation Statistics for INJACC Type V Model Using Georgia Data 

Georgia data1

Measure 

 0.04 Mile 0.05 Mile 

Years used for validation 1996-1997 1996-1997 

Number of sites 51 51 

Pearson product-moment 

correlation coefficients 

 

0.15 

 

0.15 

MPB -1.99 -1.89 

MPB/yr -1.00 -0.95 

MAD 2.89 2.82 

MAD/yr 1.45 1.41 

MSPE 11.24 11.00 

MSPE/yr2 2.81 2.75 1 Used the same coefficients as the original model, but PKLEFT2 and PKTRUCK were removed 

 from the model by dividing by the exponential value of the coefficient of these variables times 

 their average effects 

 2 K: Overdispersion value 

Figure 17 depicts the prediction performance of the original model for individual sites in 

the Georgia 0.05-mile data. It is quite evident that the original model generally does not 

fit the Georgia data well, a finding that would have been expected on the basis of the low 

Pearson product-moment coefficients. 
97 

0

2

4

6

8

10

12

14

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Sites

No. of Accidents

Predicted Injury

Observed Injury

Figure 17. Observed versus Predicted Accident Frequency: INJACC 

Intersection Related Total Injury Accident Model (INJACCI) 

The parameter estimates, their standard errors, and p-values are provided in table 94. For 

the Georgia data, the constant term, AADT1*AADT2, and VEICOM were estimated with 

the same sign but with differences in magnitude and significance. The constant term and 

AADT1*AADT2 were estimated as significant, while they were insignificant in the 

original model. The overdispersion parameters, K, were significantly higher than that for 

the original model. 

Table 95 shows the GOF measures for the original intersection related injury accident 

model (Variant 1) in the Vogt report applied to the Georgia data.(2) 

The Pearson product-moment correlation coefficient was slightly higher than for the 

TOTACCI model, and the MPB, MAD, and MSPE per year squared were smaller. 
98 

Table 94. Parameter Estimates for INJACCI Type V Model Using Georgia Data 

Variable 

Original Estimate1

(s.e., p-value) 

Georgia Data 

0.04 Mile2

(s.e., p-value) 

Georgia Data 

0.05 Mile2

 

(s.e., p-value) 

-1.5475 -5.029 -4.777 

Constant (3.0298, 0.6095) (2.904, 0.0384) (2.100, 0.0518) 

Log of 

AADT1*AADT2 

0.1290 

(0.1757, 0.4627) 

0.302 

(0.127, 0.0176) 

0.288 

(0.127, 0.0237) 

-0.0149 

PKLEFT2 (0.0066, 0.0250) N/A4 N/A4

0.0686 0.054 0.062 

VEICOM (0.0692, 0.1858) (0.187, 0.7731) (0.188, 0.7420) 

0.0282 

PKTRUCK (0.0152, 0.0628) N/A4 N/A4

K3 0.1433 0.752 0.754 1

 Vogt, 1999, (p. 124) 

2

 PKLEFT2 and PKTRUCK were not included in the model

3

 K: Overdispersion value 

 4 N/A: not available 

Table 95. Validation Statistics for INJACC Type V Model Using Georgia Data 

Georgia1

 

Measure 

0.04 Mile 0.05 Mile 

Years used for validation 1996-1997 1996-1997 

Number of sites 51 51 

Pearson product-moment 

correlation coefficients 

 

0.27 

 

0.27 

MPB -2.60 -2.52 

MPB/yr -1.30 -1.26 

MAD 3.25 3.18 

MAD/yr 1.62 1.59 

MSPE 12.84 12.56 

MSPE/yr2 3.21 3.14 1 Used the same coefficients as the original model, but PKLEFT2 and PKTRUCK were removed 

 from the model by dividing by the exponential value of the coefficient of these variables times 

 their average effects 

 2 K: Overdispersion value 

Figure 18 depicts the prediction performance of the original model for individual sites in 

the Georgia 0.05-mile data. It is quite evident that the original model generally does not 

fit the Georgia data well, a finding that would have been expected on the basis of the low 

Pearson product-moment coefficients. 
99 

0

2

4

6

8

10

12

14

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Sites

No. of Accidents

Predicted INJACCI

Observed INJACCI

Figure 18. Observed versus Predicted Accident Frequency: INJACCI 

2.6 VALIDATION ACTIVITY 3: VALIDATION OF THE ACCIDENT 

PREDICTION ALGORITHM 

Two tasks were undertaken to validate the accident prediction algorithm in Harwood et 

al.:(3) 

1. Validate the recommended base models for sites meeting “base” conditions. 

2. Validate the accident prediction algorithm against all Georgia sites and California 

and Michigan datasets for Model V. 

The Minnesota and Washington data could not be used for validating the algorithms for 

models I and II because sight distance, one of the variables for which an AMF is applied, 

was not known at these sites. 

Data Limitations in the Michigan Data 

As previously discussed for validation activity 2, it was discovered subsequent to the 

analysis and draft report that the later year crossroad accident numbers at the Michigan 

Type V sites should be systematically higher than the values used. The various measures 

of GOF statistics would be also improved if the higher numbers were used. Although the 

GOF measures should improve, the conclusions drawn from these data and the Georgia 

data would not change since Model V is in need of recalibration in any case. 
100 

2.6.1 Validation of the Base Models 

Model I 

The recommended base model for type I intersections is: 

 

 (8) 

where 

Nbi = the expected number of annual intersection-related collisions; 

AADT1 = average daily traffic volume on the major road; and 

AADT2 = average daily traffic volume on the minor road. 

The following are the base conditions to which the model applies: 

• Roadside hazard rating = 2. 

• Presence of right-turn lane on major road = none present. 

• Presence of left-turn lane on major road = none present. 

• Skew = none. 

• Sight Distance = no restrictions. 

The roadside hazard rating is not a restriction for a “base” intersection because no AMF 

is provided for roadside hazard rating. Only 11 sites in the Georgia data met the base 

conditions. Summary accident statistics for these sites are shown in table 96. 

Table 96. Summary Accident Statistics for Sites Meeting Base Conditions 

No. Sites = 11 

No. Years = 2 Mean Median Std. Deviation Minimum Maximum 

Georgia Data 0.04 Mile 

1.00 

(0.50/year) 1.00 0.77 0 2 

Georgia Data 0.05 Mile 

1.00 

(0.50/year) 1.00 0.77 0 2 

Table 97 shows the validation statistics for the 11 Type I base model intersections. 

Nbi = exp(-10.9 + 0.79lnAADT1 + 0.49lnAADT2) 
101 

Table 97. Validation Statistics for Type I Base Model Intersections 

Measure Georgia Data 0.04 Mile Georgia Data 0.05 Mile 

Years used for validation 1996-1997 1996-1997 

Number of sites 11 11 

Pearson product-moment 

correlation coefficients -0.26 -0.26 

MPB 

MPB/yr 

0.36 

0.18 

0.36 

0.18 

MAD 

MAD/yr 

0.94 

0.47 

0.94 

0.47 

MSE 

MSE/yr2 N/A1

MSPE 

MSPE/yr2

1.29 

0.32 

1.29 

0.32 

1

 MSE is unknown since these statistics were not given in the report (Harwood et al., 2000) 

2

 K: Overdispersion value 

The Pearson correlation coefficients indicate a negative correlation between the base 

model predictions and the observed number of accidents. The other statistics also indicate 

a relatively poor fit, although it should be considered that only eleven sites were available 

for this validation activity. 

Model II 

The recommended base model for type II intersections is: 

 

 (9) 

where 

Nbi = the expected number of annual intersection-related collisions; 

AADT1 = average daily traffic volume on the major road; and 

AADT2 = average daily traffic volume on the minor road. 

The following are the base conditions to which the model applies: 

• No driveways within 76.25 m (250 ft) of the intersection on the major road. 

• Presence of right-turn lane on major road = none present. 

• Presence of left-turn lane on major road = none present. 

• Skew = none. 

• Sight Distance = no restrictions. 

The number of driveways is not a restriction for a ‘base’ intersection because no AMF is 

provided for driveway density. Only nine sites in the Georgia data met the base 

conditions. Summary accident statistics for these sites are shown in table 98. 

Nbi = exp(-9.34 + 0.60lnAADT1 + 0.61lnAADT2)
102 

Table 98. Summary Accident Statistics for Sites Meeting Base Conditions 

No. Sites = 9 

No. Years = 2 Mean Median Std. Deviation Minimum Maximum 

Georgia Data 0.04 Mile 

3.00 

(1.50/yr) 1.00 4.09 0 12 

Georgia Data 0.05 Mile 

3.00 

(1.50/yr) 1.00 4.09 0 12 

Table 99 shows the validation statistics for the nine Type II base model intersections. 

Table 99. Validation Statistics for Type II Base Model Intersections 

Measure Georgia Data 0.04 Mile Georgia Data 0.05 Mile 

Years used for validation 1996-1997 1996-1997 

Number of sites 9 9 

Pearson product-moment 

correlation coefficients 0.81 0.81 

MPB 1.78 1.78 

MPB/yr 0.89 0.89 

MAD 2.15 2.15 

MAD/yr 1.08 1.08 

MSE 

MSE/yr2 N/A1

MSPE 12.90 12.90 

MSPE/yr2 3.23 3.23 1 MSE is unknown since these statistics were not given in the report (Harwood et al., 2000) 

 2 K: Overdispersion value 

The Pearson correlation coefficients indicate a high correlation between the base model 

predictions and observed number of accidents. The other statistics, however, indicate a 

poor fit, although it should be considered that only nine sites were available for validation. 

Model V 

The base model in the accident prediction algorithm is identical to the Variant 3 of the 

Vogt model for TOTACCI. 

(10) 

 

Nbi = exp(-5.46 + 0.60 lnAADT1 + 0.20 lnAADT2–0.40 PROT_LT – 0.018PKLEFT2 + 0.11 

VEICOM + 0.026 PKTRUCK + 0.041DRWY1)
103 

where 

Nbi = predicted number of total intersection-related accidents per year for nominal or base 

 conditions; 

PROT_LT = presence of protected left-turn signal phase on one or more major-road 

 approaches; = 1 if present; = 0 if not present; 

PKLEFT2 = percentage of minor-road traffic that turns left at the signal during the 

 morning and evening hours combined; 

VEICOM = grade rate for all vertical curves (crests and sags) within 76.25 m 

(250 ft)) of the intersection along the major and minor roads; 

PKTRUCK = percentage of trucks (vehicles with more than four wheels) entering the 

 intersection for the morning and evening hours combined; and 

DRWY1 = number of driveways within 76 m (250 ft) of the intersection on the major 

road. 

With the nominal conditions of PRTO_LT, PKLEFT2, VEICOM, and PKTRUCK, the 

base model reduces to: 

 (11) 

The following are the base conditions to which the model applies: 

• No PROT_LT. 

• 28.4 percent of PKLEFT2. 

• No VEICOM. 

• 9.0 percent of PKTRUCK. 

• No DRWY1. 

 

Because none of the Georgia sites met the base conditions for the base model in equation 

(11), and the independent variables in equation (10) are available in the Georgia data, the 

base model in equation (10) was used for validation. Table 113 shows the validation 

statistics for this base model. Because PKLEFT2 and PKTRUCK were not included in 

the Georgia data, they were removed from the models by dividing both sites of models by 

the exponential values of the coefficients of the variables times their average effects (the 

average effects of PKLEFT2 and PKTRUCK are the average values of PKLEFT2 and 

PKTRUCK). 

The validation statistics are shown in table 100. Lower Pearson product-moment 

correlation coefficients (0.36 and 0.22 in table 100) for the additional years of accidents 

and the Georgia data indicate that the accident predictions by the base model are not 

strongly correlated with additional years of accidents and are marginally correlated with 

the Georgia data, at best. The MPBs and MAD per year was larger than those for the 

original years. The MSPEs per year squared were higher than the MSEs per year squared. 

In particular, the MSPEs per year squared with the Georgia data were more than twice as 

high as the MSEs per year squared, which indicates that the model is performing poorly 

against the Georgia data. 

Nbi = exp(-5.73 + 0.60 lnAADT1 + 0.20 lnAADT2)
104 

Table 100. Validation Statistics for Type V Base Model Intersections 

California and Michigan1 Georgia1

Measure 93-95 Year 96-97 Year 0.04 Mile 0.05 Mile 

Years used for validation 1993-1995 1996-1997 1996-1997 1996-1997 

Number of sites 49 49 51 51 

Pearson product-moment 

correlation coefficients 0.68 0.36 0.22 0.22 

MPB -5.22 -6.37 -5.85 -5.18 

MPB/yr -1.74 -3.18 -2.93 -2.59 

MAD 6.58 7.39 9.06 8.63 

MAD/yr 2.19 3.70 4.53 4.31 

MSE 85.24 

MSE/yr2 10.58 

N/A2

 N/A2 N/A2

MSPE 86.93 129.00 118.80 

MSPE/yr2 N/A2

21.73 32.25 29.70 1

 Used the same coefficients in the Variant 3, but PKLEFT2 and PKTRUCK were removed from the model 

 by dividing by the exponential value of the coefficient of these variables times their average effects. 2

 MSE is unknown since these statistics were not given in the report (Harwood et al., 2000) 

2.6.2 Validation of the Accident Prediction Algorithm 

The accident prediction algorithm was validated against the data collected in Georgia 

using the recommended base models and AMFs provided in Harwood et al. in 2000.(3) 

These AMFs are shown in table 101. The AMFs provided in a 2002 report by Harwood et 

al. also were validated.(5) These AMFs are shown in table 101 in brackets. 
105 

Table 101. The AMFs for Type I, II, and V Intersections 

AMF 

Variable Type I Intersections Type II Intersections Type V Intersections 

Intersection Skew exp(0.004*SKEW) exp(0.0054*SKEW) 1.00 

Left-Turn Lane on 

Major 

1.00 if none exist 

0.78 if at least one exists 

(0.56 if at least one exists) 

1.00 if none exist 

0.76 on one approach 

(0.72 on one approach) 

0.58 on both 

approaches 

(0.52 on both 

approaches) 

1.00 if none exist 

0.82 on one approach 

0.67 on both approaches 

Right-Turn Lane on 

Major 

1.00 if none exist 

0.95 on one approach 

(0.86 on one approach) 

0.90 on both approaches 

(0.74 on both approaches) 

1.00 if none exist 

0.975 on one approach 

(0.96 on one approach) 

0.95 on both approaches 

(0.92 on both approaches) 

Sight Distance 1.00 if adequate in all quadrants 

1.05 if limited in one quadrant 

1.10 if limited in two quadrants 

1.15 if limited in three quadrants 

1.20 if limited in four quadrants 

1.00 

Intersection skew is defined as the deviation from an intersection angle of 90 degrees and 

carries a positive or negative sign that indicates whether the minor road intersects the 

major road at an acute or obtuse angle. 

Left-Turn Lane on Major takes a value of one if no left-turn lane exists on the major road 

and the values in table 101 where one or more exists. 

Right-Turn Lane on Major takes a value of one if no right-turn lane exists on the major 

road and the values in table 101 where one or more exists. 

Sight Distance in a quadrant is considered limited if the available sight distance is less 

than that specified by the American Association of State Highway and Transportation 

Officials (AASHTO) policy for left and right turns from the minor road for a design 

speed of 20 km/hour (km/hr) (12.5 miles/hr) less than the major road design speed.(7)

In the Georgia data, design speed of the major road was not known. The posted speed 

limit of the major road was used in lieu of subtracting 20 km/hr (12.5 miles/hr) from the 

design speed when using the AASHTO warrant for sight distance. 

In applying the algorithm, a calibration factor is applied to the model, calculated as the 

ratio of the observed number of accidents to the predicted number of accidents prior to 

the calibration factor being applied. Harwood et al. recommend that the sample for 

estimating this calibration factor be such that the distribution of traffic volumes is similar 

to that in the data used for the original calibration.(3) This was not possible for the 

Georgia data due to the small sample size. It was felt that this should not create a 

deterrent, because the calibration factor, at least in the procedure as proposed, is 
106 

independent of traffic volume and is applied to all intersections regardless of the 

distribution of traffic volumes in the jurisdiction. Therefore, it is of interest to examine if 

the procedure would work for the likely situation where the distribution of traffic 

volumes in the new jurisdiction is different from the distribution in the calibration data. 

In the tables of results, the calibration factors greater or less than 1.0 indicate whether 

intersections will experience more or less accidents than the intersections used in the 

development of the base models for the accident prediction algorithm. 

Model I 

Table 102 shows the validation statistics for Type I intersections. For comparison, the 

results for the AMFs provided in the Harwood et al. 2000 report are not bracketed, and 

the results for AMFs provided in Harwood et al. 2002 report are in brackets.(3,5) Low 

Pearson product-moment correlation coefficients with the Georgia data indicate that the 

accident predictions by the algorithm are not correlated strongly with the observed 

number of accidents in the Georgia data. Other validation statistics also suggest a lack-offit to the Georgia data. There is little difference between the two sets of AMFs for turning 

lanes. 

Table 102. Validation Statistics for the Accident Prediction Algorithm: Type I 

Measure Georgia Data 0.04 Mile Georgia Data 0.05 Mile 

Years used for validation 1996-1997 1996-1997 

Number of sites 121 121 

Pearson product-moment 

correlation coefficients 

 0.45 

(0.44) 

0.47 

(0.46) 

MPB 

MPB/yr 

0.00 

0.00 

0.00 

0.00 

MAD 

MAD/yr 

1.13 

0.57 

(1.15) 

(0.58) 

1.18 

0.59 

(1.20) 

(0.60) 

MSE 

MSE/yr2 N/A1

MSPE 

MSPE/yr2

2.59 

0.65 

(2.66) 

(0.67) 

2.82 

0.70 

(2.89) 

(0.72) 

Calibration Factor 

2.57 

(2.60) 

2.73 

(2.76) 1

 MSE is unknown since these statistics were not given in the report (Harwood et al., 2000) 

2

 K: Overdispersion value 

To compare further the two sets of AMFs for turning lanes, the validation statistics were 

calculated for only those sites with a major road turning lane, as shown in table 103. The 

AMFs from Harwood et al. (2000) provided better validation statistics than those in 

Harwood et al. (2002), although the differences in validation statistics and sample sizes 

are small.(3,5) 
107 

Table 103. Validation Statistics for the Accident Prediction Algorithm: Type I Sites 

with a Major Road Turning Lane 

Measure Georgia Data 0.04 Mile Georgia Data 0.05 Mile 

Years used for validation 1996-1997 1996-1997 

Number of sites 

7 

3 with left-turn lane 

4 with right-turn lane 

7 

3 with left-turn lane 

4 with right-turn lane 

Pearson product-moment 

correlation coefficients 

 0.85 

(0.78) 

0.66 

(0.52) 

MPB 

MPB/yr 

0.00 

0.00 

0.00 

0.00 

MAD 

MAD/yr 

0.036 

0.018 

(0.052) 

(0.026) 

0.043 

0.022 

(0.059) 

(0.030) 

MSE 

MSE/yr2 N/A1

MSPE 

MSPE/yr2

0.045 

0.011 

(0.084) 

(0.021) 

0.059 

0.015 

(0.097) 

(0.024) 

Calibration factor 

2.57 

(2.60) 

2.73 

(2.76) 1

 MSE is unknown since these statistics were not given in the report (Harwood et al., 2000) 

2

 K: Overdispersion value 

Model II 

Table 104 shows the validation statistics for Type II intersections. For comparison, the 

results for the AMFs provided in Harwood et al. (2000) are not bracketed, and the results 

for AMFs provided in Harwood et al. (2002) are in brackets.(3,5) Low Pearson productmoment correlation coefficients with the Georgia data indicate that the accident 

predictions by the algorithm are not correlated strongly with the observed number of 

accidents in the Georgia data. Other validation statistics also suggest lack-of-fit to the 

Georgia data. There is little difference between the two sets of AMFs for turning lanes. 
108 

Table 104. Validation Statistics for the Accident Prediction Algorithm: Type II 

Measure Georgia Data 0.04 Mile Georgia Data 0.05 Mile 

Number of years 2 2 

Number of sites 114 114 

Pearson product-moment 

correlation coefficients 

 

0.53 

(0.51) 

 

0.53 

(0.51) 

MPB 

MPB/yr 

0.00 

0.00 

0.00 

0.00 

MAD 

MAD/yr 

1.69 

0.85 

(1.72) 

(0.86) 

1.70 

0.85 

(1.72) 

(0.86) 

MSE 

MSE/yr2 N/A1

MSPE 

MSPE/yr2

5.45 

1.36 

(5.59) 

(1.40) 

5.46 

1.36 

(5.60) 

(1.40) 

Calibration Factor 2.15 

(2.18) 

2.17 

(2.20) 1

 MSE is unknown because these statistics were not given in the report (Harwood et al., 2000) 

2

 K: Overdispersion value 

To compare further the two sets of AMFs for turning lanes, the validation statistics were 

calculated for only those sites with a major road turning lane. As the results in table 105 

indicate, the AMFs from Harwood et al. (2000) provided better validation statistics than 

those in Harwood et al. (2002), although the differences in validation statistics and 

sample sizes are small.(3,5) 

Model V 

Again, the base model in the equation (10) was used for the accident prediction algorithm, 

because none of the sites met the nominal base conditions. PKLEFT2 and PKTRUCK 

were removed from the model by dividing by the exponential values of the coefficients of 

these variables times their average effects. 

Table 106 shows the validation statistics for Type V intersections. For comparison, the 

results for the AMFs provided in Harwood et al. (2000) are not bracketed, and the results 

for AMFs provided in Harwood et al. (2002) are in brackets.(3,5) The validation statistics 

suggest a lack-of-fit to the Georgia data. 
109 

Table 105. Validation Statistics for the Accident Prediction Algorithm: Type II Sites 

with a Major Road Turning Lane 

Measure Georgia Data 0.04 Mile Georgia Data 0.05 Mile 

Number of years 2 2 

Number of sites 

7 

6 with left-turn lane on 

both approaches 

3 with right-turn lane 

7 

6 with left-turn lane on 

both approaches 

3 with right-turn lane 

Pearson product-moment 

correlation coefficients 

0.52 

(0.47) 

0.52 

(0.47) 

MPB 

MPB/yr 

0.00 

0.00 

0.00 

0.00 

MAD 

MAD/yr 

0.158 

0.079 

(0.175) 

(0.088) 

0.158 

0.079 

(0.174) 

(0.087) 

MSE 

MSE/yr2 N/A1

MSPE 

MSPE/yr2

0.74 

0.19 

(0.89) 

(0.22) 

0.73 

0.18 

(0.88) 

(0.22) 

Calibration Factor 2.15 

(2.18) 

2.17 

(2.20) 1

 MSE is unknown since these statistics were not given in the report (Harwood et al., 2000) 

2

 K: Overdispersion value
110 

Table 106. Validation Statistics for the Accident Prediction Algorithm: Type V 

Measure Georgia Data 0.04 Mile Georgia Data 0.05 Mile 

Number of years 2 2 

Number of sites 51 51 

Pearson product-moment 

correlation coefficients 

 0.04 

(0.05) 

 0.05 

(0.05) 

MPB 

MPB/yr 

0.00 

0.00 

0.00 

0.00 

MAD 

MAD/yr 

6.99 

3.49 

(6.94) 

(3.47) 

7.14 

3.57 

(7.09) 

(3.55) 

MSE 

MSE/yr2 N/A1

MSPE 

MSPE/yr2

89.23 

22.31 

(89.56) 

(22.39) 

93.89 

23.47 

(94.18) 

(23.55) 

Calibration Factor 0.81 

(0.83) 

0.83 

(0.85) 1

 Used the same coefficients as Variant 3, but PKLEFT2 and PKTRUCK were removed from the model by 

 dividing by the exponential value of the coefficient of these variables times their average effects 2

 MSE is unknown since these statistics were not given in the report (Harwood et al., 2000) 

To compare further the two AMFs for right turn on major road, the validation statistics 

were calculated for only those sites with a major road right-turn lane. These results are 

shown in table 107. There is little difference between the two AMFs, not surprising given 

the closeness of their estimates. 
111 

Table 107. Validation Statistics for the Accident Prediction Algorithm: Type V Sites 

with a Major Road Right-Turn Lane 

Measure Georgia Data 0.04 Mile Georgia Data 0.05 Mile 

Number of years 2 2 

Number of sites 

21 

(13 with right-turn lane on 

one approach, 

8 with right-turn lane on 

both approaches) 

21 

(13 with right-turn lane on 

one approach, 

8 with right-turn lane on 

both approaches) 

Pearson product-moment 

correlation coefficients 

 

0.12 

(0.11) 

 

0.13 

(0.12) 

MPB 

MPB/yr 

0.00 

0.00 

0.00 

0.00 

MAD 

MAD/yr 

8.21 

4.11 

(8.24) 

(4.12) 

8.41 

4.11 

(8.44) 

(4.22) 

MSE 

MSE/yr2 N/A1

MSPE 

MSPE/yr2

49.55 

12.39 

(50.07) 

(12.52) 

52.82 

13.21 

(53.37) 

(13.34) 

Calibration Factor 1.40 

(1.43) 

1.43 

(1.46) 1

 MSE is unknown because these statistics were not given in the report (Harwood et al., 2000) 

2.7 DISCUSSION OF RESULTS 

Although the body of this report presented validation results in order of validation 

exercises, the results here are presented by model, beginning with Model I results and 

ending with Model V results. The validation exercises in the body of this report focused 

primarily on external validation—validation concerned with assessing performance of the 

models compared to external data. This discussion is focused on internal validation 

concerns—the internal coherence, structure, theoretical soundness, and plausibility of the 

models proposed. More focus is given to internal validation in the recalibration research 

task scheduled to follow this validation. 

The discussion provided here focuses primarily on summarizing the results that are 

detailed and discussed in the body of this report, and translating these results into 

meaningful observations and conclusions. The intent of the discussion is to provide 

insight and lay groundwork for the recalibration of the models to follow. The reader 

interested in additional details, such as sources of original results and comparison tables, 

should refer to the body of the report. Descriptions of all variable abbreviations and 

definitions used in this report are found at the beginning of this document. 

It should be noted throughout the discussion that the subjective criteria of alpha equal to 

0.10 is used. The support for this level of alpha is as follows. In statistical models of 
112 

crash occurrence, a Type II error can be argued to be more serious than a Type I error. 

With a Type I error, the analyst concludes that the null hypothesis is false when in fact it 

is true with alpha probability (this translation is not precise, but the precise and correct 

conditional probability interpretation is cumbersome and for practical purposes does not 

lend any additional insights). This means that the analyst would conclude, for example, 

that the presence of a left-turn lane reduces crashes when in reality it does not. As a result 

of this conclusion one might install left-turn lanes without realizing a reduction in crashes. 

In addition, the relatively small sample sizes and preponderance of engineering 

theoretical support for variable selection decisions also supports a relatively larger alpha. 

A Type II error occurs with beta probability. In general, the larger the alpha, the smaller 

is the beta. So choosing a larger alpha means that a smaller beta has been chosen, all else 

being equal. Thus, continuing with the previous example, making a Type II error results 

in concluding that the presence of a left-turn lane does not reduce crashes when in fact it 

does. The risk is in failing to install an effective countermeasure. To summarize, 

committing a Type I error results in applying an ineffective countermeasure, while 

committing a Type II error results in failing to apply an effective countermeasure. 

Computing the actual beta in negative binomial models is extremely difficult. However, 

knowing that a fairly liberal alpha equal to 0.10 has been used suggests that a smaller 

level of beta has also been selected. 

GOF statistics provide an ability to objectively assess the fit of a model to data. 

Comparisons between models, however, are generally subjective. In the following 

analyses the terms “serious,” “moderate,” and “marginal” are applied to denote a 

subjective evaluation of GOF comparisons between models. Serious differences in GOF 

are suggestive of noteworthy or significant model deficiencies. Moderate differences in 

GOF suggest cases where models could be improved, but improvements might be 

difficult to obtain. Marginal differences in GOF are thought to be negligible and are 

potentially explained by random fluctuations in the observed data. 

Before discussing the results, it should be noted that an attempt to reproduce variables in 

data acquired from the original research revealed some definitional problems. These 

definitional problems resulted in values of some variables that are different than they 

would have been in the original research. Small differences in the variable VCI1 for 

Models I and II are thought to stem from an inability to reproduce “exceptional” cases of 

vertical curvatures encountered in the database. For Model II, the variables AADT1 and 

DEV had small differences in the median values, and these were considered to be 

marginal. For Model V, the vertical-alignment related variables VEI1, VEI2, and 

VEICOM computed in the original models could not be reproduced precisely in data 

acquired from the original researchers. For Models III and IV, all of the variables in data 

acquired from the original researchers were reproduced within rounding-error precision. 

These differences, on the whole, are unlikely to materially affect the overall conclusions, 

although they may contribute to an explanation for some individual results. 

2.7.1 Model I 
113 

Predictive Ability Across Time 

To the extent possible, new data were collected from later time periods to validate the 

crash models (see table 3). Note that it was discovered subsequent to the analysis and 

draft report that some errors exist in the accident data due to changing mileposts although 

these errors are negligible and would have no effect on any conclusions drawn from the 

analysis. 

Table 4 shows a comparison of the parameter estimates for the original published total 

accidents model and one based on the additional data. As might be expected, variables 

that were not statistically significant in the original model were not statistically 

significant in the model based on additional years of data, with one exception. The 

variable SPD1 became a highly significant variable, compared to marginally significant 

in the original model, while, conversely, the RT MAJ and HAZRAT1 became 

statistically insignificant, with the former having the opposite sign. 

Table 5 shows the GOF statistics of Model I (total accidents model) on the additional 

years of data. The evidence in the table suggests that the original model is predicting 

future crashes as well as for the calibration data. All of the GOF statistics showed 

marginal differences between the validation data and the calibration (estimation) data. 

Predictive Ability Across Space 

Georgia data were used to investigate the model’s performance across jurisdictional 

boundaries. Data used to estimate Model I were obtained from Minnesota. Comparison of 

the recalibrated and original models for TOTAL crashes (table 53) shows that HI1, HAU, 

and RT MAJ had the opposite sign for the Georgia data, with RT MAJ becoming 

insignificant for Georgia. For INJURY crashes, all model variables, with the exception of 

the main road AADT, were insignificant when estimated with Georgia data, and HI1, RT 

MAJ, HAU, and SPD1 had the opposite signs than those in the original model (table 55). 

The validation statistics for the TOTAL crashes model (see table 54) show that the 

correlation coefficient (0.66) between observed and predicted crashes is reduced by about 

50 percent (0.31) on Georgia data—a rather serious drop. Other statistics also show 

considerable lack-of-fit of the Georgia data relative to the Minnesota data. The MSE per 

year squared of 0.19 for the recalibrated model compares to an MSPE per year squared of 

0.89, which represents a serious difference in fit. This difference suggests that the 

original model is not capturing the variability in crashes in the Georgia data. 

Crash Prediction Algorithms 

Eleven sites in Georgia were available for validating the base condition for the crash 

prediction algorithm (see table 96). Despite the small sample size, the correlation 

coefficient between predicted and observed crashes for the base condition model was 

-0.26 (see table 97), indicating a marginal to moderate model deficiency—downgraded 

from serious due to the small sample size. Because of the small sample size and the 

homogenous nature of the intersections (all possess base conditions in common), the base 

model predicts as a function of minor and major road AADTs only. 
114 

Model I Assessment and Conclusions 

The model for three-legged stop controlled intersections with two lanes both on minor 

and major roads has fairly mixed validation results. The major assessments and 

conclusions derived from the analysis include the following: 

• The model performed better in the same jurisdiction (Minnesota) in a future time 

period than across a different jurisdiction (Georgia). This suggests that variables 

that quantify differences in facility design, traffic, or environmental conditions 

across States are missing from the model. 

• Potential missing variables might include number of wet, icy, or foggy days, dark 

(nighttime) versus light (daylight) crashes. 

• Presence of right-turn lanes (RT MAJ) can pose a problem in intersection models. 

If installed at intersections due to mostly capacity problems, then the presence 

might indicate an improvement in crashes (due to reduction in conflicts and 

crashes). If installed due to high-crash conditions or in conjunction with another 

intersection improvement prompted by high-crash conditions, the presence of a 

right-turn lane might be associated with increased numbers of crashes. This 

phenomenon might explain the switching of the sign associated with the RT MAJ 

variable observed in the validation effort associated with Model I and other 

models. 

• Because the model will be used for predictions in jurisdictions other than 

Minnesota, improvements to the models predictive power is desired. 

2.7.2 Model II 

Predictive Ability Across Time 

To the extent possible, new data were collected from later time periods to validate the 

crash models. Note that Minnesota data were used in the original model calibration 

(estimation), and only the additional years of data for Minnesota data could be used for 

the validation test across time. It was discovered subsequent to the analysis and draft 

report that some errors exist in the accident data due to changing mileposts, although 

these errors are negligible and would have no effect on any conclusions drawn from the 

analysis. 

Table 13 shows a comparison of the parameter estimates for the original TOTAL crash 

model and one based on the additional years of data. The constant term and all variables 

had the same signs, but most had large differences in magnitude, in particular those with 

low significance in both models. The model based on additional years gains the HI1 

variable as statistically significant. 

Table 14 shows the GOF statistics of the Type II (TOTAL crashes model) on additional 

years of data. The linear correlation coefficient shows consistent performance into the 

future, and a comparison of MSE per year squared (0.095) and MSPE per year squared 
115 

(0.185) suggests that the variability in future crashes is not being captured as well as for 

the data on which the original model is based. 

Predictive Ability Across Space 

Georgia data were used to investigate the model’s performance across jurisdictional 

boundaries (see table 57). Data used to estimate Model II were obtained from Minnesota. 

Comparison of the original (Minnesota) and Georgia models for TOTAL crashes (table 

58) shows that the two AADT variables had similar magnitudes and are the only 

variables the two models shared as statistically significant. The variable SPD1 became 

statistically significant for Georgia, whereas the variable DRWY1 was statistically 

significant in the original (Minnesota) model. For INJURY crashes, the models again 

shared statistically significant AADT related variables, while the only other statistically 

significant variable was HAZRAT1 in the original (Minnesota) model (see table 60). 

The validation statistics for TOTAL crashes (see table 59) show that the correlation 

coefficient between observed and predicted crashes is reduced by about 50 percent on 

Georgia data—a rather serious drop. Other statistics show a moderate to serious increase 

in lack-of-fit, including increases in MAD (moderate) and a serious increase in MSPE per 

year squared (1.73) compared to MSE per year squared (0.10) in the original model. 

Crash Prediction Algorithms 

Nine sites in Georgia were available for validating the base condition for the crash 

prediction algorithm (see table 98). The correlation coefficient between predicted and 

observed crashes for the base condition model was 0.81 (see table 99), indicating a strong 

linear trend between observed and predicted values. 

Model II Assessment and Conclusions 

The model for four-legged stop controlled intersections with two lanes both on minor and 

major roads has fairly mixed validation results—although they are more favorable than 

for Model Type I. The major assessments and conclusions derived from the analysis 

include the following: 

• The model performed better in the same jurisdiction (Minnesota) in a future time 

period than across a different jurisdiction (Georgia). This suggests that variables 

that quantify differences in facility design, traffic, or environmental conditions 

across States are missing from the model. 

• Potential missing variables might include number of wet, icy, or foggy days, dark 

(nighttime) versus light (daylight) crashes. 

• The flip-flopping of variables that are statistically significant in original and 

validation models suggest that sample sizes, in general, are too small to detect the 

small effects some of the variables have on safety. 

• Since the model will be used for predictions in jurisdictions other than Minnesota, 

improvements to the models predictive power is desired. 
116 

2.7.3 Model III 

Predictive Ability Across Time 

To the extent possible, new data were collected for additional time periods to validate the 

crash models (see table 21). Data from Michigan and California from the years 1996 and 

1997 were used for the validation effort. Recall that the original model was calibrated on 

data from Michigan and California from 1993 to 1995. 

Table 22 shows a comparison of the parameter estimates for the original published 

TOTAL crash model and one based on additional years of data. Comparison of the 

original model and the model based on the later data reveals that two variables, 

MEDWDTH1 and DRWY1, have become statistically insignificant in the additional 

years model. In addition, the coefficient for log of AADT2 is 0.26 in the original model 

and 0.52 in the model based on the additional years of data. The re-estimated models for 

INTERSECTION RELATED total and INJURY crashes (variant 1 and variant 2) are 

shown in table 24, table 26, and table 28. For the INTERSECTION RELATED total 

crash model, the additional years of data did not produce statistically significant variables 

for MEDWDTH1 and DRWY1, while the original model did, and again, the coefficient 

for log of AADT2 was twice as large for the additional years model. Considering variant 

1 of the INJURY models, the variable HAU was not statistically significant for the 

additional years of data; that is unlike the case for the original calibrated model, and the 

coefficient for log of AADT2 was again twice as large for the additional years model. 

Considering variant 2, the variables HAU, DRWY1, and ABSGRD1 became statistically 

significant for the additional years of data. 

Table 23 shows the GOF statistics of Model III for TOTAL crashes on additional years of 

data. The linear correlation coefficient shows a moderate decline when calculated on the 

additional years of data. A comparison of MSE per year squared (1.22) and MSPE per 

year squared (1.39) suggests a marginal increase in lack-of-fit. Similarly, the MAD per 

year shows a marginal increase in lack-of-fit. Table 25, for INTERSECTION RELATED 

crashes, shows similar performance assessments as the model for TOTAL crashes. 

Predictive Ability Across Space 

Georgia data were used to investigate the model’s performance across jurisdictional 

boundaries. A comparison of Georgia data for Model III is shown in table 62. The table 

shows that many variables have similar magnitudes across the calibration (California and 

Michigan) and validation (Georgia) data sets. The one notable exception is 

MEDWIDTH1, which is considerably larger in the Georgia data than in the original data. 

More than half of the Georgia sites had medians on the major road compared to only 5.8 

percent of the original sites. 

Comparison of the original and Georgia models for TOTAL crashes (table 63) shows that 

the models are quite different. In fact, only the variable log of AADT2 is statistically 

significant in the model calibrated using Georgia data, while the original published model 

had all variables, log of AADT1, log of AADT 2, MEDWIDTH1, and DRWY1, as 

statistically significant. Similar results are seen for the TOTAL INTERSECTION 
117 

RELATED crash model (table 65), and variant 1 (table 67) and variant 2 (table 69) of the 

INJURY crash models. Thus, a serious lack of agreement between the originally 

calibrated models and the models estimated using Georgia data is observed. 

All of the validation statistics (see table 64 and table 66) are consistent with the lack of 

agreement in model specification between original and Georgia data. The correlation 

between predicted and observed is seriously different on Georgia data. The MPB and 

MAD statistics show a significant worsening of the fit. Finally, the MSE per year squared 

for the calibration data is considerably lower than the MSPE per year squared for Georgia 

data. The plots of observed and predicted crashes for individual intersections in figures 5 

and 6 shows that predictions are much less variable than are observations. Thus it is 

likely that some of the explanatory variables are inadequate for predicting Georgia data. 

Crash Prediction Algorithms 

There are no AMFs to validate for Model III. 

Model III Assessment and Conclusions 

The model for three-legged stop controlled intersections with two lanes on minor and 

four lanes on major roads revealed some serious model concerns. These concerns are 

summarized below: 

• The TOTAL crash model performs moderately well across time. However, even 

at the same sites the model specification changes significantly in a future time 

period—with the exclusion of two originally significant variables. The models for 

INTERSECTION RELATED TOTAL and INJURY crashes perform similarly, 

but both exhibit moderate to serious model specification difficulties. This 

suggests that variables thought to be important may in fact not be important, or 

are highly correlated with truly important variables. 

• The model was seriously deficient in predicting Georgia data, despite an apparent 

similarity in the raw data. It is clear that variables in the California and Michigan 

model are not specified appropriately for Georgia data. 

• Model III is in need of improvement, based on the validation findings across time 

and space. 
118 

2.7.4 Model IV 

Predictive Ability Across Time 

To the extent possible, new data were collected from later time periods to validate the 

crash models (see table 30). Data from Michigan and California from 1996 and 1997 

were used for this validation effort. Recall that the original model was calibrated on data 

from Michigan and California from 1993 to 1995. 

Table 31 shows a comparison of the parameter estimates for the original published 

TOTAL crash model and one based on the additional years of data. Comparison of the 

original model and the model based on the later data reveals that the model performs very 

well on later data—all of the variables in the model are statistically significant in both 

models. The largest difference is the coefficient of log of AADT2, which changes from 

0.32 in the original published model to 0.50 in the additional years model. All other 

coefficients are similar in magnitude and share the same sign. The same minor 

differences exist for the INTERSECTION RELATED total crash model, shown in table 

33. For the INJURY crash model (see table 38) and the INTERSECTION RELATED 

INJURY crash model (see table 40), the variable log of AADT1 becomes statistically 

insignificant on additional years of data. 

 

Table 32 shows the GOF statistics of Model IV for TOTAL crashes on the additional 

years of data. The linear correlation coefficient shows a marginal increase when 

calculated on the additional years of data. A comparison of MSE per year squared (3.40) 

and MSPE per year squared (2.39) suggests a moderate improvement in the fit to later 

data. The MADs per year is similar, but the MPBs per year indicates a serious lack-of-fit 

to later years of data. Table 34 shows similar performance assessments for the 

INTERSECTION RELATED total crash model. 

Predictive Ability Across Space 

Georgia data were used to investigate the model’s performance across jurisdictional 

boundaries. A comparison of TOTAL crashes compared to Georgia data for Model IV is 

shown in table 71. The table shows that many variables are similar across the calibration 

(California and Michigan) and validation (Georgia) data sets, with the exception of 

LTLNS, which is moderately smaller (70 percent had left-turn lanes) in the calibration 

data (Michigan and California) than in the validation (Georgia) data, where 83 percent 

had left-turn lanes. 

Some mathematical “work-arounds” had to be performed to circumvent a missing data 

problem in the validation data set. The coefficient for log of AADT2 becomes 

insignificant in Georgia; and the sign of LTLN1S changes from negative to positive, 

meaning that in the calibration data the presence of a left-turn lane is associated with 

decreased TOTAL crashes, while in Georgia the presence of a left-turn lane is associated 

with increased TOTAL crashes. 

All of the validation statistics (see table 75) are at least consistent with the lack of 

agreement in model specification between original and Georgia data, and perhaps suggest 
119 

a more substantial departure. The correlation between predicted and observed is 

significantly reduced, going from 0.56 (original) to 0.05 and 0.08 (Georgia). The MPB 

and MAD statistics show a moderate increase in lack-of-fit. Finally, the MSE per year 

squared (3.62) for the calibration data is moderately lower than the MSPE per year 

squared (4.63) for Georgia data. 

The plot of observed and predicted crashes for individual intersections in figure 9 shows 

that predictions are much less variable than are observations. Thus it is likely that some 

of the explanatory variables are inadequate for predicting Georgia data. The models for 

INTERSECTION RELATED and the two variants for INJURY crashes are more 

seriously deficient than the TOTAL crash models. None of the models had statistically 

significant variables that corresponded with the original models. Table 76, table 78, and 

table 80 show the serious differences between original published models and the models 

estimated using Georgia data. 

Crash Prediction Algorithms 

There are no AMFs to validate for Model IV. 

Model IV Assessment and Conclusions 

The model for four-legged stop controlled intersections, two lanes on minor roads, and 

four lanes on major roads revealed model deficiencies ranging from moderate to serious. 

These concerns are summarized below: 

• The model performs well across time. The model for TOTAL crashes performs 

better than the models for INTERSECTION RELATED and INJURY crashes, but 

all models show only marginal to moderate deficiencies. 

• All models were seriously deficient in predicting Georgia data, as evidenced by 

the lack-of-fit and the inability of the Georgia data to fit the specified models. 

• Model IV needs to be improved, based on the validation findings across time and 

space. The observations suggest that the most important differences are 

jurisdictional in nature—pointing towards the consideration of design, traffic, and 

environmental variables that are not included in the model. 

2.7.5 Model V 

Predictive Ability Across Time 

To the extent possible, new data were collected from later time periods to validate the 

crash models (see table 39). Data from Michigan and California from years 1996 and 

1997 were used for the validation effort. Recall that the original model was calibrated on 

data from Michigan and California from 1993 to 1995. For signalized intersections in 

Michigan, the accident data for 1996 and 1997 did not include the crossroad accidents 

where the crossroad was a State route, because the crossroad milepost information was 

not available at the time of analysis. As a result, the later year crossroad accident 

numbers of the State routes should be systematically higher than those supposed to be. 

However, these differences would not have any effect on the conclusions drawn from the 

analysis. 
120 

Table 40 shows a comparison of the parameter estimates for the original published 

TOTAL crash model and one based on the later data. This comparison reveals that there 

are moderate to serious differences between the models. PKLEFT2 and VEICOM are not 

statistically significant in the model based on additional years of data. 

Table 41 shows the GOF statistics of Model V for TOTAL crashes on the later data. The 

linear correlation coefficient between observed and predicted data shows a moderate to 

serious decrease when calculated on future year data (0.73 to 0.40). A comparison of 

MSE per year squared (8.56) and MSPE per year squared (21.19) suggests a poor fit to 

the additional years of data. The MAD per year shows a moderate increase in lack-of-fit, 

while the MPB per year indicates a serious lack-of-fit. Table 42, 44, 46, 48, and 50 for 

INTERSECTION RELATED TOTAL and INJURY crash models and their variants also 

show serious differences between the original and models based on later data. However, 

the models are deficient in different ways, with different sets of variables becoming 

statistically insignificant. 

Predictive Ability Across Space 

Georgia data (see table 82) were used to investigate the model’s performance across 

jurisdictional boundaries. A comparison of TOTAL crashes compared to Georgia data for 

model V is shown in table 84. The table shows moderate to serious departures between 

the original published models and the models based on Georgia data. The variables 

PROT_LT, log of AADT2, and VEICOM were not statistically significant in the Georgia 

data. 

All of the validation statistics (see table 85) are consistent with the serious lack of 

agreement in model specification between original and Georgia data. The correlation 

between predicted and observed is substantially reduced, going from 0.73 (original) to 

0.18 (Georgia). The MPB per year and MAD per year statistics show a poor fit. Finally, 

the MSE per year squared for the calibration data is significantly lower than the MSPE 

per year squared for Georgia data, again suggesting a serious deficiency. 

The plot of observed and predicted crashes for individual intersections in figure 13 shows 

that predictions are much less variable than are observations, and also shows some 

systematic prediction error, with a tendency to overpredict crashes. 

The predictive ability of the models and their variants for INTERSECTION RELATED 

Total and INJURY crashes are difficult to assess, since the original models could not be 

duplicated with similar results. Specifically, many or all of the statistically significant 

variables in the original published models could not be duplicated in the recalibration-so 

assessing the predictive ability is difficult, at best. 

Crash Prediction Algorithms 

Fifty-one sites in Georgia were available for validating the base condition equation for 

the crash prediction algorithm (see table 100). The correlation coefficient between 
121 

predicted and observed crashes for the base condition model was 0.22, indicating a weak 

linear trend between observed and predicted values, and a serious to moderate decline 

from the same statistics calculated on the original published data (0.68 and 0.36 for 

different base years). Other statistics show moderate to serious lack-of-fit. 

Model V Assessment and Conclusions 

The model for signalized intersections of two-lane roads revealed model deficiencies 

ranging from moderate to serious. These concerns are summarized below: 

• The inability to recreate the original data hampered the ability to fully validate 

these models. 

• The models did not appear to perform adequately over time; however, part of the 

lack-of-fit is likely due to the inability to reproduce the original results. The 

models exhibited a serious lack-of-fit to the Georgia data. 

• Model V is likely in need of improvement; however, a better understanding of the 

model deficiencies can be gained only by recreating the original data. 

123 

3. RECALIBRATION 

This chapter presents recalibration results for the five types of rural intersections that 

were the subject of the validation exercise undertaken in the first part of the project. The 

first section provides a discussion of the recalibration approach. In the second section, the 

data and related issues are discussed. Third, AADT model estimation results are 

presented, followed by fully parameterized model estimation results. Sensitivity analysis 

results for the AMFs derived in this research then are given. Finally, a discussion and 

conclusions as a result of model recalibration are provided. 

3.1 RESEARCH APPROACH 

This model recalibration effort complemented the comprehensive model validation 

previously conducted as part of a larger technical evaluation of crash prediction models. 

It should be acknowledged that several anticipated end-uses of the crash prediction 

models guided all decisions made throughout this careful evaluation, which resulted in 

some specific overriding considerations while conducting the model recalibration: 

• The most likely end-use of the crash prediction models is embedded code within 

the IHSDM, with the sole intent to predict future crashes at intersections 

throughout the United States. 

• The models need to be able to predict the change in safety as a result of changes 

in traffic and geometric features relative to nominal conditions, corrected for 

intersection type and State- or regional-specific effects. 

• Environmental effects on safety, such as adverse weather and lighting conditions, 

while important factors, will be accounted for in State or regional correction 

factors. 

Considering the likely end uses of the crash prediction models within the IHSDM, 

considerable time was spent identifying a strategy for recalibrating statistical models. A 

strategy was needed for several reasons. First, there were multiple levels and types of 

models in the source documents—requiring a prioritization of models to be calibrated. 

Second, there are numerous methodological approaches reflected in the source 

documents, which need to be prioritized. Finally, the treatment of explanatory variables is 

dependent upon the methodological approach taken. Before describing the research 

technical strategy, some guiding philosophical principles used to guide the model 

recalibration effort are presented. 

It was felt that the majority of effort in the recalibration should be devoted to refinements 

to existing models. This includes changes to parameter estimates, and perhaps minor 

changes to model functional forms. This approach is based on the collective opinion that 

prior work, including the estimation of statistical models, was done carefully by experts 

in the field of transportation safety, and decisions such as variable selection, model 

functional form, and statistical model selection represent state-of-the-art knowledge with 

respect to intersection crash prediction models. Past documentation, critical evaluation, 
124 

and discussion with other experts in the field confirm prior beliefs that the existing set of 

models represents a defensible and sound starting point. It is believed that moderate to 

serious departures from existing models should be accompanied by detailed and 

defensible descriptions of the how, why, and in what cases departures from previous 

methods and/or models were thought necessary and useful. Finally, capabilities with 

regard to model recalibration are limited, simply because of existing data limitations, 

availability of explanatory variables, and intersection representativeness across States. 

When these limitations are thought to be critical they are identified and discussed. 

The technical strategy applied in this research effort is now described. Each of the 

strategies represents different possible end uses of the models, influenced by the stated 

guiding philosophical principles. 

AADT Models: One set of models represents intersection crash models that forecast 

crashes in frequency-per-year based on minor and major road AADT-only. There are no 

other independent variables in these models. The intended use of these models is to 

provide a baseline crash forecast, which can then be modified with AMFs representing 

the effects of various geometric, roadside, and other relevant safety-related factors. The 

sample available for calibrating these models was much larger than the sample available 

for calibrating full models that, in a sense, partly compensates for the loss of statistical 

precision resulting from the omission of variables other than AADT. 

Full Models: Another set of models represents statistical models with a full set of 

explanatory variables, including major and minor road AADT. These models are meant 

to provide a fuller understanding of the geometric, roadside, and operational features of 

intersections that influence on crashes. Another use might be to develop or infer 

additional crash modification factors for the various types of intersections examined in 

this research. 

 

AMFs: A final set of “models” represents estimated effects of various geometric, 

roadside, and operational features. These provide a complement to the AADT models. 

The intended use of the AMFs is to provide percentage corrections to expected crash 

frequencies that result from the application of various crash countermeasures. AMFs 

represent a fairly intuitive approach to evaluating safety countermeasures, and are 

handled rather simply in the IHSDM. 

When comparing and refining the three types models, several GOF measures were used 

in addition to inspection of model coefficients, collection of explanatory variables, and tstatistics and their associated p-values. Numerous measures are relied upon to avoid 

basing decisions on one single measure. Unfortunately, there is no one single criterion 

that dominates to the point of rendering the remaining measures as invalid or unimportant. 

It is through the assessment of many measures that a “best” model is chosen, and it is not 

always a clear winner. 
125 

3.1.1 Model Functional Forms 

The negative binomial model form, which is identical to that used in previous efforts, was 

used to provide the best fit to the data.(1,2) The following model form and error 

distribution were assumed to represent the underlying phenomenon: 

AADT Only Models

 (12)

where 

^

Y = the mean number of accidents to be expected at site i in a given time period; 

α = the estimated intercept term; and 

β1 β2, estimated coefficients. 

Fully Parameterized Models 

The following model form and error distribution were assumed to represent the 

underlying phenomenon: 

 (13)

where 

^

Y = the mean number of accidents to be expected at site i in a given time period; 

α = the estimated intercept term; 

Xi1, Xi2....Xin, = the values of the non-traffic highway variables at site i during that time 

period; and 

βi1 βi2.....βin, = estimated coefficients. 

(14)

where 

Var{m} = the estimated variance of the mean accident rate; 

E{m} = the estimated mean accident rate from the model; and 

K = the estimated overdispersion constant. 

3.1.2 Goodness-of-Fit Evaluation 

Four GOF measures were used in the model selection process (refer to chapter 2 for a 

description of the GOF measures.). A fifth approach to evaluating the GOF and in 

particular the suitability of alternate model forms was the Cumulative Residuals (CURE) 

method, proposed by Hauer and Hauer and Bamfo, in which the cumulative residuals (the 

difference between the actual and fitted values for each intersection) are plotted in 

increasing order for each covariate separately.(8,9) The graph shows how well the model 

fits the data with respect to each individual covariate. Figure 19 illustrates the CURE plot 

for the covariate AADT1 for the total accidents for the selected AADT-only model for 

( ) i 1AADT1 2AADT2 Y exp ˆ = α + β + β

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = α + ∑β

=

β β n

j 3

i 1 2 ijXij Yˆ AADT AADT exp 1 2

2 Var{m} = E{m}+ K * E{m}
126 

Type III intersections (presented in table 142). The indication is that the fit is very good 

for this covariate in that the cumulative residuals oscillate around the value of zero and 

lie between the two standard deviation boundaries. Figure 20 is a CURE plot for an 

alternate model. Clearly, the alternate model cannot be judged to be an improvement over 

the selected model. Appendix D contains CURE plots for the TOTACC AADT models 

for all intersection types. 

-25

-20

-15

-10

-5

0

5

10

15

20

25

0 10000 20000 30000 40000 50000 60000 70000 80000

Major AADT

Cumulative Residuals

Adj Cum Residuals

Standard Deviation

Standard Deviation

Figure 19. CURE Plot for Type III TOTACC AADT Model 
127 

-25

-20

-15

-10

-5

0

5

10

15

20

25

0 10000 20000 30000 40000 50000 60000 70000 80000

Major AADT

Cumulative Residuals

Adj Cum Residuals

Standard Deviation

Standard Deviation

Figure 20. CURE Plot for Type III TOTACC AADT Model Using the CURE 

Method: Alternative Model 

Now that the model’s end uses, guiding research philosophies, and technical modeling 

strategy have been described, the details of the technical modeling efforts are presented 

and discussed. It is useful to first describe the data that were used in the model 

recalibration efforts, and to identify any difficulties, anomalies, and peculiar 

circumstances that needed to be remedied in the effort. 

3.2 DESCRIPTION OF DATA 

Different variables were used in developing statistical models for Types I and II 

compared to Types III, IV, and V. Although average daily traffic variables are common 

to all models, in general there were a larger number of variables available for estimation 

of model Types III, IV, and V. The abbreviation employed in the modeling efforts and 

their descriptions are provided in the following section. 

3.2.1 Summary of Datasets 

The data used for recalibration were obtained from three sources. The first two sets were 

identical to the data used for the validation exercise described in chapter 2. The first set 

was the original calibration data used by Vogt and Bared from Minnesota and Vogt from 

California and Michigan.(1,2) Additional years of accident and traffic data were obtained 

for those sites which did not experience a change in major variables, such as traffic 

control or number of legs. There were primarily minor differences in the summary 

statistics between those calculated on the available data and those stated in the reports, 

particularly for the vertical curvature variables for Type V sites. However, existing 
128 

differences are sufficiently minor that further clarification was not necessary. The 

accident data obtained for the original sites included data for both the original and 

additional years. Differences were found in the accident counts between the original data 

obtained and this new dataset for the original years. Again, although small differences 

exist, their causes are unknown and these discrepancies were small enough that the data 

could confidently be used for recalibration. The second source of data was for those sites 

selected in Georgia to provide and an independent set of validation data. The third source 

of data was the California HSIS database. This data set was acquired to increase the size 

of the recalibration datasets with the aim of providing improved models with smaller 

standard errors of parameter estimates. These data were collected with a minimum 

amount of effort with assistance from the HSIS staff. However, as site visits were not 

conducted, fewer variables were available for these sites. Table 108 summarizes the 

sources of data used for recalibrating Models I to V. 

Table 108. Sources of Data 

No. of Sites No. of Total (Injury Accidents) 

State 

Years of 

Data 

Available 

Type 

I 

Type 

II 

Type 

III 

Type 

IV 

Type 

V Type I

Type 

II Type III Type IV Type V

Minnesota 1985-98 270 250 N/A4 N/A4 N/A4 

2029

(788)

1892

(878) N/A4 N/A4 N/A4 

California1 1991-98 1432 748 294 222 75

6494

(2978)

6063

(3058)

2136 

(847) 

1956

(899)

1159

(370)

California2 1993-98 N/A4 N/A4 60 54 18 N/A4 N/A4 

427 

(196) 

478

(268)

507

(200)

Michigan3 1993-97 N/A4 N/A4 24 18 31 N/A4 N/A4 

248 

(63) 

277

(92)

1262

(159)

Georgia 1996-97 116 108 52 52 51

295

(110)

255

(142)

124 

(56) 

222

(104)

489

(118)

Total 1818 1106 430 346 124

8818

(3908)

8210

(4078)

2935 

(1162) 

2933

(1363)

3417

(847) 1 These data come from the California HSIS database and do not include variables, such as vertical 

 curvature, not available electronically in that database 2 Only the original sites were used to develop the base models for Types III, IV, and V, and only the 

 California HSIS sites were used to develop the full models 

3 For Type V, Only 1996-97 injury accidents were available 4 N/A: not available 

In this section, summary statistics are provided for the data available for recalibrating the 

full models (i.e. models with explanatory variables other than traffic volumes). For model 

Types III, IV, and V, the California HSIS sites were not included due to the limited 

availability of variables relevant to these models. 

It is also appropriate and useful to examine which variables strongly correlate positively 

or negatively with crashes and which potential independent variables are correlated to 

one another. These statistics are also provided in this section of the report. 
129 

3.2.2 Type I 

A summary of the full data for Type I intersections is shown in table 109. This dataset 

includes the original sites in Minnesota, with the additional years of accident and traffic 

data, the Georgia sites and the California HSIS sites. Some of the Minnesota sites 

experienced changes in some design feature or location information during the 1990–98 

period and were not included in the analysis. Note that some variables are not available in 

the data for the Minnesota sites and California sites. The frequency column indicates the 

number of sites for which the information was available. Summary statistics by State are 

available in appendix C. 

Table 109. Summary Statistics for Type I Sites 

Variables Frequency Mean Median Minimum Maximum 

TOTACC per year 1818 0.6074 0.3750 0 6.75 

INJACC per year 1818 0.2660 0.1250 0 4.13 

AADT1 1818 6011 4475 401 35750 

AADT2 1818 492 270 100 10001 

RT MAJ Total 

0 

1 

1818 

1563 (86%) 

255 (14%) N/A1

RT MIN Total 

0 

1 

1818 

1770 (97.4%) 

48 (2.6%) N/A1

LT MAJ Total 

0 

1 

1818 

1382 (76%) 

436 (24%) N/A1

LT MIN Total 

0 

1 

1818 

1804 (99.2%) 

14 (0.8%) N/A1

MEDIAN Total 

0 

1 

1818 

1738 (95.6%) 

80 (4.4%) N/A1

TERRAIN Total 

Flat 

Rolling 

Mountainous 

1548 

568 (31.2%) 

547 (30.1%) 

433 (23.8%) N/A1

SPD1 381 50.89 55 23 55 

DRWY1 386 1.38 1 0 8 

HAZRAT1 386 2.56 2 1 7 

HAU 386 -1.451 0 -90 85.1 

SHOULDER1 1547 4.75 4 0 16 

VCI1 386 0.477 0 0 14.0 

HI1 386 1.6553 0 0 29.0 1 N/A: not available 

Table 110 shows correlation statistics and p-values that indicate the association between 

crash counts and the independent variables for type I intersections. Table 111 shows 
130 

correlations between the independent variables. Only those correlations that are 

significant at the 90 percent level are shown. 

As expected, major and minor road AADTs correlate positively with crashes. Turning 

lanes on the major and minor roads are also positively correlated with crashes, although 

this correlation is much less than that of vehicle volumes and the correlation for right-turn 

lane on major roads is not significant. Surprisingly, terrain and posted speed are 

negatively correlated with crashes, meaning that areas with rolling or mountainous terrain 

experience a lower crash risk than flatter terrains and that higher speeds are associated 

with fewer crashes. This counterintuitive result may arise because, as shown in Appendix 

C, Georgia sites have higher accident frequencies than California and Minnesota sites, as 

well as lower average posted speeds and a higher percentage of sites in rolling or 

mountainous terrain. With the presence of a median, VCI1 and HI1 were positively 

correlated with crashes, while HAU was negatively correlated with crashes although this 

correlation was not as strong. Shoulder width and number of driveways were not 

significantly correlated with crashes. 

Table 110. Correlation Between Crashes and Independent Variables for Type I Sites 

TOTACC per YEAR INJACC per YEAR 

Variables Corr. p-value Corr. p-value 

AADT1 0.426 0.000 0.402 0.000

AADT2 0.428 0.000 0.327 0.000

RT MAJ 0.030 0.202 0.005 0.841

RT MIN 0.116 0.000 0.106 0.000

LT MAJ 0.165 0.000 0.149 0.000

LT MIN 0.059 0.012 0.056 0.016

TERRAIN -0.085 0.001 -0.101 0.000

MEDIAN 0.076 0.001 0.074 0.002

SPD11 -0.127 0.013 -0.065 0.205

DRWY11 0.030 0.558 0.020 0.694

HAU1 -0.072 0.157 -0.052 0.312

SHOULDER12 -0.020 0.427 0.013 0.619

VCI11 0.081 0.110 0.033 0.516

HI11 0.087 0.088 0.089 0.080 1 These variables are unknown for the California sites 2 These variables are unknown for the Minnesota sites 
131 

Table 111. Summary of Correlations for Independent Variables for Type I Sites 

Variable Positive Correlates1 Negative Correlates1

AADT1 

AADT2, RT MIN, LT MAJ, MEDIAN, 

SHOULDER1 VCI1, HI1, TERRAIN 

AADT2 

AADT1, RT MAJ, RT MIN, LT MAJ, LT 

MIN, MEDIAN, HI1 TERRAIN 

RT MAJ 

AADT2, RT MIN, LT MAJ, LT MIN, 

SPD1, SHOULDER1 HAZRAT1, VCI1, HI1 

RT MIN 

AADT1, AADT2, RT MAJ, LT MAJ, LT 

MIN, MEDIAN, TERRAIN 

LT MAJ 

AADT1, AADT2, RT MAJ, RT MIN, LT 

MIN, MEDIAN, SHOULDER1 TERRAIN, HAZRAT1, VCI1 

LT MIN 

AADT2, RT MAJ, RT MIN, LT MAJ, 

MEDIAN 

MEDIAN 

AADT1, AADT2, RT MIN, LT MAJ, LT 

MIN, VCI1 TERRAIN, SPD1, SHOULDER1 

TERRAIN RT MIN, HAZRAT1, HI1 

AADT1, AADT2, LT MAJ, 

MEDIAN, SPD1, SHOULDER1 

SPD1 RT MAJ, SHOULDER1 

MEDIAN, TERRAIN, NODRWAY, 

HAZRAT1, VCI1, HI1 

DRWY1 HI1 SPD1 

HAZRAT1 TERRAIN, VCI1, HI1 RT MAJ, LT MAJ, SPD1 

HAU 

SHOULDER1 AADT1, RT MAJ, LT MAJ, SPD1 MEDIAN, TERRAIN, VCI1 

VCI1 MEDIAN, HAZRAT1 

AADT1, RT MAJ, LT MAJ, SPD1, 

SHOULDER1 

HI1 AADT2, TERRAIN, DRWY1, HAZRAT1 

1 Only those correlations are shown for which p-values are less than 0.10. 2 Not all variables are available for Minnesota or California sites 

3.2.3 Type II 

A summary of the full data for Type II intersections is shown in table 112. This dataset 

includes the original sites in Minnesota, with additional years of accident and traffic data, 

the Georgia sites and the California HSIS sites. Some of the Minnesota sites experienced 

changes in some design feature or location information during 1990–98 and were not 

included in the analysis. Note that some variables are not available in the data for the 

Minnesota sites and California sites. The frequency column indicates the number of sites 

for which the information was available. Summary statistics by State are available in 

appendix C. 
132 

Table 112. Summary Statistics for Type II Sites 

Variables Frequency Mean Median Minimum Maximum 

TOTACC per year 1106 0.9227 0.5357 0 7.13 

INJACC per year 1106 0.4665 0.2500 0 4.75 

AADT1 1106 5487 4245 407 38126 

AADT2 1106 532 344 100 7460 

RT MAJ Total 

0 

1 

1106 

911 (82.4%) 

195 (17.6%) N/A1

RT MIN Total 

0 

1 

1106 

1080 (97.6%) 

26 (2.4%) N/A1

LT MAJ Total 

0 

1 

1106 

883 (79.8%) 

223 (20.2%) N/A1

LT MIN Total 

0 

1 

1106 

1105 (99.9%) 

1 (0.1%) N/A1

MEDIAN Total 

0 

1 

1106 

1069 (96.7%) 

37 (3.3%) N/A1

TERRAIN Total 

Flat 

Rolling 

Mountainous 

856 

520 (47%) 

238 (21.5%) 

98 (8.9%) N/A1

SPD1 355 52 55 30 55 

DRWY1 358 0.83 0 0 6 

HAZRAT1 358 2.45 2.00 1 6 

HAU 358 0.364 0 -120 150 

SHOULDER1 855 5.426 6 0 16 

VCI1 358 0.43 0.05 0 8 

HI1 358 0.896 0 0 14.553 1 N/A: not available 

Table 113 shows correlation statistics and p-values that indicate the association between 

crash counts and the independent variables for Type II intersections. Table 114 shows 

correlations between the independent variables. Only those correlations that are 

significant at the 90 pecent level are shown. Note that some variables are not included in 

the data for the Minnesota and California sites. 

As expected, major and minor road AADTs correlate positively with crashes. Right-turn 

lanes on the major roads were negatively correlated with crashes, while right-turn lanes 

on the minor roads were positively correlated with crashes. Left-turn lanes on the major 

roads were positively correlated with crashes, however left-turn lanes on the minor roads 

were not significantly correlated with crashes. Again, terrain and posted speed are 
133 

negatively correlated with crashes, meaning that areas with rolling or mountainous terrain 

experience a higher crash risk than flatter geographies and that higher speeds are 

associated with less crashes. Presence of a median, number of driveways, HI1, and 

roadside hazard rating on the major roads were all positively correlated with crashes. 

Intersection angle (HAU), shoulder width, and VCI1 were not significantly correlated 

with crashes. 

Table 113. Correlation Between Crashes and Independent Variables for 

Type II Sites 

TOTACC per YEAR INJACC per YEAR 

Variables Corr. p-value Corr. p-value 

AADT1 0.443 0.000 0.384 0.000

AADT2 0.434 0.000 0.425 0.000

RT MAJ -0.133 0.000 -0.126 0.000

RT MIN 0.111 0.000 0.105 0.000

LT MAJ 0.258 0.000 0.265 0.000

LT MIN 0.027 0.364 0.028 0.353

TERRAIN -0.103 0.003 -0.115 0.001

MEDIAN 0.088 0.003 0.060 0.046

SPD11 -0.246 0.000 -0.184 0.001

DRWY11 0.251 0.000 0.197 0.000

HAZRAT11 0.152 0.004 0.101 0.057

HAU1 -0.041 0.444 0.007 0.895

SHOULDER13 0.008 0.821 -0.001 0.970

VCI11 0.029 0.580 0.046 0.390

HI11 0.086 0.106 0.123 0.020 1 These variables are unknown for the California sites 2 These variables are unknown for the Minnesota sites 
134 

Table 114. Summary of Correlations for Independent Variables for Type II Sites 

Variable1 Positive Correlates2 Negative Correlates2

AADT1 

AADT2, RT MIN, LT MAJ, LT MIN, 

MEDIAN, DRWY1, HAZRAT1, 

SHOULDER1 RT MAJ 

AADT2 

AADT1, RT MIN, LT MAJ, MEDIAN, 

TERRAIN, DRWY1, HAZRAT1 SPD1 

RT MAJ RT MIN, TERRAIN, SPD1, SHOULDER1 

AADT1, DRWY1, HAZRAT1, 

VCI1, HI1 

RT MIN 

AADT1, AADT2, RT MAJ, LT MAJ, LT 

MIN 

LT MAJ 

AADT1, AADT2, RT MIN, LT MIN, 

MEDIAN, TERRAIN, HAZRAT1, 

SHOULDER1, VCI1, HI1 

LT MIN AADT1, RT MIN, LT MAJ, MEDIAN 

MEDIAN 

AADT1, AADT2, LT MAJ, LT MIN, 

TERRAIN SHOULDER1 

TERRAIN 

AADT2, RT MAJ, LT MAJ, MEDIAN, 

HAZRAT1, VCI1, HI1 SPD1, SHOULDER1 

SPD1 RT MAJ, SHOULDER1 

AADT2, TERRAIN, DRWY1, 

HAZRAT1, VCI1, HI1 

DRWY1 AADT1, AADT2, HAZRAT1, VCI1, HI1 RT MAJ, SPD1 

HAZRAT1 

AADT1, AADT2, LT MAJ, TERRAIN, 

DRWY1, VCI1, HI1 RT MAJ, SPD1, HAU 

HAU HAZRAT1 

SHOULDER1 AADT1, RT MAJ, LT MAJ, SPD1 MEDIAN, TERRAIN, HAZRAT1 

VCI1 

LT MAJ, TERRAIN, DRWY1, HAZRAT1, 

HI1 RT MAJ, SPD1 

HI1 

LT MAJ, TERRAIN, DRWY1, HAZRAT1, 

VCI RT MAJ, SPD1 1 Not all variables are available for Minnesota or California sites 2 Only those correlations are shown for which p-values are less than 0.10 

3.2.4 Type III 

A summary of the full data for Type III intersections is shown in table 115. In total, 42 

variables were available for model development. The HSIS California data were excluded 

in developing Type III full models because this data set has only a few variables (turning 

lanes, median, terrain, etc) of relevance. This left the California and Michigan sites from 

the original study, with the additional years of accident data, for inclusion in the database. 

Some California sites experienced changes in some design features during 1996–98. For 

these, only 1993–95 data were used. As before the frequency column indicates the 

number of sites for which the information was available. 
135 

Table 115. Summary Statistics for Type III Sites 

Variables Frequency Mean Median Minimum Maximum 

TOTACC per year 136 1.35 0.80 0.00 10.60 

INJACC per year 136 0.55 0.33 0.00 4.00 

AADT1 136 13011 12100 2360 33333 

AADT2 136 709 430 15 9490 

MEDTYPE1 Total 

No Median 

Painted 

Curbed 

Other 

136

 69(50.7%)

45(33.1%)

14(10.3%)

8(5.9%)

 

N/A1

MEDWIDTH1 136 12.6 6 0 63 

HAU 136 1.3 0 -65 90 

HAZRAT1 Total 

1 

2 

3 

4 

5 

6 

7 

136

 16(11.8%)

58(42.6%)

26(19.1%)

25(18.4%)

8(5.9%)

2(1.5%)

1(0.7%) N/A1

HAZRAT2 Total 

1 

2 

3 

4 

5 

6 

7 

52

 0(0%)

2(4.0%)

20(40.0%)

16(32.0%)

6(12.0%)

6(12.0%)

2(4.0%) N/A1

COMDRWY1 136 1.5 0 0 14 

RESDRWY1 136 1.0 0 0 7 

DRWY1 136 2.5 1.0 0.0 15.0 

NoCOMDRWY2 52 0.4 0 0 3 

RESDRWY2 52 0.6 0 0 6 

DRWY2 52 1.0 1.0 0.0 6.0 

SPD1 136 52.5 55 30 65 

SPD2 136 33.7 35 15 55 1 N/A: not available 
136 

Table 115. Summary Statistics for Type III Sites (Continued) 

Variables Frequency Mean Median Minimum Maximum 

LIGHT Total 

0 

1 

136

97(71.3%)

39(28.7%) N/A1

TERRAIN1 Total 

Flat 

Rolling 

Mountainous 

136

 83(61.0%)

42(30.9%)

11(8.1%) N/A1

TERRAIN2 Total 

Flat 

Rolling 

Mountainous 

52

 24(17.6%)

21(15.4%)

7(5.1%) N/A1

RTLN1 Total 

0 

1 

136

108(79.4%)

28(20.6%) N/A1

LTLN1 Total 

0 

1 

136

48(35.3%)

88(64.7%) N/A1

RTLN2 Total 

0 

1 

136

117(86.0%)

19(14.0%) N/A1

LTLN2 Total 

0 

1 

136

131(96.3%)

5(3.7%) N/A1

HI1 136 1.26 0.00 0 14.29 

HEI1 136 2.01 0.73 0 26.63 

GRADE1 136 1.0 0.7 0.0 5.9 

GRADE2 52 1.5 1.2 0.0 4.7 

VEI1 136 0.9 0.6 0.0 6.7 

VI2 52 4.0 2.8 0.0 24.0 

LEGACC1 52 0.0 0.0 0.0 1.0 

LEGACC2 52 0.1 0.0 0.0 1.0 

SHOULDER1 52 4.0 4.0 0.0 10.0 

PKTRUCK 84 9.15 7.79 1.18 28.16 

PKTURN 84 6.68 4.28 0.27 53.09 

PKLEFT 84 3.28 2.16 0.13 25.97 1 N/A: not available 
137 

Table 115. Summary Statistics for Type III Sites (Continued) 

Variables Frequency Mean Median Minimum Maximum 

PKLEFT1 84 1.47 0.69 0.00 21.29 

PKLEFT2 84 55.31 60.29 0.00 100.00 

SD1 136 1515 2000 500 2000 

SDL2 136 1418 1510 40 2000 

SDR2 136 1428 1555 80 2000 

Table 116 shows correlation statistics and p-values that indicate the association between 

crash counts and the independent variables for Type III intersections. Table 114 shows 

correlations between the independent variables. Only those correlations that are 

significant at the 90 percent level are shown. 

Major and minor road AADTs correlate positively with crashes as expected. Peak turning 

movement volumes also correlate with crashes, both positively and negatively. PKTURN, 

PKLEFT, and PKLEFT1 correlate positively with crashes, while PKTRUCK and 

PKLEFT2 correlate negatively with crashes. According to table 114, PKTRUCK 

correlates negatively with the AADT variables. This suggests that the negative 

correlation of crashes with PKTRUCK may, in part, be a consequence of the positive 

correlation of crashes with AADT variables. PKLEFT1 and PKLEFT2 are also 

negatively correlated with each other. There are several variables for which the 

correlation results are unexpected. Roadside hazard rating on major and minor roads, 

number of residential driveways on major and minor roads, posted speed limits on major 

and minor roads, terrain on major roads, shoulder width on major roads, “LIGHT,” and 

the presence of left-and right-turn lane on minor roads, as well as other variables are 

correlated with crashes in the opposite direction to that expected, although many of these 

correlations are insignificant. 

Table 116. Correlation Between Crashes and Independent Variables for Type III 

 Sites 

TOTACC per YEAR INJACC per YEAR 

Variables Corr. p-value Corr. p-value 

AADT1 0.3330 0.0001 0.2943 0.0005

AADT2 0.4829 0.0000 0.3606 0.0000

MEDWDTH1 -0.0774 0.3703 -0.0051 0.9534

HAU 0.1190 0.1677 0.1917 0.0254

COMDRWY1 0.3959 0.0000 0.1765 0.0398

RESDRWY1 -0.0697 0.4201 -0.1211 0.1603

DRWY1 0.2842 0.0008 0.0854 0.3229

COMDRWY2 0.0044 0.9756 0.0486 0.7321

RESDRWY2 -0.2342 0.0947 -0.2062 0.1425

DRWY2 -0.1956 0.1647 -0.1416 0.3168

SPD1 -0.3299 0.0001 -0.1184 0.1696

SPD2 -0.0675 0.4352 0.0519 0.5483

LIGHT 0.2882 0.0007 0.1307 0.1295
138 

Table 116. Correlation Between Crashes and Independent Variables for Type III 

Sites (Continued) 

TOTACC per YEAR INJACC per YEAR 

Variables Corr. p-value Corr. p-value 

L1RT 0.0118 0.8915 0.0344 0.6911

L1LT -0.1511 0.0791 0.0192 0.8243

L3RT 0.2298 0.0071 0.1717 0.0456

L3LT 0.2025 0.0181 0.2373 0.0054

HI1 0.0309 0.7208 0.0615 0.4771

HEI1 0.0052 0.9520 0.1628 0.0583

GRADE1 0.0027 0.9748 0.0485 0.5751

GRADE2 0.0968 0.4949 0.1977 0.1601

VEI1 0.1534 0.0746 0.1247 0.1481

VI2 -0.1039 0.4633 -0.0831 0.5582

LEGACC1 -0.0721 0.6116 -0.1020 0.4719

LEGACC2 0.2099 0.1353 -0.0129 0.9278

SHOULDER1 0.1392 0.3249 -0.0140 0.9216

PKTRUCK -0.1943 0.0766 -0.1205 0.2749

PKTURN 0.2617 0.0162 0.2527 0.0204

PKLEFT 0.2304 0.0350 0.2296 0.0357

PKLEFT1 0.2744 0.0115 0.2479 0.0230

PKLEFT2 -0.1610 0.1436 -0.0994 0.3685

SD1 -0.0752 0.3843 -0.0003 0.9970

SDL2 -0.0633 0.4642 -0.0300 0.7284

SDR2 -0.0585 0.4986 -0.0214 0.8043

Table 117. Summary of Correlations for Independent Variables for Type III Sites 

Variable Positive Correlates1 Negative Correlates1

AADT1 L1RT, L1LT 

MEDTYPE2, PKTRUCK,PKLEFT2, 

SDL2 

AADT2 

L1RT, L3RT, L3LT, PKTURN, 

PKLEFT,PKLEFT1, SHOULDER1, SPD1, PKTRUCK 

MEDWDTH1 

HAU, SPD1, SPD2, L1RT, L1LT, 

PKTRUCK, SHOULDER1, SDR2 

COMDRWY1, RESDRWY1, DRWY1, 

LIGHT, TERRAIN, HI1, GRADE1, 

VI2, 

HAU MEDWDTH1, PKTRUCK, LEFACC2, MEDTYPE2, RESDRWY1, DRWY2, 

HAZRAT1 

HAZRAT2, SPD1, SPD2, TERRAIN1, 

L1LT, GRADE1, VEI1 

COMDRWY1, RESDRWY1, DRWY1, 

LIGHT, L1LT, SDR2 

DRWY1 

COMDRWY1, RESDRWY1, 

COMDRWY2, DRWY2, LIGHT, 

PKTURN, HI1 

MEDTYPE1, MEDTYPE2, 

MEDTYPE3, HAZRAT1, SPD1, 

SPD2, L1RT, L1LT, PKTRUCK, 

PKLEFT2, SDL3, SDR3 
139 

Table 117. Summary of Correlations for Independent Variables for Type III Sites 

(Continued) 

Variable Positive Correlates1 Negative Correlates1

SPD1 

MEDTYPE1,MEDTYPE3, MEDWDTH1, 

SPD2, TERRAIN1, L1RT, L1LT, 

PKTRUCK, LEGACC2, SD1, SDL2, 

SDR2 

AADT2, COMDRWY1, RESDRWY1, 

DRWY1, COMDRWY2, DRWY2, 

LIGHT, HI1, GRADE2, VEI1 

SPD2 

MEDTYPE1, MEDWDTH1, HAZRAT1, 

SPD1, TERRAIN1, L1RT, L1LT, L3LT, COMDRWY1, DRWY1, LIGHT 

LIGHT 

(no=0, yes=1) 

COMDRWY1, PKTURN, HI1, 

LEFACC1, DRWY1, PKLEFT, PKLEFT1 

MEDTYPE2, MEDTYPE3, 

MEDWDTH1, HAZRAT1, SPD1, 

SPD2, L1LT, PKTRUCK, SD1, SDR2 

TERRAIN1 

MEDTYPE1, HAZRAT1, HAZRAT2, 

SPD1, SPD2, L1RT, GRADE1, GRADE2, 

VEI1, VI2 SD1, SDL2, SDR2 

L1RT 

AADT1, AADT2, MEDWDTH1, SPD1, 

SPD2, TERRAIN1, L1LT, L3RT, L3LT, 

GRADE1, LEFACC2, SHOULDER1 

HAZRAT2, COMDRWY1, 

RESDRWY1, DRWY1, COMDRWY2, 

GRDE2, TERRAIN2 

L1LT 

AADT1, MEDTYPE1, MEDTYPE2, 

MEDWDTH1, HAZRAT1, SPD1, SPD2, 

L1RT, L3LT, SD1, SDR3 

HAZRAT2, COMDRWY1, 

RESDRWY1, DRWY1, LIGHT, 

TERRAIN2 

L3RT 

AADT2, L1RT, L3LT, PKTURN, 

SHOULDER1, PKTURN, PKLEFT, 

PKLEFT1 HAZRAT2, TERRAIN2 

L3LT 

AADT2, MEDTYPE1, SPD2, L1RT, 

L1LT, L3RT, PKTURN, PKLEFT, 

PKLEFT1 HAZRAT2 

PKTRUCK 

MEDTYPE1, MEDTYPE3, 

MEDWDTH1, HAU, SPD1, SPD2, SD1, 

SDL2, SDR2 

AADT1, AADT2, COMDRWY1, 

RESDRWY1, DRWY1, LIGHT, HI1, 

VEI1, 

PKTURN 

AADT2, LIGHT, L3RT, L3LT, PKLEFT, 

PKLEFT1 

VEI1 

AADT1, HAZRAT1, TERRAIN1, HI1, 

GRADE1, SPD1, PKTRUCK, SD1, SDL2, SDR2 

HEI1 MEDTYPE1, HI, VI2 

GRADE1 

MEDTYPE1, HAZRAT1, TERRAIN1, 

L1RT, HI1, VEI1 MEDWDTH1, SD1, SDL2, SDR2 

SDL2 SPD1, PKTRUCK, SD1, SDR2 

AADT1, RESDRWY1, DRWY1, 

TERRAIN1, TERRAIN2, HI1, 

GRADE1, GRADE2, VEI1, LEGACC2 

SDR2 

MEDWDTH1, SPD1, L1LT, PKTRUCK, 

SD1, SDL3 

HAZRAT1, HAZRAT2, LIGHT, 

TERRAIN1, HI1, GRADE1, GRADE2, 

VEI1, DRWY1 1

Only those correlations are shown for which p-values are less than 0.10 

3.2.5 Type IV 

A summary of the full data for type IV intersections is shown in table 118. In total, 53 

variables were available for model development. The HSIS California data were again 

excluded because of a lack of sufficient variables (turning lanes, median, terrain, etc.) of 

relevance. Instead, the California and Michigan sites from the original study, with the 

additional years of accident data were included in the database. Some California sites 

experienced changes in some design features during 1996–98. For these, only 1993–95 
140 

data were used. As before, frequency indicates the number of sites for which the 

information was available. 

Table 118. Summary Statistics for Type IV Sites 

Variables Frequency Mean Median Minimum Maximum 

TOTACC per YEAR 124 2.0 1.4 0.0 10.8 

INJACC per YEAR 124 0.9 0.5 0.0 5.7 

AADT1 124 12881 11496 3150 73799 

AADT2 124 621 430 21 2990 

MEDTYPE on major Total 

0: No Median 

1: Painted 

2: Curbed 

3: Other 

124

70(56.5%)

27(21.8%)

22(17.7%)

5(4.0%) N/A1

MEDTYPE on minor Total 

0: No Median 

52

52(100%) N/A1

MEDWDTH1 124 16.1 6.5 0 60 

MEDWDTH2 52 0.0 0 0 1 

SHOULDER1 52 4.2 4 2 6 

SHOULDER2 52 0.3 0 0 2 

L1RT Total 

0 

1 

2 

124

69(55.6%)

20(16.1%)

35(28.2%) N/A1

L3RT Total 

0 

1 

2 

124

72(58.1%)

13(10.5%)

39(31.5%) N/A1

L3LT Total 

0 

1 

124

122(98.4%)

2(1.6%) N/A1

LEGACC1 Total 

0 

1 

52

49(94.2%)

3(5.8%) N/A1

LEGACC2 Total 

0 

1 

52

49(94.2%)

3(5.8%) N/A1

HAZRAT1 

1 

2 

3 

4 

5 

6 

7 

124

24(19.4%)

43(34.7%)

32(25.8%)

21(16.9%)

2(1.6%)

2(1.6%)

0(0%) N/A1

1 N/A: not available 
141 

Table 118. Summary Statistics for Type IV Sites (Continued) 

Variables Frequency Mean Median Minimum Maximum 

HAZRAT2 

1 

2 

3 

4 

5 

6 

7 

52

0(0%)

7(13.5%)

15(28.8%)

16(30.8%)

12(23.1%)

2(3.8%)

0(0%) N/A1

COMDRWY1 124 0.6 0 0 12 

RESDRWY1 124 0.7 0 0 7 

DRWY1 124 1.3 0 0 15 

COMDRWY2 52 0.4 0 0 4 

RESDRWY2 52 0.4 0 0 3 

DRWY2 52 0.8 0 0 6 

LIGHT Total 

0 

1 

124

87(70.2%)

37(29.8%) N/A1

TERRAIN1 Total 

Flat 

Rolling 

Mountainous 

124

90(72.6%)

25(20.2%)

9(7.3%) N/A1

TERRAIN2 Total 

Flat 

Rolling 

Mountainous 

52

19(36.5%)

27(51.9%)

6(11.5%) N/A1

VEI1 124 0.87 0.35 0.00 12.50 

VCEI1 124 0.63 0.00 0.00 12.50 

VI1 124 0.62 0.00 0.00 12.50 

VCI1 124 0.43 0.00 0.00 12.50 

VEI2 52 3.05 2.84 0.32 10.18 

VCEI2 52 2.97 2.31 0.00 11.36 

VI2 52 2.62 2.08 0.00 9.66 

VCI2 52 2.08 1.02 0.00 12.50 

GRADE1 124 0.94 0.71 0.00 5.80 

GRADE2 51 1.65 1.48 0.60 3.71 

HI 124 0.92 0.00 0.00 7.33 

HEI 124 3.28 0.60 0.00 233.33 

HAU 124 1.5 0 -50 55 

SPD1 124 55.6 55 25 65 

1 N/A: not available 
142 

Table 118. Summary Statistics for Type IV Sites (Continued) 

Variables Frequency Mean Median Minimum Maximum 

SPD2 124 34.7 35 25 55 

PKTRUCK 72 10.95 8.36 1.75 37.25 

PKTHRU1 72 94.41 96.95 67.77 100.00 

PKTURN 72 9.47 6.56 0.00 48.52 

PKLEFT 72 4.80 3.08 0.00 25.26 

PKLEFT1 72 2.78 1.51 0.00 13.96 

PKTHRU2 72 15.69 10.82 0.00 68.09 

PKLEFT2 72 38.89 36.66 0.00 100.00 

SD1 124 1399 1332 400 2000 

SDL2 124 1314 1262 324 2000 

SDR2 124 1329 1354 215 2000 

1 N/A: not available 

Table 119 shows correlation statistics and p-values that indicate the association between 

crash counts and the independent variables for Type IV intersections. Table 120 shows 

correlations between the independent variables. Only those correlations that are 

significant at the 90 pecent level are shown. 

Major and minor road AADTs correlate positively with crashes, as expected. Peak 

turning movements also correlate with crashes, both positively and negatively. There are 

several variables for which the correlation results are contrary to expectations. Shoulder 

width on the road, right-and left-turn lane on minor roads, acceleration lane on major 

roads, residential driveway and total driveway on minor roads, light, terrain on major and 

minor roads, vertical curves on major and minor roads, horizontal curves on major roads, 

absolute grades on major and minor roads, intersection angle, posted speed limit on major 

roads, and others are correlated with crashes in the opposite direction than expected, 

although many of these correlations are insignificant. For example, median width on 

major road is insignificant with a counterintuitive sign. However, as table 120 shows, 

there is a negative correlation between median width on major roads and median types, 

the result of which is that median type is skewing the effect of median width at Type IV 

intersections. 
143 

Table 119. Correlation Between Crashes and Independent Variables for Type IV Sites 

TOTACC per YEAR INJACC per YEAR 

Variables Corr. p-value Corr. p-value 

AADT1 0.2258 0.0117 0.2285 0.0107

AADT2 0.2600 0.0035 0.1594 0.0770

MEDWDTH1 0.0314 0.7289 0.0572 0.5277

MEDWDTH2 -0.0104 0.9418 -0.0657 0.6434

SHOULDER1 -0.1631 0.2481 -0.1040 0.4633

SHOULDER2 0.2089 0.1372 0.2209 0.1155

L1RT -0.0084 0.9267 0.0608 0.5026

L1LT -0.0695 0.4432 0.0738 0.4152

L3RT 0.0350 0.6999 0.0995 0.2714

L3LT 0.1428 0.1137 0.1929 0.0319

LEGACC1 0.1633 0.2474 0.2323 0.0975

LEGACC2 -0.1092 0.4411 0.0000 1.0000

COMDRWY1 0.1017 0.2613 0.0942 0.2979

RESDRWY1 0.1547 0.0863 0.0015 0.9867

DRWY1 0.1569 0.0818 0.0596 0.5109

COMDRWY2 0.1900 0.1772 0.1732 0.2195

RESDRWY2 -0.2809 0.0437 -0.2474 0.0770

DRWY2 -0.0367 0.7963 -0.0283 0.8423

LIGHT 0.0592 0.5137 -0.0176 0.8459

VEI1 0.0099 0.9133 0.0373 0.6806

VCEI1 0.0765 0.3984 0.0698 0.4408

VI1 -0.0174 0.8476 0.0191 0.8332

VCI1 0.0151 0.8676 0.0490 0.5887

VEI2 -0.2156 0.1248 -0.0692 0.6257

VCEI2 -0.2626 0.0600 -0.0361 0.7994

VI2 -0.2665 0.0562 -0.0672 0.6360

VCI2 -0.2147 0.1263 -0.0506 0.7215

GRADE1 -0.0033 0.9709 0.0211 0.8161

GRADE2 -0.1825 0.1999 -0.0318 0.8245

HI1 -0.0329 0.7171 -0.0846 0.3503

HEI1 -0.0055 0.9519 -0.0581 0.5212

HAU -0.1184 0.1905 -0.0892 0.3243

SPD1 -0.1839 0.0409 -0.0607 0.5033

SPD2 0.0301 0.7397 0.1964 0.0288

PKTRUCK -0.3268 0.0051 -0.3369 0.0038

PKTHRU1 -0.3058 0.0090 -0.2324 0.0494

PKTURN 0.3242 0.0055 0.2544 0.0311

PKLEFT 0.3099 0.0081 0.2526 0.0323

PKLEFT1 0.3550 0.0022 0.3028 0.0097

PKTHRU2 0.1876 0.1145 0.1500 0.2086

PKLEFT2 -0.0492 0.6815 -0.0627 0.6006

SD1 -0.1331 0.1407 -0.1220 0.1770

SDL2 -0.1408 0.1187 -0.0849 0.3486

SDR2 -0.2826 0.0015 -0.1705 0.0583
144 

Table 120. Summary of Correlations for Independent Variables for Type IV Sites 

Variable Positive Correlates1 Negative Correlates1

AADT1 

MEDTYPE1, L1LT, SPD1, 

PKTHRU1, PKLEFT2 

VCEI2, PKTRUCK, PKTURN, PKLEFT, 

PKLEFT1, PKTHRU2 

AADT2 

MEDWDTH1, MEDWDTH2, 

TERRAIN2, HEI1, HAU, PKTURN, 

PKLEFT, PKLEFT1, PKTHRU2 

MEDTYPE1, GRADE1, PKTURCK, 

PKTHRU1, PKLEFT2 

MEDWDTH1 

AADT2, L1RT, L1LT, L3RT, 

HAZRAT1, HAU, SPD1, SPD2, 

PKTHRU1 

MEDTYPE1, MEDTYPE2, HAZRAT2, 

COMDRWY1, RESDRWY1, 

COMDRWY2, RESDRWY2, DRWY1, 

DRWY2, LIGHT, TERRAIN1, VEI2, 

VCEI2, VI2, VCI2, PKTURN, PKLEFT, 

PKLEFT1 

HAU AADT2, MEDWDTH1, TERRAIN2 LIGHT 

HAZRAT1 

MEDTYPE1, MEDWDTH1, 

TERRAIN1, GRADE1, HI1, 

MEDTYPE2, L1RT, L3RT, SD1, SDL2, 

SDR2, PKTRUCK, PKTHRU2 

DRWY1 

HAZRAT1, COMDRWY1, 

RESDRWY1, COMDRWY2, 

RESDRWY2, DRWY2, LIGHT, VI2, 

HEI1, PKTURN, PKLEFT, PKLEFT1 

MEDTYPE2, MEDWDTH1, L1RT, 

L1LT, L3RT, SPD1, SPD2, PKTRUCK, 

PKTHRU1, SD1, SDL2, SDR2 

SPD1 

AADT1, MEDTYPE2, MEDWDTH1, 

SHOULDER2, L1RT, L1LT, L3RT, 

TERRAIN2, SPD2, PKTRUCK, 

PKTHRU1, SD1, SDL2, SDR2 

COMDRWY1, RESDRWY1, DRWY1, 

COMDRWY2, DRWY2, LIGHT, HEI1, 

PKTURN, PKLEFT, PKLEFT1 

SPD2 

MEDWDTH1, L1RT, L1LT, L3RT, 

SPD1 

HAZRAT2, COMDRWY1, RESDRWY1, 

DRWY1, RESDRWY2, DRWY2, LIGHT, 

VEI2, VCEI2, VI2, VCI2, HEI1 

LIGHT (no=0,yes=1) 

COMDRWY1, RESDRWY1, DRWY1, 

COMDRWY2, DRWY2, HEI1, 

PKTURN, PKLEFT, PKLEFT1 

MEDTYPE2, MEDWDTH1, L1RT, 

L1LT, L2RT, HAU, SPD1, SPD2, 

PKTRUCK, PKTHRU1 

TERRAIN1 

MEDTYPE1, MEDWDTH2, 

SHOULDER2, L1LT, LEGACC1, 

HAZRAT1, GRADE1, HI1, 

MEDWDTH1, PKTRUCK, PKTHRU2, 

PKLEFT2, SD1, SDL2, SDR2 

L1RT 

MEDTYPE2, MEDTYPE3, 

MEDWDTH1, L1LR, L3RT, 

LEGACC1, SPD1, SPD2, PKTRUCK, 

PKLEFT 

HAZRAT1, RESDRWY1, DRWY1, 

LIGHT, TERRAIN2, GRADE1, 

GRADE2, HI1, PKTURN, PKLEFT, 

PKLEFT1 

L1LT 

AADT1, MEDTYPE1, MEDTYPE2, 

MEDWDTH1, L1RT, L3RT, 

TERRAIN1, SPD1, SPD2, PKTRUCK 

COMDRWY1, RESDRWY1, DRWY1, 

RESDRWY2, DRWY2, LIGHT, VEI2, 

VCEI2, VI2, VCI2, GRADE2, HEI, 

PKTURN, PKLEFT, PKLEFT1 

L3RT 

MEDTYPE2, MEDWDTH1, 

SHOULDER2, L1LT, L1RT, SPD1, 

SPD2, PKTRUCK, PKTHRU1 

MEDTYPE1, MEDTYPE3, HAZRAT1, 

HAZRAT2, COMDRWY1, RESDRWY2, 

COMDRWY2, RESDRWY2, DRWY1, 

DRWY2, LIGHT, VEI2, VCI2, GRADE1, 

GRADE2, HI1, PKTURN PKLEFT, 

PKLEFT1 

L3LT MEDTYPE3, PKLEFT1, PKTHRU2 
145 

Table 120. Summary of Correlations for Independent Variables for Type IV Sites 

(Continued) 

Variable Positive Correlates1 Negative Correlates1

PKTRUCK 

MEDTYPE2, L1RT, L1LT, L3RT, SPD1, 

PKTHRU2, SD1, SDL2, SDR2 

AADT1, AADT2, HAZRAT1, DRWY1, 

LIGHT, TERRAIN1, PKTURN, 

PKLEFT, PKLEFT1, 

PKTURN 

AADT2, RESDRWY1, DRWY1, LIGHT, 

PKLEFT, PKLEFT1, PKLEFT2 

AADT1, MEDTYPE1, MEDTYPE2, 

MEDWDTH1, L1RT, L1LT, L3RT, 

SPD1, PKTRUCK, PKTHRU1 

VEI1 VI1, VCI1, GRADE1 MEDTYPE2, SD1, SDL2, SDR2 

HEI1 

AADT2, L1LT, RESDRWY1, DRWY1, 

DRWY2, LIGHT, 

SHOUDLER2, L1LT, SPD1, SPD2, 

SD1, SDL2 

GRADE1 

MEDTYPE1, HAZRAT1, TERRAIN1, 

VEI1,VI2, HI1 

AADT2, MEDTYPE2, L1RT, 

PKTHRU2, SD1, SDL2, SDR2 

SDL2 

MEDTYPE2, HAZRAT2, 

HAZRAT2,VCI2, SPD1, PKTRUCK, 

SD1, SDR2 

HAZRAT1, COMDRWY1, 

RESDRWY1, DRWY1, TERRAIN1, 

VEI1, VCEI1, GRADE1, HI1, HEI1 

SDR2 

MEDTYPE2, SHOULDER1, LEGACC2, 

HAZRAT2, RESDRWY2, VCI2, SPD1, 

PKTRUCK, PKTHRU2, SD1, SDL2 

HAZRAT1, COMDRWY1, 

RESDRWY1, DRWY1, TERRAIN1, 

VEI1, VCEI1, GRADE1, HI1 1 Only those correlations are shown for which p-values are less than 0.10. 

3.2.6 Type V 

A summary of the full data for Type V intersections is shown in table 121. In total, 53 

variables were available for model development. The HSIS California data were again 

excluded because only five Type V sites were available. This left the California and 

Michigan sites from the original study, with the additional years of accident data for 

inclusion in the database. Some California sites experienced changes in some design 

features during 1996–98 period. For these, only 1993–95 data were used. As before, the 

frequency column indicates the number of sites for which the information was available. 

Table 121. Summary Statistics for Type V Sites 

Variables Frequency Mean Median Minimum Maximum 

TOTACC per YEAR 100 5.9 5.3 0.0 26.5 

INJACC per YEAR 100 1.8 1.5 0.0 6.5 

AADT1 100 9126 8700 430 25132 

AADT2 100 3544 3100 420 12478 
146 

Table 121. Summary Statistics for Type V Sites (Continued) 

Variables Frequency Mean Median Minimum Maximum 

SIGTYPE Total 

0:Pre-timed 

1:Actuated 

2:Semi-actuated 

 100

33(33%)

45(45%)

22(22%) N/A1

MEDTYPE on major Total 

0:No Median 

1:Painted 

2:Other 

100

87(87%)

12(12%)

1(1%) N/A1

MEDTYPE on minor Total 

0:No Median 

1:Painted 

2:Other 

51

48(94.1%)

3(5.9%)

0(0%) N/A1

MEDWDTH1 100 1.3 0 0 13

MEDWDTH2 100 0.3 0 0 12

SHOULDER1 51 1.9 2 0 10

SHOULDER2 51 1.5 2 0 10

L1RT Total 

0 

1 

2 

100

51(51%)

21(21%)

28(28%) N/A1

L1LT Total 

0 

1 

2 

100

23(23%)

2(2%)

75(75%) N/A1

L3RT Total 

0 

1 

2 

100

59(59%)

20(20%)

21(21%) N/A1

L3LT Total 

0 

1 

2 

100

45(45%)

5(5%)

50(50%) N/A1

LEGACC1 Total 

0 

1 

51

46(90.2%)

5(9.8%) N/A1

 1 N/A: not available 
147 

Table 121. Summary Statistics for Type V Sites (Continued) 

Variables Frequency Mean Median Minimum Maximum 

LEGACC2 Total 

0 

1 

51

50(98%)

1(2%) N/A1

PROTLT1 Total 

0 

1 

100

70(70%)

30(30%) N/A1

PROTLT2 Total 

0 

1 

51

47(92.2%)

4(7.8%) N/A1

HAZRAT1 Total 

1 

2 

3 

4 

5 

6 

7 

100

12(12%)

29(29%)

27(27%)

16(16%)

13(13%)

3(3%)

0(0%) N/A1

HAZRAT2 Total 

1 

2 

3 

4 

5 

6 

7 

51

1(2%)

8(15.7%)

17(33.3%)

14(27.5%)

8(15.7%)

3(5.9%)

0(0%) N/A1

COMDRWY1 100 2.64 2 0 11 

RESDRWY1 100 0.52 0 0 6 

DRWY1 100 3.16 3 0 15 

COMDRWY2 100 2.44 2 0 10 

RESDRWY2 100 0.69 0 0 8 

DRWY2 100 3.13 3 0 11 

LIGHT Total 

0 

1 

100

29(29%)

71(715) N/A1

 1 N/A: not available 
148 

Table 121. Summary Statistics for Type V Sites (Continued) 

Variables Frequency Mean Median Minimum Maximum 

TERRAIN1 Total 

Flat 

Rolling 

Mountainous 

100

59(59%)

38(38%)

3(3%) N/A1

TERRAIN2 Total 

Flat 

Rolling 

Mountainous 

51

18(35.3%)

31(60.8%)

2(3.9%) N/A1

SD1 100 1314 1246 235 2000 

SD2 100 1213 1091 224 2000 

SDL1 100 774 673 122 2000 

SDL2 100 910 750 142 2000 

SDR1 51 822 798 103 2000 

SDR2 51 1042 934 224 2000 

VEI1 100 1.45 1.19 0.00 11.97 

VEI2 100 1.91 1.39 0.00 13.50 

VEICOM 100 1.81 1.59 0.00 8.13 

VCEI1 100 1.10 0.45 0.00 10.79 

VCEI2 100 1.54 0.90 0.00 14.00 

VCEICOM 100 1.32 1.03 0.00 7.00 

GRADE1 100 1.20 1.00 0.00 4.98 

GRADE2 100 1.50 1.28 0.00 7.79 

HEI 100 3.95 0.61 0.00 94.87 

HI 100 2.15 0.00 0.00 60.00 

HEI2 100 2.52 0.00 0.00 36.41 

HI2 100 2.58 0.00 0.00 47.44 

HEICOM 100 2.56 0.58 0.00 32.54 

HICOM 100 2.36 0.00 0.00 42.05 

HAU 100 0.07 0.00 -45.00 40.00 

SPD1 100 45.2 45 25 65 

SPD2 100 40.9 40 20 55 

PKTRUK 49 8.96 7.71 2.69 45.43 

PKTURN 49 35.64 34.48 7.07 72.66 

PKTHRU1 49 71.19 73.77 18.01 96.73 

PKTHRU2 49 43.90 41.99 8.45 84.09 

PKLEFT 49 18.17 17.97 4.20 37.07 

PKLEFT1 49 14.99 13.15 1.78 43.23 

PKLEFT2 49 28.21 24.88 2.59 75.73 1 N/A: not available 

Table 122 shows correlation statistics and p-values that indicate the association between 

crash counts and the independent variables for type V intersections. Table 123 shows 

correlations between the independent variables. Only those correlations that are 

significant at the 90 percent level are shown. 
149 

Again, as expected, major and minor road AADTs correlate positively with crashes. Peak 

turning movement volume also correlates with crashes, both positively and negatively. 

Shoulder width on major and minor roads, left-and right-lane on major and minor roads, 

acceleration lane on major and minor roads, protected left lane on major and minor roads, 

residential driveway on major and minor roads, terrains, sight distance, vertical curves, 

absolute grades, horizontal curves, intersection angle, and other variables are correlated 

with crashes in the opposite direction than expected, although many of these correlations 

are insignificant. 

Table 122. Correlation Between Crashes and Independent Variables for Type V 

Sites 

TOTACC per YEAR INJACC per YEAR Variables Corr. p-value Corr. p-value 

AADT1 0.2581 0.0095 0.2964 0.0027

AADT2 0.4313 0.0000 0.3056 0.0020

MEDWDTH1 -0.0095 0.9251 0.0123 0.9035

MEDWDTH2 -0.0385 0.7036 -0.0942 0.3513

SHOULDER1 0.2324 0.1008 0.2826 0.0445

SHOULDER2 0.0818 0.5684 0.0557 0.6979

L1RT 0.2271 0.0231 0.1591 0.1138

L1LT 0.1516 0.1323 0.2033 0.0424

L3RT 0.2883 0.0036 0.2113 0.0348

L3LT 0.2178 0.0295 0.0771 0.4458

LEGACC1 0.3602 0.0094 0.2391 0.0911

LEGACC2 0.1079 0.4510 0.1461 0.3064

PROTLT1 0.1340 0.1837 0.1408 0.1622

PROTLT2 0.3652 0.0084 0.2452 0.0828

COMDRWY1 0.1012 0.3163 -0.1315 0.1922

RESDRWY1 -0.0130 0.8976 -0.0500 0.6212

DRWY1 0.0850 0.4004 -0.1377 0.1718

COMDRWY2 0.0015 0.9883 -0.1598 0.1122

RESDRWY2 -0.1924 0.0552 -0.0474 0.6399

DRWY2 -0.1149 0.2552 -0.1633 0.1044

LIGHT -0.1885 0.0603 -0.2801 0.0048

SD1 0.1064 0.2919 0.1325 0.1888

SD2 0.1072 0.2886 0.1667 0.0975

SDL1 0.1692 0.0925 0.2437 0.0146

SDL2 0.1400 0.1649 0.2545 0.0106

SDR1 0.2057 0.1475 0.1938 0.1731

SDR2 0.0692 0.6296 0.1321 0.3556
150 

Table 122. Correlation Between Crashes and Independent Variables for 

Type V Sites (Continued) 

TOTACC per YEAR INJACC per YEAR Variables Corr. p-value Corr. p-value 

VEI1 0.1228 0.2234 0.0510 0.6144

VEI2 0.0378 0.7090 0.0467 0.6443

VEICOM 0.1276 0.2059 0.1032 0.3070

VCEI1 0.1167 0.2474 0.0229 0.8208

VCEI2 0.0376 0.7103 0.0275 0.7857

VCEICOM 0.1009 0.3179 0.0367 0.7169

GRADE1 -0.0487 0.6302 -0.1739 0.0836

GRADE2 -0.0312 0.7580 -0.1208 0.2312

HEI -0.0181 0.8578 -0.0292 0.7734

HI -0.1541 0.1258 -0.0822 0.4162

HEI2 -0.0369 0.7155 -0.1023 0.3112

HI2 0.0222 0.8268 -0.0070 0.9450

HEICOM -0.1692 0.0924 -0.1403 0.1639

HICOM -0.0882 0.3829 -0.0572 0.5722

HAU -0.1326 0.1886 -0.1988 0.0474

SPD1 0.2103 0.0357 0.4325 0.0000

SPD2 0.1837 0.0674 0.3819 0.0001

PKTRUK 0.2097 0.1482 0.2116 0.1445

PKTURN 0.1950 0.1794 -0.1203 0.4105

PKTHRU1 -0.2396 0.0973 0.0702 0.6317

PKTHRU2 0.1079 0.4604 0.1468 0.3141

PKLEFT 0.2106 0.1464 -0.0904 0.5368

PKLEFT1 0.3471 0.0145 0.1895 0.1922

PKLEFT2 -0.2983 0.0374 -0.3784 0.0073

Table 123. Summary of Correlations for Independent Variables for Type V Sites 

Variable Positive Correlates1 Negative Correlates1

AADT1 

AADT2, SIGTYPE2, MEDTYPE2, L1LT, 

PROTLT1, RESDRWY2, LIGHT, 

PKTHRU1 

GRADE1, PKTURN, PKTHRU2, 

PKLEFT 

AADT2 

AADT1, SIGTYPE1, L1RT, L1LT, L3RT, 

L3LT, LEGACC1, SDR1, HEI1, HI2, 

PKTURN, PKLEFT, PKLEFT1 

SIGTYPE3, HAZRAT1, HAZRAT2, 

GRADE2, HAU, PKTHRU1 

PROTLT1 

AADT1, SIGTYPE2, L1RT, L1LT, 

LEGACC1, LEGACC2, PROTLT2, 

RESDRWY2, TERRAIN2, VEI2,VEICOM, 

VCEI1, VCEICOM, HEI, HEI2, HI2, 

HEICOM, HICOM SIGTYPE1, DRWY1, COMDRWY2, 
151 

Table 123. Summary of Correlations for Independent Variables for 

Type V Sites (Continued) 

Variable Positive Correlates1

 Negative Correlates1

MEDWDTH1 

MEDTYPE1, MEDTYPE1minor, 

MEDWDTH2, L1LT, VEI2, VEICOM, 

VCEICOM, PKLEFT1 SIGTYPE1 

HAU TERRAIN1, VEI2, PKTHRU1 

AADT2, METYPE1minor, 

MEDWDTH2, L3LT 

HAZRAT1 

SIGTYPE3, MEDTYPE2, HAZRAT2, 

TERRAIN1, VEI1, VCEI1, VCEICOM, 

GRADE1, GRADE2, HEICOM 

AADT2, SIGTYPE1, SHOULDER1, 

SHOULDER2, L1RT, L1LT, L3RT, 

L4LT, LEGACC1, PROTLT2, SD1, 

SD2, SDL1, SDL2, SDR1, SDR2, 

SPD1, SPD2 

DRWY1 

COMDRWY1, RESDRWY1, 

COMDRWY2, DRWY2, LIGHT, PKTURN, 

PKLEFT, PKLEFT1 

L1RT, L1LT, PRTLT1, SD2, SDL1, 

SDL2, SDR1, SPD1, SPD2, 

PKTHRU1 

SPD1 

SIGTYPE2, L1RT, L1LT, L3RT, L3LT, 

SD1, SD2, SDL1, SDL2, SDR1, SDR2, 

SPD2, PKTRUCK 

HAZRAT1, HAZRAT2, 

COMDRWY1, DRWY1, 

COMDRWY2, DRWY2, LIGHT, 

VCEICOM, GRADE2, HEI1, 

PKTURN, PKLEFT 

SPD2 

L1RT, L1LT, L3RT, L3LT, SDD1, SD2, 

SDL1, SDL2, SDR1, SDR2, SPD1, 

PKTRUCK, PKTHRU2 

HAZRAT1, HAZRAT2, 

COMDRWY1, DRWY1, 

COMDRWY2, RESDRWY2, 

DRWY2, LIGHT, GRADE2, HEI1, 

HEI2, HI2, HEICOM, HICOM, 

PKLEFT2 

LIGHT 

(no=0,yes=1) 

AADT1, SIGTYPE1, PROTLT1, 

COMDRWY1, DRWY1, COMDRWY2, 

DRWY2, PKLEFT2 

SIGTYPE3, L1RT, L3RT, SDL1, 

SDL2, SPD1, SPD2, PKLEFT1 

TERRAIN1 

MEDTYPE2, HAZRAT1, TERRAIN2, 

VEI1, VEICOM, VCEI1, VCEICOM, 

GRADE1, GRADE2, HICOM, HAU 

L1RT, L1LT, SD1, SD2, SDL1, 

SDL2, SDR2 

L1RT 

L1LT, L3RT, L3LT, LEGACC1, PROTLT1, 

SD1, SD2, SDL1, SDL2, SPD1, SPD2 

HAZRAT1, COMDRWY1, DRWY1, 

LIGHT, TERRAIN1, VEI1, VCEI1, 

GRADE1, HEI1, HI1, HICOM 

L1LT 

AADT1, SIGTYPE2, MEDTYPE1, 

MEDWDTH1, L1RT, L3LT, PROTLT1, 

SD1, SDR2, SPD1, SPD2 

SIGTYPE1, HAZRAT1, HAZRAT2, 

COMDRWY1, DRWY1, 

COMDRWY2, DRWY2, TERRAIN1, 

GRADE1 
152 

Table 123. Summary of Correlations for Independent Variables for 

Type V Sites (Continued) 

Variable Positive Correlates1

 Negative Correlates1

L3RT 

AADT2, SHOULDER1, L1RT, L3LT, 

SDL1, SDL2, SDR1, SDR2, HEI2, HI2, 

SPD1, SPD2, PKTHRU2 

HAZRAT1, DRWY2, LIGHT, VEI2, 

VEICOM, PKLEFT2 

L3LT 

AADT2, L1RT, L3RT, LEGACC1, 

PROTLT1, SD2, SDL2, VEI1, SPD1, SPD2, 

PKTHRU2 

HAZRAT1, COMDRWY1, 

COMDRWY2, RESDRWY2, 

DRWY2, HAU, PKTHRU1 

PKTRUCK PROTLT1, SPD1, SPD2 

PKTURN 

AADT2, COMDRWY1, DRWY1, 

COMDRWY2, VEI1, VEICOM, VCEI1, 

VCEICOM, GRADE1, HEI1, HI2, PKLEFT, 

PKLEFT1 

AADT1, SIGTYPE2, RESDRWY2, 

SPD1, PKTHRU1, PKTHRU2 

VEICOM 

MEDWDTH1, LEGACC2, PROTLT1, 

TERRAIN2, VEI1, VEI2, VCEI1, VCEI2, 

VCEICOM, GRADE1, GRADE2, HI1, 

PKTURN, PKLEFT1 L3RT, SD1, SDR1, SDR2, PKTHRU1 

HEICOM 

PROTLT1, HAZRAT1, HAZRAT2, VEI1, 

GRADE1, GRADE2, HEI1, HI1, HEI2, HI2, 

HICOM, PKLEFT2 SD1, SD2, SDL1, SDL2, SDR1, SPD2 

GRADE1 

HAZRAT1, HAZRAT2, TERRAIN1, VEI1, 

VEICOM, VCEI1, VCEICOM, GRADE2, 

HI1, HEI2, HEICOM, HICOM, PKTURN, 

PKLEFT 

AADT1, L1RT, L1LT, SD1, SD2, 

SDL1, SDL2, SDR2, PKTHRU1 

SDL2 

SHOULDER1, L1RT, L3RT, L3LT, SD1, 

SD2, SDL1, SDR1, SDR2, SPD1, SPD2 

HAZRAT1, HAZRAT2, 

COMDRWY1, DRWY1, DRWY2, 

LIGHT, TERRAIN1, TERRAIN2, 

GRADE1, GRADE2, HEI1, HI2, 

HEICOM, HICOM 

SDR2 

SHOULDER1, L1LT, L3RT, SD1, SD2, 

SDL1, SDL2, SDR1, SPD1, SDP2 

HAZRAT1, HAZRAT2, TERRAIN1, 

VEI1, VEI2, VEICOM, VCEI1, 

VCEI2, VCEICOM, GRADE1, 

GRADE2 1 Variables only significant with p-value of 0.1 were selected 
153 

3.3 AADT MODEL ESTIMATION RESULTS 

This section discusses the development of AADT-only models. Two types of models are 

presented for Types I and II sites, and three types of models are given for Type III, IV, 

and V sites in this report. First, models were calibrated using all available data from the 

HSIS California database, the original sites from Minnesota and Michigan, and the 

Georgia validation data. This group of data is referred to as Group B. Second, Types I to 

IV models were developed for a subset of these sites that met specified conditions for 

possible use as base models in the IHSDM accident prediction algorithm. For Types III, 

IV, V sites, additional AADT models were calibrated from a dataset that met the base 

conditions of the significant variables in the full models. These AADT-only models used 

the data for the original sites from California and Michigan along with the Georgia 

validation data. This group of data is referred to as Group A. Table 124 shows the 

summary of the data used for AADT-only models. 

Table 124. Summary of AADT Models Recalibrated and Data Used 

Model Site Types and Data Used 

Description Types I and II Type III Type IV Type V 

Group B Sites: 

AADT Model for 

all sites, including 

California HSIS1 

California HSIS 

Minnesota 

Georgia 

California HSIS 

Michigan 

Georgia

California HSIS 

Michigan 

Georgia 

California HSIS 

Michigan 

Georgia 

Subset of Group B 

Sites: 

AADT Model for 

sties meeting base 

conditions for 

project data plus 

California HSIS1 

California HSIS 

Minnesota 

Georgia 

California HSIS 

Michigan 

Georgia

California HSIS 

Michigan 

Georgia Not calibrated 

Subset of Group A 

Sites: 

Model for sites 

meeting base 

conditions for 

project data Not calibrated 

California project 

Michigan 

Georgia 

California project 

Michigan 

Georgia 

California project 

Michigan 

Georgia 1 The California project data for Types III, IV, and V were not used 

Models were developed for total accidents (TOTACC) and injury (fatal + nonfatal injury) 

accidents (INJACC) using accidents within 76.25 m (250 ft) of the intersection center. 

3.3.1 Description of Base Conditions 

The accident prediction algorithm outlined in the “Red Book” provides AMFs for four 

variables: intersection skew angle; left-turn lanes on major approach; right-turn lanes on 

major approach; and the number of intersection quadrants with inadequate sight 

distance.(3) It was sought to develop AADT-only base models using sites which met the 

base condition criteria for these AMFs and for any other variables that logically and 

practically could provide additional AMFs. 
154 

Base conditions were defined by examining the distribution of variables and selecting the 

most common condition, keeping in mind that enough sites must remain to calibrate 

reliable models. Whether a variable exhibited an impact on safety was also considered in 

defining base conditions. 

Group A and B Data 

For type I and II intersections, the base models were developed using all of the Minnesota, 

Georgia, and California HSIS data, the combination of which is referred to as Group B. 

For Type III and IV intersections, base models were developed from two datasets. The 

first included the Michigan, original California, and Georgia sites (Group A). The second 

included the Michigan, Georgia, and California HSIS sites (Group B). 

The Group B dataset has more sample sites but fewer variables than the Group A dataset 

for Type I to IV sites. Therefore, while the Group B dataset is more useful for the AADT 

model development, the Group A datasets benefit the full model development because of 

the large number of variables. Type III and IV considered both Group A and B sites for 

the full model and AADT model development. Type V base models were calibrated only 

for the Group A sites because only five sites could have been added from the Group B 

California HSIS data. 

Group B Base Conditions 

Intersection skew angle was not included as a base condition because the California HSIS 

data does not contain this variable and the skew angle at those sites where it is known is 

in fact highly variable. Selecting a skew angle of zero as a base condition would have left 

few sites for calibrating a base condition model. 

For the Minnesota sites and the California HSIS sites, sight distance information is not 

available, and was therefore not included as a base condition. However, it is reasonable to 

believe that the majority of sites have adequate sight distance since roads are constructed 

to design standards and exceptions are made only where necessary. Thus, the base 

models developed could be applied assuming they represent sites with adequate sight 

distance, and that inadequate sight distance could be taken into account with the use of an 

AMF. In the event that many of the sites did, in fact, have deficient site distance, the base 

models calibrated with a contrary assumption would produce artificially high predictions 

if crashes actually increased with deficient sight distance. 

The Group B nominal or base conditions and the number of sites meeting these 

conditions for model types I to IV are presented in table 125. For Types I and II, 

approximately 65 percent of all the sites met all of the specified base conditions, while 

for Types III and IV, the percentage of sites that met all of the base conditions was 

approximately 20 percent and 15 percent, respectively. 

For Types I and II, no turning lanes on the major or minor road and no medians on the 

major road were selected as base conditions. 
155 

Table 125. Group B Base Conditions for Type I to IV AADT Models 

Variable 

Type 

I and II 

Base 

Condition 

Type I 

Frequency 

(Percent) 

Type II 

Frequency 

(Percent) 

Type 

III and IV 

Base 

Condition 

Type III 

Frequency 

(Percent) 

Type IV 

Frequency 

(Percent) 

Right turn on major No 1563 (85.97) 911 (82.40) No 253 (86.05) 164 (73.87)

Right turn on minor No 1770 (97.36) 1080 (97.60) No 268 (91.16) 176 (79.28)

Left turn on major No 1382 (76.02) 883 (79.84) Yes 174 (59.18) 145 (65.32)

Left turn on minor No 1804 (99.23) 1105 (99.91) No 292 (99.32) 219 (98.65)

Median on major No 1738 (96.60) 1069 (96.65) Yes 212 (73.87) 148 (66.67)

Terrain on major N/A1 Flat 164 (55.78) 148 (66.67)

Total sites meeting 

all base conditions 1213 (66.72) 718 (64.92) 62 (21.09) 34 (15.32)

Total sites 1818 (100.00)

1106 

(100.00) 294 (100.00) 222 (100.00) 1 N/A: not available 

Unlike Types I and II, terrain on major road was included as a base condition for Types 

III and IV because it showed a significant impact on safety. Also for Types III and IV, 

and unlike the cases for Types I and II, the base conditions included the presence of a 

left-turn lane on the major road and the presence of a median on the major road. 

Group A Base Conditions 

The Group A nominal or base conditions and the number of sites meeting these 

conditions for model Types III to V are presented in tables 126 to 131. Separate base 

conditions were defined for TOTACC and INJACC models. The percentage of sites 

meeting all of the base conditions ranged from approximately 26 percent to 54 percent. 

Type III 

For total accidents, vertical curves on the major road, commercial driveways on the major 

road, and intersection angle were selected as significant variables from the full models. 

Table 126 shows the base conditions for these variables. For vertical curves, only a few 

sites met the “no vertical curve” condition and, therefore, a VEI less than 1 degree per 

30.5 m (100 ft) (which is relatively flat) was used for the base condition. Similarly, an 

intersection angle between plus or minus 5 degrees was defined as the base condition 

representing “no skew.” No commercial driveways within 76.25 m (250 ft) of the 

intersection center is the final base condition. 
156 

Table 126. Group A Base Conditions for Type III TOTACC AADT Models 

Variable Base Conditions Frequency (Percent) 

VEI1 Flat (≤1° per 100 ft) 88 (64.7) 

COMDRWY1 0 83 (61.0) 

HAU -5° ~ 5° 89 (65.4) 

Total sites meeting all base conditions 39 (28.68) 

Total sites 136 (100.0) 

For injury accidents, hazard rating on the major road, commercial driveways on the major 

road, and intersection angle were selected as significant variables from the full models. 

Table 127 shows base conditions for these variables. For hazard rating, values of 1 and 2 

were taken as the base condition. An intersection angle between plus and minus 5 

degrees and no commercial driveways within 76.25 m (250 ft) of the intersection center 

were the other base conditions. 

Table 127. Group A Base Conditions for Type III INJACC AADT Models 

Variable Base Conditions Frequency (Percent) 

COMDRWY1 0 83 (61.0) 

HAU -5° ~ 5° 89 (65.4) 

HAZRAT1 1 or 2 74 (54.4) 

Total sites meeting all base conditions 36 (26.47) 

Total sites 136 (100.0) 

Type IV 

For total accidents, “right” sight distance from minor road and median type on major road 

were selected as significant variables from the full models. Table 128 shows the base 

conditions for these variables. Adequate sight distance and no median are the base 

conditions. The same rule was applied to judge adequate sight distance as the rule 

described on page 48 of the Harwood et al. report.(3)

Table 128. Group A Base Conditions for Type IV TOTACC AADT Models 

Variable Base Conditions Frequency (Percent) 

SDR2 Adequate right sight distance 116 (96.0) 

MEDTYPE No median type 70 (56.5) 

Total sites meeting all base conditions 67 (54.03) 

Total sites 124 (100.0) 

For injury accidents, right sight distance from minor road, median type on major roads, 

and posted speed limit on minor road were selected as significant variables from the full 

models. Table 129 shows the base conditions for these variables. Adequate sight distance, 

no median type, and speed limit between 48 and 56 kilometers per hour (km/h) (30 and 

35 miles per hour (mi/h)) are the base conditions. As for total accidents, the same rule 

was applied to estimate adequate sight distance as was described on page 48 of the 

Harwood et al. report.(3) For posted speed limit, not enough sites with a single posted 
157 

speed limit could represent a base condition. Therefore, a range with the highest 

frequency (48 to 56 km/h (30 to 35 mi/h)) was considered as the base condition. 

Table 129. Group A Base Conditions for Type IV INJACC AADT Models 

Variable Base Conditions Frequency (Percent) 

SDR2 Adequate right sight distance 116 (96.0) 

MEDTYPE1 No median type 70 (56.5) 

SPD2 30 ~ 35 mi/h 84 (67.7) 

Total sites meeting all base conditions 38 (30.65) 

Total sites 124 (100.0) 

Type V 

Total accidents HEICOM for major and minor roads, median type on major roads, and 

posted speed limit on major roads were estimated as significant in the full models and 

used for base conditions. Table 130 shows the base conditions for these variables. For 

HEICOM, radium larger than 458 m (1500 ft) was considered as the base condition. For 

posted speed limit, the speed range between 72–88 km/h (45–55 mi/h) was used as the 

base condition since this range had the highest frequency. 

Table 130. Group A Base Conditions for Type V TOTACC AADT Models 

Variable Base Conditions Frequency (Percent) 

HEICOM ≤ 3.82 (radius ≥ 1500 ft) 80 (80.0) 

MEDTYPE No median type 87 (87.0) 

SPD1 72–88 km/h (45 ~ 55 mi/h) 66 (66.0) 

Total sites meeting all base conditions 49 (49.00) 

Total sites 100 (100.0) 

For injury accidents, posted speed limit on major road and presence of lighting at 

intersection were selected as significant variables from the full models. Table 131 shows 

the base conditions for these variables. Presence of lighting and speed range between 72 

and 89 km/h (45 and 55 mi/h) were considered as the base conditions. 

Table 131. Group A Base Conditions for Type V INJACC AADT Models 

Variable Base Conditions Frequency (Percent) 

SPD1 72–88 km/h (45 ~ 55 mi/h) 66 (66.0) 

LIGHT Yes 71 (71.0) 

Total sites meeting all base conditions 39 (39.00) 

Total sites 100 (100.0) 

3.3.2 Model Results 

The AADT-only modeling results are discussed next. In the tables below, the data for and 

models calibrated using all available sites are referred to in the table headings as main 

models. 
158 

Type I Models 

The datasets used to develop Type I AADT-only models included the Minnesota sites 

from the original study, with the additional years of accident data, the Georgia sites, and 

sites extracted from the California HSIS database. Sites with very low volume typically 

are not representative of sites in the general population. These low volume counts, 

sometimes as low as one vehicle per day, appear to be of suspect quality. With a large 

number of available sites, intersections with a major road AADT below 400 or a minor 

road AADT below 100 were removed from the data. The total number of sites and the 

number of Group B base condition sites are given in table 132. Summary statistics on 

these datasets are presented in table 133. 

Table 132. Number of Sites Used for Type I Main and Group B Base AADT Models 

Dataset All Sites Group B Base 

Condition Sites 

Percent (Base/All Sites) 

Minnesota 1985–98 270 133 49.3 

Georgia 1996–97 116 107 92.2 

California 1991–98 1432 973 67.9 

Table 133. Summary Statistics for Type I Sites: Main and Group B Base 

AADT Models 

All Sites Group B Base Condition Sites 

Variable Mean Median Minimum Maximum Mean Median Minimum Maximum

TOTACC/yr 0.6074 0.3750 0 6.75 0.5326 0.3750 0 6.00 

INJACC/yr 0.2660 0.1250 0 4.13 0.2368 0.1250 0 4.13 

AADT1 6011 4475 401 35750 4885 3800 401 20190 

AADT2 492 270 100 10001 374 201 100 6480 

Tables 134 and 135 report the parameter estimates for the Type I TOTACC and INJACC 

models calibrated using all sites as well as for those sites meeting the Group B base 

conditions. A unique constant term was estimated for each location to account for the 

differences in accident reporting and other characteristics between jurisdictions. Separate 

values of K, the overdispersion parameter, have been estimated for each location using a 

specially written maximum likelihood program. 

Vogt and Bared did not report AADT-only models for Type I intersections, but AADTonly base models subsequently were derived by Harwood et al. by setting default values 

of two for HAZRAT1 and no right-turn lane on the major road in a model for predicting 

total intersection related accidents.(1,3) A comparison between this model applied to the 

recalibration data and the recalibrated model for TOTACC is given. A similar model for 

INJACC from the original calibration is not available for comparison. The comparison 

indicates the recalibrated model for total accidents is improved as measured by the GOF 

using the K value. 

The CURE method described earlier was used to suggest any alternate model forms that 

could provide an improved fit to the data. The results indicated that the recalibrated 
159 

model using the original exponential model form adequately fit the data and that the 

various adjustments to this model form did not improve the AADT models. Specifically, 

the Pearson product-moment correlation coefficient, MPB per year, and MAD per year 

were negligibly different. Therefore it was decided to retain the original model form. 

Appendix D shows the CURE plot for the Type I AADT TOTACC model. 

Tables 134 and 135 indicate that the β coefficient of the log of major road AADT is 

about two times that for minor road AADT, which seems to be a reasonable expectation 

on the basis of other models reported in the literature. For the TOTACC model, the base 

conditions model was estimated with a lower overall K than the model using all sites. 

This would be expected, because the base condition sites should be more homogeneous in 

their design characteristics. For the INJACC model, the overall K was the same for the 

two AADT models. 

Table 134. Parameter Estimates for Recalibrated TOTACC Type I: Main and 

Group B AADT Models 

Variable 

All Sites 

Estimate 

(s.e., p-value) 

Original 

AADT Model1

Applied to All 

Sites 

Group B Base 

Condition Sites 

Estimate 

(s.e., p-value) 

Original 

AADT Model1

Applied to Base 

Condition Sites 

Minnesota 

constant

-8.055 

(0.225, <0.001) 

-10.900 

(0.148, <0.001) 

-8.030 

(0.294, <0.001) 

-10.9 

(0.148, <0.001) 

Georgia constant 

-7.140 

(0.246, <0.001) 

-7.132 

(0.315, <0.001) 

California constant 

-8.229 

(0.232, <0.001) N/A2 -8.206 

(0.303, <0.001) N/A2

Log of AADT1 

0.6180 

(0.0249, <0.001) 

0.7900 

(0.0630, <0.001) 

0.6445 

(0.0310, <0.001) 

0.7900 

(0.0630, <0.001) 

Log of AADT2 

0.3872 

(0.0215, <0.001) 

0.4900 

(0.0680, <0.001) 

0.3540 

(0.0296, <0.001) 

0.4900 

(0.0680, <0.001) 

K–all locations 

K–Minnesota 

K–Georgia 

K–California 

0.417 

0.256 

0.161 

0.476 0.540 

0.370 

0.244 

0.192 

0.400 0.540 

Pearson productmoment correlation 

coefficient 0.668 0.658 0.600 0.584 

MPB/yr -0.001 0.280 -0.004 0.293 

MAD/yr 0.368 0.394 0.321 0.367 

1 The base model published in Harwood et al., 2000, (p. 21) 

 2 N/A: not available 
160 

Table 135. Parameter Estimates for Recalibrated INJACC Type I: Main and 

 Group B AADT Models1

Variable 

All Sites 

Estimate (s.e., p-value) 

Group B Base Condition Sites 

Estimate (s.e., p-value) 

Minnesota constant

-8.778 

(0.275, <0.001) 

-8.834 

(0.376, <0.001) 

Georgia constant 

-7.942 

(0.304, <0.001) 

-8.035 

(0.405, <0.001) 

California constant 

-8.788 

(0.283, <0.001) 

-8.8524 

(0.388, <0.001) 

Log of AADT1 

0.6159 

(0.0306, <0.001) 

0.6426 

(0.0397, <0.001) 

Log of AADT2 

0.3551 

(0.0253, <0.001) 

0.3382 

(0.0364, <0.001) 

K–all locations 

K–Minnesota 

K–Georgia 

K–California 

0.435 

0.263 

0.303 

0.500 

0.435 

0.227 

0.294 

0.476 

Pearson product-moment 

correlation coefficient 0.586 0.520 

MPB/yr -0.0001 0.0001 

MAD/yr 0.195 0.182 

1

No previously calibrated AADT-only model for injury accidents exists for comparison for Type I 

 sites 

Type II Models 

The datasets used to develop the Type II main and Group B base models included the 

Minnesota sites from the original study, with the additional years of accident data, the 

Georgia sites, and sites extracted from the California HSIS database. As for Type I, the 

large number of sites available allowed for the removal of those sites with a major road 

AADT less than 400 or a minor road AADT less than 100, the rationale again being that 

the omitted sites either have errors in AADTs or are unrepresentative of those in the 

general population. The total number of sites and the number of Group B base condition 

sites are given in table 136. Summary statistics on these datasets are presented in table 

137. 

Table 136. Number of Sites Used for Type II Main and Group B Base 

AADT Models 

Dataset All Sites Group B Base Condition 

Sites 

Percent (Base/All Sites) 

Minnesota 1985–98 250 120 48.0 

Georgia 1996–97 108 100 92.6 

California 1991–98 748 498 66.6 
161 

Table 137. Summary Statistics for Type II Sites: Main and Group B Base 

AADT Models 

All Sites Group B Base Condition Sites 

Variable Mean Median Minimum Maximum Mean Median Minimum Maximum

TOTACC/yr 0.9227 0.5357 0 7.13 0.8440 0.5000 0 7.07 

INJACC/yr 0.4665 0.2500 0 4.75 0.4249 0.2500 0 3.50 

AADT1 5487 4245 407 38126 4855 3907 407 28860 

AADT2 532 344 100 7460 448 310 100 5801 

Tables 138 and 139 report the parameter estimates for the Type II TOTACC and INJACC 

models, which were calibrated using all sites and those meeting the base conditions. A 

unique constant term was estimated for each location to account for the differences in 

accident reporting and other characteristics between jurisdictions. Separate values of K, 

the overdispersion parameter, have been estimated for each location using the specially 

developed maximum likelihood program. 

Vogt and Bared did not report AADT-only models for Type II intersections.(1) However, 

AADT-only base models were subsequently derived by setting default values of “no 

intersection skew angle” and “no driveways within 76.25 m (250 ft) of the intersection” 

on the major road for a model for predicting total intersection related accidents.(3) A 

comparison between this model applied to the recalibration data and the recalibrated 

model for TOTACC is given. A similar model for INJACC for the original calibration is 

not available for comparison. The comparison indicates the recalibrated model for total 

accidents has an inferior GOF compared to the Vogt and Bared models using the K value 

for all States, both combined and individually. In particular, the model does a poorer job 

for the Georgia and California sites. 

The CURE method was again used to suggest any alternate model forms that could 

provide an improved fit the data. The results indicated that the recalibrated model using 

the original exponential model form adequately fit the data, and the various adjustments 

to this model form did not improve the AADT models. Specifically, there was a 

negligible difference in Pearson product-moment correlation coefficient, MPB per year, 

and MAD per year. Therefore it was decided to retain the original model form. Appendix 

D shows the CURE plot for the Type II AADT TOTACC model. 

Table 138 indicates that the β coefficient of the log of major road AADT is about 35 

percent higher than that for minor road AADT value. Table 139 indicates that the β

coefficient of the log of major road AADT is about 10 to 20 percent higher than that for 

minor road AADT, which is consistent with previous modeling efforts. For both the 

TOTACC and INJACC models, the base condition models were estimated with a lower 

overall K than the model using all sites. Again, this would be expected, because the base 

condition sites should be more homogeneous in their design characteristics. 
162 

Table 138. Parameter Estimates for Recalibrated TOTACC Type II: Main and 

Group B AADT Models 

Variable 

All Sites 

Estimate 

(s.e., p-value) 

Original 

AADT Model1

Applied to All Sites 

Group B Base 

Condition Sites 

Estimate 

(s.e., p-value) 

Original 

AADT Model1

Applied to Base 

Condition Sites 

Minnesota constant 

-8.747 

(0.294, <0.001) 

-9.340 

(0.720, <0.001) 

-9.494 

(0.407, <0.001) 

-9.340 

(0.720, <0.001) 

Georgia constant 

 -8.299 

(0.312, <0.001) 

-8.970 

(0.424, <0.001) 

California constant 

-8.832 

(0.301, <0.001) N/A1 -9.4532 

(0.415, <0.001) N/A1

Log of AADT1 

0.6723 

(0.0331, <0.001) 

0.6010 

(0.0780, <0.001) 

0.7128 

(0.0423, <0.001) 

0.6010 

(0.0780, <0.001) 

Log of AADT2 

0.4873 

(0.0267, <0.001) 

0.6100 

(0.0690, <0.001) 

0.5445 

(0.0361, <0.001) 

0.6100 

(0.0690, <0.001) 

K–all locations 

K–Minnesota 

K–Georgia 

K–California 

0.400 

0.256 

0.556 

0.435 0.240 

0.370 

0.256 

0.588 

0.385 0.240 

Pearson productmoment correlation 

coefficient 0.686 0.669 0.747 0.733 

MPB/yr -0.010 0.305 -0.004 0.335 

MAD/yr 0.532 0.542 0.480 0.514 1 The base model published in Harwood et al., 2000 (p. 22) 2 N/A: not available 
163 

Table 139. Parameter Estimates for Recalibrated INJACC Type II: Main and 

Group B AADT Models 1

Variable 

All Sites 

Estimate (s.e., p-value) 

Base Condition Sites 

Estimate (s.e., p-value) 

 -9.266 -9.707 

Minnesota constant (0.339, <0.001) (0.472, <0.001) 

 -8.636 -9.071 

Georgia constant (0.361, <0.001) (0.492) 

California constant 

-9.213 

(0.347, <0.001) 

-9.5611 

(0.481) 

Log of AADT1 0.6210 0.6282 

 (0.0380, <0.001) (0.0490, <0.001) 

Log of AADT2 0.5118 0.5692 

 (0.0301, <0.001) (0.0411, <0.001) 

K–all locations 0.417 0.385 

K–Minnesota 0.294 0.303 

K–Georgia 0.161 0.217 

K–California 0.476 0.435 

Pearson product-moment 

correlation coefficient 0.626 0.679 

MPB/yr -0.005 -0.001 

MAD/yr 0.302 0.279 

1 No previously calibrated AADT-only model for injury accidents exists for comparison 

 for type II sites 

Type III Models 

The dataset used to develop the main Type III model included the Michigan sites from 

the original study, with the additional years of accident data, the Georgia sites, and those 

extracted from the California HSIS database. Unlike the case for Types I and II models, 

the researchers did not have the luxury of removing sites with a minor road AADT less 

than 100, because as many as 87 out of the 294 available sites had an AADT on the 

minor road of less than 100. 

Base models were calibrated using both the Group A and Group B datasets. The total 

number of sites and the number of Group B base condition sites are given in table 140. 

Summary statistics on these datasets are presented in table 141. 
164 

Table 140. Number of Sites Used for Type III Main and Group B Base 

Condition AADT Models 

Dataset All Sites Group B Base Condition 

Sites 

Percent (Base/All Sites) 

Michigan 1993–97 24 0 0.0 

Georgia 1996–97 52 14 27.0 

California 1991–98 218 48 22.0 

Table 141. Summary Statistics for Type III Sites: Main and Group B 

Base AADT Models 

All Sites Group B Base Condition Sites 

Variable Mean Median Minimum Maximum Mean Median Minimum Maximum 

TOTACC/yr 1.13 0.50 0.00 15.13 1.05 0.63 0 6.88 

INJACC/yr 0.45 0.25 0.00 5.13 0.57 0.38 0 4.13 

AADT1 17002 12909 1902 74500 18933 15433 6500 57731 

AADT2 449 206 1 9490 466 325 10 2500 

Tables 142 and 143 report parameter estimates for the main Type III TOTACC and 

INJACC models, calibrated using all sites and as well as those meeting the Group B base 

conditions. Unlike models for Type I and II intersections, a unique constant term was not 

included for each State, because the State indicator variables were insignificant. 

For reference, comparisons between the Vogt AADT models applied to the recalibration 

data and the recalibrated models for TOTACC and INJACC are also given in tables 142, 

143, and 145. The comparisons indicate the recalibrated models for TOTACC and 

INJACC have a better GOF measures compared to the Vogt models. 

The CURE plot method proposed by Hauer was also used to suggest any alternate model 

forms that could provide an improved fit for the data. The results indicated that the 

recalibrated models using the original exponential model form adequately fit the data and 

that the various adjustments to this model form did not improve the AADT models. 

Specifically, the differences in Pearson product-moment correlation coefficient, MPB per 

year, and MAD per year were negligible. Therefore the original model form was retained. 

Appendix D shows the CURE plot for the Type III AADT TOTACC model. 

Table 142 indicates that the β coefficient of the log of major road AADT is about two to 

three times that for minor road AADT, a reasonable expectation. Table 143 shows that β

coefficient of the log of major road AADT is about three to four times that for minor road 

AADT, which is also consistent with previous efforts. Pearson product-moment 

correlation coefficients for TOTACC and INJACC models were approximately 0.65. 
165 

Table 142. Parameter Estimates for Recalibrated TOTACC Type III: Main and 

Group B Base AADT Models 

Variable 

All Sites 

Estimate 

(s.e., p-value) 

Original 

AADT Model1

Applied to All 

Sites 

Group B Base 

Condition Sites 

Estimate 

(s.e., p-value) 

Original 

AADT Model1

Applied to Base 

Condition Sites 

 -9.6835 -12.9243 -12.1332 -12.9243 

Constant (0.6109, 0.0000) (2.3682,0.0001) (1.9357, 0.0000) (2.3682,0.0001) 

 0.8238 1.1989 1.0941 1.1989 

Log of AADT1 (0.0613, 0.0000) (0.2477,0.0001) (0.1762, 0.0000) (0.2477,0.0001) 

 0.3206 0.3027 0.2544 0.3027 

Log of AADT2 (0.0317, 0.0000) (0.0892,0.0007) (0.0636, 0.0001) (0.0892,0.0007) 

K 0.5849 0.5256 0.3125 0.5256 

Pearson productmoment correlation 

coefficient 0.66 0.68 0.67 0.58 

MPB/yr 0.03 -0.52 0.02 -0.70 

MAD/yr 0.71 1.02 0.60 0.96 

1 The AADT model published in Vogt, 1999, (p. 111) 

Table 143. Parameter Estimates for Recalibrated INJACC Type III: Main and 

Group B Base AADT Models 

Variable 

All Sites 

Estimate 

(s.e., p-value) 

Original 

AADT Model1

Applied to All 

Sites 

Group B Base 

Condition Sites 

Estimate 

(s.e., p-value) 

Original 

AADT Model1

Applied to Base 

Condition Sites 

 -12.0590 -13.1685 -15.2817 -13.1685 

Constant (0.8435, 0.0000) (3.0319,0.0001) (2.2629, 0.0000) (3.0319,0.0001) 

 0.9980 1.2028 1.3316 1.2028 

Log of AADT1 (0.0814, 0.0000) (0.3082,0.0001) (0.2081, 0.0000) (0.3082,0.0001) 

 0.2720 0.1925 0.2648 0.1925 

Log of AADT2 (0.0366, 0.0000) (0.0931,0.0388) (0.0717, 0.0002) (0.0931,0.0388) 

K 0.5162 0.5649 0.3074 0.5649 

Pearson productmoment correlation 

coefficient 0.67 0.66 0.63 0.62 

MPB/yr 0.01 0.08 0.01 -0.20 

MAD/yr 0.32 0.59 0.32 0.49 

1 The AADT model published in Vogt, 1999, (p.113) 

Summary statistics on the Group A base condition datasets are presented in table 144. 
166 

Table 144. Summary Statistics for Type III Sites: Group A Base AADT Models

Group A Base Condition Sites TOTACC 

No. of Sites = 39 

Group A Base Condition Sites INJACC 

No. of Sites = 36 

Variable Mean Median Minimum Maximum Mean Median Minimum Maximum 

ACC/yr 0.76 0.50 0 4.20 0.23 0.00 0 1.60 

AADT1 12087 10977 2360 33333 11610 10217 4794 28000 

AADT2 324 180 20 2500 359 292 15 1128 

Table 145 reports the parameter estimates for the Group A Type III TOTACC and 

INJACC base models. The β coefficient of the log of major road AADT is about three to 

four times that for minor road AADT, which is reasonable. The INJACC models differed 

from the TOTACC models in the use of LOG (AADT1 * AADT2) rather than the 

individual logs of the major and minor road AADTs. For INJACC, the coefficient of the 

log of AADT2 was quite insignificant because of large standard error. Pearson productmoment correlation coefficients of TOTACC and INJACC AADT models were 0.65 and 

0.47, respectively. 

Table 145. Parameter Estimates for Type III Group A TOTACC and 

INJACC Base Models 

Variable 

TOTACC 

Estimate 

(s.e., p-value) 

Original 

TOTACC 

AADT Model1

Applied to 

Group A Sites 

INJACC 

Estimate 

(s.e., p-value) 

Original 

INJACC 

AADT Model2

Applied to 

Group A Sites 

Constant 

-13.8087 

(2.5448, 0.0000) 

-12.9243 

(2.3682,0.0001)

-6.3924 

(2.4337, 0.0086) 

-13.1685 

(3.0319,0.0001) 

Log of AADT1 

1.2194 

(0.2874, 0.0000) 

1.1989 

(0.2477,0.0001) N/A3

1.2028 

(0.3082,0.0001) 

Log of AADT2 

0.3693 

(0.1326, 0.0054) 

0.3027 

(0.0892,0.0007) N/A3

0.1925 

(0.0931,0.0388) 

Log of 

(AADT1*AADT2) N/A3

 N/A3

0.3280 

(0.1614, 0.0421) N/A3

K 0.5227 0.5256 0.7691 0.5649 

K–Vogt, 1999 0.5256 0.5649 

Pearson productmoment correlation 

coefficient 0.65 0.58 0.47 0.64 

MPB/yr -0.01 0.05 0.00 -0.23 

MAD/yr 0.55 0.58 0.25 0.35 

1 The TOTACC AADT model published in Vogt, 1999, (p. 111) 

2 The INJACC AADT model published in Vogt, 1999, (p. 113) 

 3 N/A: not available 

Type IV Models 

The datasets used to develop the main Type IV model included the Michigan sites from 

the original study, with the additional years of accident data, the Georgia sites, and those 

extracted from the California HSIS database. Again, a large number of sites (52 out of 
167 

222) had a minor road AADT of less than 100, so, unlike the case for Types I and II, the 

researchers could not remove sites with a minor road AADT less than 100. 

Base models were calibrated using both the Group A and Group B datasets. The total 

number of sites and the number of Group B base condition sites are given in table 146. 

Summary statistics on these datasets are presented in table 147. 

Table 146. Number of Sites Used for Type IV Main and Group B 

Base Condition AADT Models 

Dataset All Sites 

Group B Base Condition 

Sites Percent (Base/All Sites) 

Michigan 1993–97 18 0 0.0 

Georgia 1996–97 52 1 1.9 

California 1991–98 152 33 21.7 

Table 147. Summary Statistics for Type IV Sites: Main and Group B 

Base AADT Models 

All Sites Group B Base Condition Sites 

Variable Mean Median Minimum Maximum Mean Median Minimum Maximum

TOTACC/yr 1.6 1.0 0.0 10.8 1.3 0.6 0 5.4 

INJACC/yr 0.7 0.4 0.0 4.5 0.7 0.4 0 3.3 

AADT1 15477 12950 2192 69521 18385 13865 2367 43167 

AADT2 552 420 10 7400 345 186 11 2625 

Tables 148 and 149 report the parameter estimates for the main Type IV TOTACC and 

INJACC models, calibrated using all sites and those sites meeting the Group B base 

conditions. Unlike models for Type I and II intersections, a State indicator variable was 

insignificant. For reference, the estimated overdispersion parameter for the original full 

models is also given. 

The CURE method was again used to suggest any alternate model forms that could 

provide an improved fit the data. The results indicated that the various adjustments to this 

model form did not improve the AADT models. Specifically, the Pearson productmoment correlation coefficient, MPB per year, and MAD per year were negligibly 

different. Therefore, the original model form was retrained. Appendix D shows the 

CURE plot for the Type IV AADT TOTACC model. 

Table 148 indicates that, as expected, the β coefficient of the log of major road AADT is 

significantly larger than that for minor road AADT. Table 149 shows that, again, the β

coefficient of the log of major road AADT for the INJACC model is also significantly 

larger than that for minor road AADT. Pearson product-moment correlation coefficients 
168 

for TOTACC and INJACC models were 0.75 and 0.63 using all sites, and 0.90 and 0.89 

for the base sites. 

Comparisons between the Vogt AADT models applied to the recalibration data and the 

recalibrated models for TOTACC and INJACC are also given in tables 148, 149, and 151. 

The comparisons indicate the recalibrated models for TOTACC and INJACC have better 

GOF measures compared to the Vogt models. 

Table 148. Parameter Estimates for Recalibrated TOTACC Type IV: Main and 

Group B Base AADT Models 

Variable 

All Sites 

Estimate 

(s.e., p-value) 

Original 

AADT Model1

Applied to All 

Sites 

Group B Base 

Condition Sites 

Estimate 

(s.e., p-value) 

Original 

AADT Model1

Applied to Base 

Condition Sites 

Constant 

-8.0289 

(0.8553, 0.0000) 

-6.9352 

(2.3767,0.0035)

-14.9469 

(1.5082, 0.0000) 

-6.9352 

(2.3767,0.0035) 

0.6136 0.4683 1.2826 0.4683 

Log of AADT1 (0.0959, 0.0000) (0.2330,0.0444) (0.1398, 0.0000) (0.2330,0.0444) 

0.4359 0.5135 0.4671 0.5135 

Log of AADT2 (0.0360, 0.0000) (0.0896,0.0001) (0.0779, 0.0000) (0.0896,0.0001) 

K 0.6677 0.6144 0.2070 0.6144 

Pearson productmoment 

correlation 

coefficient 0.75 0.73 0.90 0.78 

MPB/yr 0.03 -0.27 0.00 -0.23 

MAD/yr 0.98 1.10 0.48 0.76 

1 The AADT model published in Vogt, 1999, (p. 116) 
169 

Table 149. Parameter Estimates for Recalibrated INJACC Type IV: Main and 

Group B Base AADT Models 

Variable 

All Sites 

Estimate 

(s.e., p-value) 

Original 

AADT Model1

Applied to All 

Sites 

Group B Base 

Condition Sites 

Estimate 

(s.e., p-value) 

Original 

AADT Model1

Applied to Base 

Condition Sites 

Constant 

-8.2849 

(0.9947, 0.0000) 

-9.8454 

(2.5675,0.0001)

-15.1858 

(1.7442, 0.0000) 

-9.8454 

(2.5675,0.0001) 

0.5844 0.7224 1.2513 0.7224 

Log of AADT1 (0.1128, 0.0000) (0.2591,0.0053) (0.1688, 0.0000) (0.2591,0.0053) 

0.3961 0.4778 0.4535 0.4778 

Log of AADT2 (0.0445, 0.0000) (0.1401,0.0007) (0.0811, 0.0000) (0.1401,0.0007) 

K 0.7490 0.5741 0.1486 0.5741 

Pearson productmoment correlation 

coefficient 0.63 0.61 0.89 0.86 

MPB/yr 0.02 -0.22 -0.01 -0.15 

MAD/yr 0.53 0.63 0.29 0.39 

1 The AADT model published in the Vogt’s report, 1999, (p. 118) 

Summary statistics on the Group A base condition datasets are presented in table 150. 

Table 150. Summary Statistics for Type IV Sites: Group A Base AADT Models

Group A Base Condition Sites TOTACC 

No. of Sites = 67 

Group A Base Condition Sites 

INJACC 

No. of Sites = 38 

Variable Mean Median Minimum Maximum Mean Median Minimum Maximum

ACC/year 2.39 2.00 0 10.80 0.93 0.82 0 3.33

AADT1 12444 12601 4210 25799 12417 13740 4210 25799 

AADT2 764 592 21 2990 717 498 43 2990 

Table 151 reports the parameter estimates for the Group A Type IV TOTACC and 

INJACC base models. This table indicates that the β coefficient of the log of major road 

AADT is about one and one half times that for minor road AADT, conforming to 

expectations. As was the case for Type III, the INJACC model used LOG (AADT1 * 

AADT2) because log of AADT2 was quite insignificant. However, even with LOG 

(AADT1 * AADT2), the p-value was not statistically significant. It appears that the 

sample size of 38, with a relatively low number of injury accidents, was not sufficient to 

provide reasonable coefficients and p-values for the INJACC model. 
170 

Table 151. Parameter Estimates for Type IV Group A TOTACC and INJACC 

Base Models 

Variable 

TOTACC 

Estimate 

(s.e., p-value) 

Original 

TOTACC 

AADT Model1

Applied to 

Group A Sites 

INJACC 

Estimate 

(s.e., p-value) 

Original INJACC 

AADT Model2

Applied to Group 

A Sites 

Constant 

-7.2677 

(2.7953, 0.0093) 

-6.9352 

(2.5675,0.0001)

-3.8217 

(2.9225, 0.1910) 

-9.8454 

(2.5675,0.0001) 

Log of AADT1 

0.5947 

(0.2712, 0.0283) 

0.4683 

(0.2330,0.0444) N/A3

0.7224 

(0.2591,0.0053) 

Log of AADT2 

0.3964 

(0.1685, 0.0187) 

0.5135 

(0.0896,0.0001) N/A3

0.4778 

(0.1401,0.0007) 

Log of 

(AADT1*AADT2) N/A3 N/A3

0.2407 

(0.1858, 0.1952) N/A3

K 0.5771 0.6144 0.6768 0.5741 

Pearson productmoment correlation 

coefficient 0.64 0.62 0.72 0.63 

MPB/yr -0.04 0.16 -0.03 -0.10 

MAD/yr 1.63 1.63 0.73 0.75 

1 The TOTACC AADT model published in the Vogt’s report, 1999, (p. 116) 

2 The INJACC AADT model published in the Vogt’s report, 1999, (p. 118) 

 3 N/A: not available 

Type V Models 

The datasets used to develop the Type V main models included the Michigan sites from 

the original study, the additional years of accident data, the Georgia sites, and those 

extracted from the California HSIS database. Only five sites were available from the 

California HSIS database, so it was decided not to calibrate Group B base models that 

would have included these data. Only Group A base models, using the Georgia data and 

the original sites for Michigan and California, were calibrated. 

 

The numbers of sites comprising the dataset used for the main model are given in 

table152. Summary statistics are presented in table 153. As seen, for Michigan, the 

INJACC model used only the additional years of accident data, because injury data for 

the original years were not available. 

Table 152. Number of Sites Used for Type V Main AADT Model 

Dataset All Sites 

Michigan 1993–97 

(only 1996–97 INJACC used) 18 

Georgia 1996–97 51 
171 

Table 153. Summary Statistics for Type V Sites: Main AADT Model 

All Sites 

Variable Mean Median Minimum Maximum 

TOTACC/yr 4.9 4.1 0.0 26.5 

INJACC/yr 2.2 1.5 0.0 12.0 

AADT1 9643 9000 430 26000 

AADT2 2995 2700 420 10600 

Tables 154 and 155 report the parameter estimates for the main Type V TOTACC and 

INJACC models calibrated using all sites. Unlike models for Type I and II intersections, 

a State indicator variable was insignificant. Both tables show that the β coefficient of the 

log of major road AADT is, in accord with expectations, about two to three times that for 

minor road AADT. Pearson product-moment correlation coefficients for TOTACC and 

INJACC were 0.66 and 0.44, respectively. 

Unlike the case for Types III and IV, the Vogt report does not provide AADT-only 

models for Type V. Therefore, a comparison between the Vogt models and the newly 

calibrated AADT models for TOTACC and INJACC could not be done. 

The CURE plot method proposed by Hauer was used to explore alternate model forms 

that could provide an improved fit the data. The results indicated that the recalibrated 

models using the original exponential model form adequately fit the data and that the 

various adjustments to this model form did not improve the AADT models. Specifically, 

the differences in Pearson product-moment correlation coefficient, MPB per year, and 

MAD per year were negligible. Therefore, the original model form was retained. 

Appendix D shows the CURE plot for the Type V AADT TOTACC model. 

Table 154. Parameter Estimates for Recalibrated TOTACC Type V: 

Main AADT Model 

Variable 

All Sites 

Estimate (s.e., p-value) 

Constant 

-4.2638 

(2.2267, 0.0555) 

Log of AADT1 

0.4771 

(0.2285, 0.0368) 

Log of AADT2 

0.1970 

(0.0908, 0.0300) 

K 0.5776 

Pearson product-moment correlation coefficient 0.66 

MPB/yr -0.01 

MAD/yr 2.95 

* There are no Type V AADT models for TOTACC in the Vogt report, 1999 
172 

Table 155. Parameter Estimates for Recalibrated INJACC Type V: 

Main AADT Model 

Variable 

All Sites 

Estimate (s.e., p-value) 

-9.7110 

Constant (2.3118, 0.0000) 

0.8599 

Log of AADT1 (0.2210, 0.0001) 

0.3372 

Log of AADT2 (0.1547, 0.0292) 

K 0.7267 

Pearson product-moment correlation coefficient 0.44 

MPB/yr 0.02 

MAD/yr 1.64 

* There are no Type V AADT models for INJACC in the Vogt report, 1999 

Summary statistics on the Group A base condition datasets are presented in table 156. 

Table 156. Summary Statistics for Type V Sites: Group A Base AADT Models

Group A Base Condition Sites TOTACC 

No. of Sites = 49 

Group A Base Condition Sites 

INJACC 

No. of Sites = 39 

Variable Mean Median Minimum Maximum Mean Median Minimum Maximum 

ACC/yr 7.23 6.00 0.50 26.50 1.94 2.00 0 5.50 

AADT1 9238 8700 1700 20067 10059 8750 700 25132 

AADT2 3890 3459 430 10280 3772 3452 430 10280 

Table 157 reports the parameter estimates for the Group A Type V TOTACC and 

INJACC base models. This table indicates that the β coefficient of the log of major road 

AADT is about two to three times greater than that for minor road AADT, which is 

reasonable. As was the case for Type III and IV models, the INJACC model used LOG 

(AADT1 * AADT2) because the individual logs for separate AADT terms were 

insignificant. Pearson product-moment correlation coefficients of TOTACC and INJACC 

AADT models were 0.70 and 0.57, respectively. 
173 

Table 157. Parameter Estimates for Type V Group A TOTACC and INJACC Base 

Models

Variable 

TOTACC 

Estimate (s.e., p-value) 

INJACC 

Estimate (s.e., p-value) 

Constant 

-4.0357 

(1.7087, 0.0182) 

-3.4199 

(2.2752, 0.1328) 

Log of AADT1 

0.5005 

(0.1966, 0.0109) N/A1

Log of AADT2 

0.1815 

(0.1063, 0.0878) N/A1

Log of (AADT1*AADT2) N/A1

0.2396 

(0.1350, 0.0759) 

K 0.2429 0.2891 

Pearson product-moment 

correlation coefficient 0.70 0.57 

MPB/yr -0.05 -0.08 

MAD/yr 3.10 1.08 

* No AADT models previously calibrated 

1 N/A: not available 

3.4 FULLY PARAMETERIZED STATISTICAL MODEL 

ESTIMATION RESULTS 

This section discusses the development of the fully parameterized statistical models. 

Unlike the AADT models, these models include many variables with the intent to explain 

as much of variation in crash occurrence as possible, given the available set of potential 

explanatory variables. For Types I and II, models were developed using two different 

datasets. Types III, IV, and V used only one dataset. Table 158 summarizes what data 

was used for each model. 

Table 158. Summary of Models Recalibrated and Data Used 

Model Site Types and Data Used 

Description Types I and II Type III Type IV Type V 

Group A Sites: 

Full Model with 

variables in 

project data 

Minnesota 

Georgia 

California project 

Michigan 

Georgia 

California project 

Michigan 

Georgia 

California project 

Michigan 

Georgia 

Group B Sites: 

Full Model with 

variables from 

California HSIS 

California HSIS 

Minnesota 

Georgia Not calibrated Not calibrated Not calibrated * The California project data for Types II, IV, and V were not used 

As before, models for total accidents (TOTACC) and injury (fatal + nonfatal injury) 

accidents (INJACC) within 76.25 m (250 ft) of the intersection were developed. 
174 

3.4.1 Type I Models 

Full models were developed using two groups of data. As indicated earlier, the first, 

Group A, was comprised of the sites from Minnesota and Georgia and consisted of many 

variables, including horizontal and vertical curvature. The California HSIS sites were not 

in this group because many of the variables were not available. The second, Group B, 

included the California HSIS sites, but fewer variables were available for modeling. 

As was the case for the AADT-only models, sites with a major road AADT below 400 or 

a minor road AADT below 100 were not used. 270 sites from Minnesota and 116 sites 

from Georgia were used. The Group B data set contained an additional 1432 sites from 

the California HSIS database. Summary statistics on these datasets by State are available 

in appendix C. 

Two model variants are reported. The first includes a State indicator term and the second 

does not. For reference the recalibrated models are compared to the models calibrated 

using data from Minnesota and recommended by Vogt and Bared.(1)

Group A

Tables 159 and 160 report the parameter estimates for the Type I TOTACC and INJACC 

models for the Group A data. 
175 

Table 159. Parameter Estimates for Recalibrated TOTACC Full Models: 

Type I Group A 

Variant 1 Variant 2 

Original 

Main Model1

 Applied 

to Full Model Data 

Variables 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Intercept for Minnesota 

-7.972 

(0.398, <0.001) 

Intercept for Georgia 

-7.086 

(0.407, <0.001) 

-8.825 

(0.438, <0.001) 

-12.992 

(1.151, 0.0001) 

LOG of AADT1 

0.6529 

(0.0416, <0.001) 

0.7001 

(0.0460, <0.001) 

0.8052 

(0.0639, 0.0001)) 

LOG of AADT2 

0.3211 

(0.0439, <0.001) 

0.3785 

(0.0470, <0.001) 

0.5037 

(0.0708, 0.0001) 

HI1 

0.0263 

(0.0107, 0.014) 

0.0314 

(0.0113, 0.005) 

0.0339 

(0.0327, 0.3004) 

RT MAJ 

-0.1887 

(0.0841, 0.025) 

0.2671 

(0.1398, 0.0561) 

RT MIN 

0.419 

(0.244, 0.086) 

LT MAJ 

-0.155 

(0.110, 0.157) 

N/A2

HAZRAT1 

0.1433 

(0.0362, <0.001) 

0.1726 

(0.0677, 0.0108) 

VCI1 

0.1204 

(0.0362, <0.001) 

0.2901 

(0.2935, 0.3229) 

SPD1 

0.0285 

(0.0177) 

HAU 

N/A2

N/A2

0.0045 

(0.0032, 0.1578) 

K–overall 0.233 0.263 0.481 

K–Minnesota 0.250 

K–Georgia 0.141 

N/A2

 N/A2

Pearson product-moment 

correlation coefficients 0.742 0.726 0.726 

MPB/yr -0.010 0.048 0.026 

MAD/yr 0.400 0.416 0.030 

1 Vogt and Bared, 1998, (p. 115) 2 N/A: not available 
176 

Table 160. Parameter Estimates for Recalibrated INJACC Full Models: Type I 

Group A 

Variant 1 Variant 2 

Original 

Main Model1

 Applied 

to Full Model Data 

Variables 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Intercept for Minnesota 

-8.934 

(0.523, <0.001) 

Intercept for Georgia 

-8.120 

(0.537, <0.001) 

-9.727 

(0.566, <0.001) 

-13.037 

(1.791, 0.0001) 

LOG of AADT1 

0.6809 

(0.0552, <0.001) 

0.7174 

(0.0596, <0.001) 

0.8122 

(0.0973, 0.0001) 

LOG of AADT2 

0.2870 

(0.0556, <0.001) 

0.3251 

(0.0569, <0.001) 

0.4551 

(0.0977, 0.0001) 

HI1 

0.0286 

(0.0136, 0.035) 

0.0337 

(0.0139, 0.016) 

0.0335 

(0.0327, 0.3047) 

RT MAJ N/A2

0.3620 

(0.1814, 0.0460) 

LT MAJ 

-0.258 

(0.132, 0.051) N/A2

HAZRAT1 

0.1678 

(0.0457, <0.001) 

0.2065 

(0.0930, 0.0263) 

VCI1 

0.0846 

(0.0557, 0.129) 

0.1869 

(0.3657, 0.6092) 

SPD1 

0.0156 

(0.0269, 0.5618) 

DRWY1 

-0.0120 

(0.0714, 0.8671) 

HAU 

N/A2

N/A2

0.0051 

(0.0045, 0.2594) 

K–overall 0.256 0.278 0.494 

K–Minnesota 0.256 

K–Georgia 0.256 

N/A2

 N/A2

Pearson product-moment 

correlation coefficients 0.691 0.690 0.660 

MPB/yr -0.001 0.003 0.002 

MAD/yr 0.212 0.022 0.010 

1 Vogt and Bared, 1998, (p. 116) 2 N/A: not available 

There were similarities and differences between the recalibrated models and the Vogt and 

Bared models. For total accidents, posted speed on major roads and the angle variable 

HAU were not included in the recalibrated model, while right-turn lane on minor roads 

and left-turn lanes on major roads were included. For injury accidents, right-turn on 

major roads, posted speed on major roads, number of driveways on major roads, and the 

angle variable HAU were not included, while left-turn lane on major roads were included. 
177 

When a State indicator variable was used in the models in addition to the logs of AADTs, 

only the variable HI1 proved to be significant. Without the State indicator, more 

geometric variables were statistically significant. The variables RT MAJ, RT MIN, LT 

MAJ, HAZRAT1, HI1, and VCI1 were all estimated to be significant at the 10 percent 

level or better in one or both of the TOTACC and INJACC models. However, the 

overdispersion parameter K is higher for the models without the State indicator variable 

and with more variables. 

The data summary in appendix C shows that the Georgia sites experience, on average, 

more accidents than sites in Minnesota and also are higher in values for HI1, VCI1, and 

HAZRAT1, while being less likely to have a turning lane on the major road. The question 

arises then, whether the significantly higher accident risk in Georgia is due to differences 

in these geometric features or other fundamental reasons such as reporting levels, weather, 

and sociodemographics. Because the models, including the State location term, have 

lower overdispersion parameters, it can be concluded that this model should be used. The 

following analysis further supports this conclusion. 

Figure 21 plots the cumulative residuals (Y-axis) versus major AADT (X-axis) for the 

TOTACC model without the State location variable. The cumulative residuals on 

occasion go outside the 95 percent confidence intervals for a random walk around 0, 

indicating that the model is performing poorly. 

-150.000

-100.000

-50.000

0.000

50.000

100.000

150.000

0 5000 10000 15000 20000 25000

Adj Cum Residual

Standard Deviation

Standard Deviation

Major AADT

Cumulative 

Residuals

Figure 21. CURE Plot for Alternate TOTACC Type I Group A Model 

Figure 22 plots the cumulative residuals (Y-axis) versus major AADT (X-axis) for the 

TOTACC model, including the State location variable. Although the cumulative residuals 

go outside the 95 percent plots for few sites at low volumes and AADTs above 15000, 

the results are a slight improvement over the model without the State location variable in 

that the oscillations tend to be closer to the x-axis. 
178 

-150

-100

-50

0

50

100

150

0 5000 10000 15000 20000 25000

Adj Cum Residual

Standard Deviation

Standard Deviation

Major AADT

Cumulative 

Residuals

Figure 22. CURE Plot for TOTACC Type I Group A Model 

 

The GOF as measured by K was improved over the Vogt and Bared models, although the 

measures of MPB per year and MAD per year were better for the original model with the 

exception of the MPB per year for the TOTACC and INJACC Variant 1 models. 

Group B 

Tables 161 and 162 report the parameter estimates for the Type I TOTACC and INJACC 

models for the Group B data. 
179 

Table 161. Parameter Estimates for Recalibrated TOTACC Full Models: 

Type I Group B 

Variant 1 Variant 2 

Original 

Main Model1

Variables 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Intercept for Minnesota 

-8.413 

(0.244, <0.001) 

Intercept for Georgia 

-7.603 

(0.265, <0.001) 

Intercept for California 

-8.641 

(0.251, <0.001) 

-8.435 

(0.250, <0.001) 

-12.992 

(1.151, 0.0001) 

LOG of AADT1 

0.6557 

(0.0264, <0.001) 

0.6112 

(0.0263, <.001) 

0.8052 

(0.0639, 0.0001)) 

LOG of AADT2 

0.4128 

(0.0222, <0.001) 

0.4607 

(0.0224, <0.001) 

0.5037 

(0.0708, 0.0001) 

HI12 N/A3 N/A3

0.0339 

(0.0327, 0.3004) 

RT MAJ 

-0.1326 

(0.0630, 0.035) 

-0.0800 

(0.0574, 0.164) 

0.2671 

(0.1398, 0.0561) 

RT MIN 

0.3010 

(0.1140, 0.009) 

0.265 

(0.118, 0.024) 

LT MAJ 

-0.2042 

(0.0500, <0.001) 

-0.2838 

(0.0509, <.001) 

N/A3

HAZRAT12

0.1726 

(0.0677, 0.0108) 

VCI12

0.2901 

(0.2935, 0.3229) 

SPD12

0.0285 

(0.0177) 

HAU2

N/A3

 N/A3

0.0045 

(0.0032, 0.1578) 

K–overall 0.400 0.435 0.481 

K–Minnesota 0.250 

K–Georgia 0.189 

K–California 0.455 

N/A3

 N/A3

Pearson product-moment 

correlation coefficients 0.669 0.657 N/A3

MPB/yr -0.003 0.021 N/A3

MAD/yr 0.367 0.379 N/A3

1 Vogt and Bared, 1998, (p. 115) 

2 These variables area not available in the Group B data 

3 N/A: not available
180 

Table 162. Parameter Estimates for Recalibrated INJACC Full Models: 

Type I Group B 

Variant 1 Variant 2 

Original 

Main Model1

Variables 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Intercept for Minnesota 

-9.182 

(0.300, <0.001) 

Intercept for Georgia 

-8.463 

(0.329, <0.001) 

Intercept for California 

-9.248 

(0.309, <0.001) 

-9.182 

(0.303, <0.001) 

-13.037 

(1.791, 0.0001) 

LOG of AADT1 

0.6590 

(0.0325, <0.001) 

0.6402 

(0.0320, <0.001)) 

0.8122 

(0.0973, 0.0001) 

LOG of AADT2 

0.3820 

(0.0261, <0.001) 

0.4069 

(0.0260, <0.001) 

0.4551 

(0.0977, 0.0001) 

HI12 N/A3 N/A3

0.0335 

(0.0327, 0.3047) 

RT MAJ 

-0.1346 

(0.0760, 0.077) 

-0.1360 

(0.0677, 0.045) 

0.3620 

(0.1814, 0.0460) 

RT MIN 

0.3060 

(0.1330, 0.022) 

0.3000 

(0.1340, 0.025) 

LT MAJ 

-0.2253 

(0.0596, <0.001) 

-0.2655 

(0.0597, <0.001) 

N/A3

HAZRAT12

0.2065 

(0.0930, 0.0263) 

VCI12

0.1869 

(0.3657, 0.6092) 

SPD12

0.0156 

(0.0269, 0.5618) 

DRWY12

-0.0120 

(0.0714, 0.8671) 

HAU2

N/A3 N/A3

0.0051 

(0.0045, 0.2594) 

K – overall 0.417 0.435 0.494 

K – Minnesota 0.256 

K – Georgia 0.345 

K – California 0.476 

N/A3 N/A3

Pearson product-moment 

correlation coefficients 0.593 0.588 N/A3

MPB/yr -0.0004 0.009 N/A3

MAD/yr 0.194 0.195 N/A3

1 Vogt and Bared, 1998, (p. 116) 

2 These variables area not available in the Group B data 

3 N/A: not available 

The GOF as measured by K was improved over the Vogt and Bared models. In the 

recalibrated models, right-turn lanes on minor roads and left-turn lanes on major roads 

are significant in addition to right-turn lanes on major roads. 
181 

3.4.2 Type II Models 

As for Type I, full models were developed using two groups of data. The first, Group A, 

consisted only of the sites from Minnesota and Georgia and included many variables, 

such as horizontal and vertical curvature. The California HSIS sites were not included in 

this group because many of the variables were not available. The second, Group B, 

included the California HSIS sites, but fewer variables were available for modeling. 

As was the case for the AADT-only models, sites with a major road AADT below 400 or 

a minor road AADT below 100 were not included. 250 sites from Minnesota and 108 

sites from Georgia were used. The Group B data contained an additional 748 sites from 

the California HSIS database. Summary statistics on these datasets are available in 

chapter 3.2, and listed by State in appendix C. 

Two variants of models were calibrated. As for Type I, the first variant included a State 

indicator term and the second did not. For reference, the recalibrated models are 

compared to the models calibrated by Vogt and Bared.(1)

Group A 

Tables 163 and 164 report the parameter estimates for the Type II TOTACC and INJACC 

models for the Group A data. 
182 

Table 163. Parameter Estimates for Recalibrated TOTACC Full Models: 

Type II Group A 

Variant 1 Variant 2 

Original 

Main Model1

 Applied 

to Full Model Data 

Variables 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Intercept for Minnesota 

-9.080 

(0.488, <0.001) 

Intercept for Georgia 

-8.630 

(0.499, <0.001) 

-9.248 

(0.475, <.001) 

-10.426 

(1.317, 0.0001) 

LOG of AADT1 

0.6990 

(0.0529, <0.001) 

0.7079 

(0.0537, <.001) 

0.6026 

(0.0836, 0.0001) 

LOG of AADT2 

0.4774 

(0.0531, <0.001) 

0.5153 

(0.0529, <.001) 

0.6091 

(0.0694, 0.0001) 

RTMAJ 

0.1735 

(0.0832, 0.037) N/A2 N/A2

DRWY1 

0.1219 

(0.0277, <0.001) 

0.1375 

(0.0282, <.001) 

0.1235 

(0.0519, 0.0173) 

HI1 

0.0449 

(0.0473, 0.3431) 

SPD1 

N/A2

0.0187 

(0.0176, 0.2875) 

VCI1 

0.0766 

(0.0554, 0.167) 

0.2885 

(0.2576, 0.2628) 

HAU 

N/A2

N/A2

-0.0049 

(0.0033, 0.1341) 

K–overall 0.256 0.278 0.206 

K–Minnesota 0.227 

K–Georgia 0.500 

N/A2

 N/A2

Pearson product-moment 

correlation coefficients 0.777 0.777 0.753 

MPB/yr -0.003 0.033 0.053 

MAD/yr 0.431 0.440 0.111 

1 Vogt and Bared, 1998, (p. 115) 

 2 N/A: not available 
183 

Table 164. Parameter Estimates for Recalibrated INJACC Full Models: 

Type II Group A 

Variant 1 Variant 2 

Original Main Model1

Applied to Full Model Data 

Variables 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Intercept for Minnesota 

-9.800 

(0.557, <0.001) 

Intercept for Georgia 

-9.304 

(0.570, <0.001) 

-10.303 

(0.565, <.001)

-10.783 

(1.766, 0.0001) 

LOG of AADT1 

0.6196 

(0.0619, <0.001) 

0.6392 

(0.0638, <.001)

0.6339 

(0.1055, 0.0001) 

LOG of AADT2 

0.5893 

(0.0612, <0.001) 

0.6584 

(0.0614, <.001)

0.6229 

(0.0870, 0.0001) 

DRWY1 

0.0824 

(0.0328, 0.012) 

0.0944 

(0.0337, 0.005)

0.0857 

(0.0639, 0.1799) 

HI1 

0.0408 

(0.0266, 0.125) 

0.0626 

(0.0272, 0.021)

0.0729 

(0.0635, 0.2513) 

SPD1 

0.0112 

(0.0251, 0.6567) 

VCI1 

0.2789 

(0.4623, 0.5464) 

HAZRAT1 

-0.1225 

(0.0720, 0.0889) 

RT MAJ 

0.0451 

(0.1665, 0.7865) 

HAU 

N/A2

 N/A2

-0.0043 

(0.0044, 0.3258) 

K–overall 0.250 0.278 0.181 

K–Minnesota 0.263 

K–Georgia 0.154 

N/A2 N/A2

Pearson product-moment 

correlation coefficients 0.747 0.727 0.724 

MPB/yr -0.001 0.033 0.033 

MAD/yr 0.249 0.254 0.063 1 Vogt and Bared, 1998, (p. 117) 

2 N/A: not available 

There were some similarities and differences between the recalibrated models and the 

Vogt and Bared models. For the recalibrated models, significant variables at 

approximately the 85 percent level or better for TOTACC included major and minor road 

AADTs, right-turn lanes on major roads, and the number of driveways for the variant that 

included a State indicator variable, and number of driveways and the vertical curvature 

variable VCI1 for the variant without the State indicator variable. The Vogt and Bared 

model also included the angle variable HAU, the major road posted speed, and the 

horizontal curvature variable HI1, although the last two were of low significance. For the 

INJACC models, number of driveways and horizontal curvature within 76.25 m (250 ft) 

of the intersection center were significant at the 10 percent level or better for both the 

State indicator and non-State indicator variants. The Vogt model included roadside 

hazard rating as a significant variable and others that were not significant. The GOF as 

measured by K was not as good as for the Vogt and Bared model. 
184 

Group B 

Tables 165 and 166 report the parameter estimates for the Type II TOTACC and INJACC 

models using the Group B data. 

Table 165. Parameter Estimates for Recalibrated TOTACC Full Models: 

Type II Group B 

Variant 1 Variant 2 

Original 

Main Model1

Variables 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Intercept for Minnesota 

-8.648 

(0.296, <0.001) 

Intercept for Georgia 

-8.275 

(0.316, <0.001) 

Intercept for California 

-8.799 

(0.304, <0.001) 

-8.718 

(0.321, <.001) 

-10.426 

(1.317, 0.0001) 

LOG of AADT1 

0.6674 

(0.0331, <0.001) 

0.6483 

(0.0327, <.001) 

0.6026 

(0.0836, 0.0001) 

LOG of AADT2 

0.4905 

(0.0268, <0.001) 

0.5200 

(0.0274, <.001) 

0.6091 

(0.0694, 0.0001) 

RTMAJ 

-0.1462 

(0.0686, 0.033) 

-0.1070 

(0.0633, 0.091) 

LTMAJ 

-0.1535 

(0.0633, 0.015) 

N/A3

DRWY12

0.1235 

(0.0519, 0.0173) 

HI12

0.0449 

(0.0473, 0.3431) 

VCI12

0.2885 

(0.2576, 0.2628) 

SPD12

0..0187 

(0.0176, 0.2875) 

HAU2

N/A3

N/A3

-0.0049 

(0.0033, 0.1341) 

K–overall 0.400 0.400 0.206 

K–Minnesota 0.278 

K–Georgia 0.555 

K–California 0.435 

N/A3 N/A3

Pearson product-moment 

correlation coefficients 0.694 0.695 N/A3

MPB/yr -0.008 0.009 N/A3

MAD/yr 0.528 0.528 N/A3

1 Vogt and Bared, 1998, (p. 115) 

2 These variables area not available in the Group B data 

3 N/A: not available 
185 

Table 166. Parameter Estimates for Recalibrated INJACC Full Models: 

Type II Group B 

Variant 1 Variant 2 

Original 

Main Model1

Variables 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Intercept for Minnesota 

-9.285 

(0.343, <0.001) 

Intercept for Georgia 

-8.729 

(0.366, <0.001) 

Intercept for California 

-9.298 

(0.352, <0.001) 

-9.130 

(0.334, <.001) 

-10.783 

(1.766, 0.0001) 

LOG of AADT1 

0.6295 

(0.0382, <0.001) 

0.6006 

(0.0346, <.001) 

0.6339 

(0.1055, 0.0001) 

LOG of AADT2 

0.5182 

(0.0299, <0.001) 

0.5376 

(0.0299, <.001) 

0.6229 

(0.0870, 0.0001) 

MEDIAN 

-0.3320 

(0.1410, 0.019) 

-0.325 

(0.143, 0.023) N/A3

RT MAJ 

-0.1646 

(0.0780, 0.035) 

-0.2014 

(0.0727, 0.006) 

0.0451 

(0.1665, 0.7865) 

DRWY12

0.0857 

(0.0639, 0.1799) 

HI12

0.0729 

(0.0635, 0.2513) 

VCI12

0.2789 

(0.4623, 0.5464) 

HAZRAT12

-0.1225 

(0.0720, 0.0889) 

HAU2

-0.0043 

(0.0044, 0.3258) 

SPD12

N/A3

 N/A3

0.0112 

(0.0251, 0.6567) 

K–overall 0.400 0.417 0.181 

K–Minnesota 0.303 

K–Georgia 0.204 

K–California 0.455 N/A1

N/A3

Pearson product-moment 

correlation coefficients 0.645 0.642 N/A3

MPB/yr -0.003 0.010 N/A3

MAD/yr 0.299 0.0001 N/A3

1 Vogt and Bared, 1998, (p. 117) 

2 These variables area not available in the Group B data 

3 N/A: not available 

For TOTACC, significant variables in addition to major and minor road AADTs, include 

right-turn lane on major road for the variant with the State indicator variable and rightturn lane on major road and left-turn lane on major road for the variant without the State 

indicator variable. For INJACC, median and right-turn lane on major road were 

significant for both the State indicator and non-State indicator variants. The GOF as 

measured by K was not as good as that for the Vogt and Bared model. 
186 

3.4.3 Type III Models 

The data used to calibrate full models consisted of the California and Michigan sites from 

the original study, additional years of accident data from the California and Michigan 

sites, and the Georgia sites. Some of the California sites experienced changes in their 

design features during the 1996–98 period. For such sites, accidents during the 1996–98 

period were not included, and only 1993–95 accident data were used. Summary statistics 

on the data are provided in section 3.2. 

Two models each are reported for TOTACC and INJACC. The main model was selected 

based on the highest Pearson product-moment correlation coefficient, lowest 

overdispersion, MPB per year, and MAD per year. The other model was the one judged 

to be next best on in terms of these measures. 

For TOTACC, major and minor AADTs, vertical curve rate on major roads, intersection 

angle, commercial driveways on major roads, median width on major roads, and painted 

medians on major roads were found to be significant in the main models (15 percent level 

or better). State indicator variables were statistically insignificant and therefore not 

included in the models. 

For INJACC, major and minor AADTs, roadside hazard rating on major road, 

intersection angle, commercial driveways on major road, peak turning percentage, and 

peak truck percentage were found to be significant in the main model at the 15 percent 

level or better. State indicator variables were again statistically insignificant. 

For reference a comparison between Vogt’s full models applied to the recalibration data 

and the newly recalibrated models for TOTACC and INJACC also is given. As expected, 

there were some differences between the recalibrated models and the Vogt models. For 

TOTACC, the recalibrated main model had the additional terms COMDRWY1, VEI1, 

HAU, and MEDTYPE1 compared to the Vogt model but did not include DRWY1, which 

was in the Vogt model. For the INJACC, the recalibrated main model had the additional 

terms COMDRWY1, HAZRAT1, PKTRUCK, and PKTURN compared to the Vogt 

model. The GOF as measured by Pearson product-moment correlation coefficients, MPB 

per year, and MAD per hear indicates that the recalibrated main models for TOTACC 

and INJACC provide better GOF than the Vogt models. However, the GOF as measured 

by K was not as good as those for the Vogt models. 

Tables 167 and 168 report the model results for TOTACC and INJACC. 
187 

Table 167. Parameter Estimates for Recalibrated TOTACC Full Models: Type III 

Main Model Variant 1 

Original 

Main Model1 Applied 

to Full Model Data 

Variables 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Intercept 

-10.1914 

(1.5232,0.0000) 

-9.9214 

(1.5100,0.0000) 

-12.2196 

(2.3575,0.0001) 

LOG of AADT1 

0.8877 

(0.1666,0.0000) 

0.8509 

(0.1665,0.0000) 

1.1479 

(0.2527,0.0001) 

LOG of AADT2 

0.3228 

(0.0585,0.0000) 

0.2972 

(0.0590,0.0000) 

0.2624 

(0.0866,0.0024) 

COMDRWY1 

0.0681 

(0.0281,0.0154) 

0.0912 

(0.0276,0.0010) 

VEI1 

0.1081 

(0.0556,0.0519) 

0.1044 

(0.0523,0.0461) 

HAU 

0.0101 

(0.0059,0.0861) 

0.0088 

(0.0054,0.1014) 

N/A3

MEDWDTH1 

-0.0106 

(0.0060,0.0760) 

-0.0546 

(0.0249,0.0285) 

MEDTYPE12

-0.3209 

(0.1771,0.0700) N/A3

DRWY1 N/A3

N/A3

0.0391 

(0.0239,0.1023) 

K 

0.4229 

(0.1064,0.0001) 

0.4552 

(0.1109,0.0000) 

0.3893 

(0.1160,0.0008) 

Pearson product-moment 

correlation coefficients 0.70 0.70 0.68 

MPB/yr 0.09 -0.02 0.37 

MAD/yr 0.84 0.88 0.90 

1 The main model published in Vogt, 1999, (p. 111) 

2 Median Type 1 (painted) on major roads 

3 N/A: not available 
188 

Table 168. Parameter Estimates for Recalibrated INJACC Full Models: Type III 

Main Model Variant 1 

Original 

Main Model1

Applied to Full 

Model Data 

Variables 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Intercept 

-10.6443 

(2.0474,0.0000) 

-10.4453 

(2.0845,0.0000) 

-12.3246 

(2.8076, 0.0001) 

LOG of AADT1 

0.8498 

(0.2097,0.0001) 

0.8260 

(0.2146,0.0001) 

1.1436 

(0.2763,0.0001) 

LOG of AADT2 

0.2188 

(0.0949,0.0212) 

0.2460 

(0.0901,0.0063) 

0.1357 

(0.1029,0.1872) 

COMDRWY1 

0.0627 

(0.0353,0.0756) 

0.0607 

(0.0346,0.0797) 

HAZRAT1 

0.1889 

(0.0923,0.0407) 

0.1897 

(0.0930,0.0412) 

N/A2

HAU 

0.0163 

(0.0053,0.0021) 

0.0168 

(0.0054,0.0019) 

0.0230 

(0.0131,0.0790) 

PKTRUCK 

-0.0253 

(0.0135,0.0605) 

-0.0331 

(0.0186,0.0762) 

PKTURN 

0.0254 

(0.0135,0.0592) N/A2

PKLEFT N/A2

0.0333 

(0.0188,0.0758) 

N/A2

K 

0.5102 

(0.1426,0.0003) 

0.5178 

(0.1437,0.0003) 

0.3787 

(0.1792,0.0346) 

Pearson product-moment 

correlation coefficients 0.66 0.64 0.56 

MPB/yr -0.05 -0.14 -0.05 

MAD/yr 0.43 0.47 0.47 

1 INJACC Variant 1 Model; there is no main INJACC model in Vogt, 1999 

2 N/A: not available 

3.4.4 Type IV Models 

The data used to calibrate full models include the California and Michigan sites from the 

original study, with the additional years of accident data, and the Georgia sites. Some of 

the California sites experienced changes in their design features during the 1996–98 

period. For such sites, accidents during the 1996–98 period were ignored, and only 1993–

95 accident data were used. Summary statistics on the data are provided in section 3.2. 

Two models were developed for both TOTACC and INJACC. Again, the main model 

was selected based on the highest Pearson product-moment correlation coefficient, and 

lowest overdispersion, MPB per year, and MAD per year. 

For TOTACC, major and minor road AADTs, peak left-turn percentages, peak through 

percentages on minor roads, peak truck percentages, and right-side sight distance on 

minor roads were found to be significant in the main model at the 10 percent level or 

better. State indicator variables were statistically insignificant in the main model and 
189 

were therefore not included. However, Variant 1, the second best model, includes a 

Michigan indicator variable, which means there was more influence of the Michigan data 

on the model. 

For INJACC, major and minor road AADTs, peak left-turn percentages on major roads, 

peak truck percentages, and speed limits on minor roads were selected as significant in 

the main model at the 10 percent level or better. State indicator variables were 

statistically insignificant. 

For reference, a comparison between Vogt’s full models applied to the recalibration data 

and the newly recalibrated models for TOTACC and INJACC is given. As expected, 

there were some differences between the recalibrated models and the Vogt’s models. For 

TOTACC, the recalibrated main model had additional terms SDR2, PKTRUCK, 

PKTHRU2, and PKLEFT compared to the Vogt model, but did not include PKLEFT1 

and LTLN1S, which were in the Vogt model. For the INJACC, the recalibrated main 

model included the additional term PKTRUCK compared to the Vogt model. The GOF as 

measured by Pearson product-moment correlation coefficients, MPB per year, and MAD 

per year indicates that the recalibrated models for TOTACC and the main model for 

INJACC provide better GOF than the Vogt models. However, the GOF as measured by K

was not as good as those for the Vogt models. 

Tables 169 and 170 report the model results for TOTACC and INJACC, respectively. 
190 

Table 169. Parameter Estimates for Recalibrated TOTACC Full Models: Type IV 

Main Model Variant 1 

Original 

Main Model1

Applied to Full 

Model Data 

Variables 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Intercept 

-7.4713 

(1.8930,0.0001) 

-7.4350 

(1.6933,0.0000) 

-9.4631 

(2.5991,0.0003) 

LOG of AADT1 

0.7350 

(0.1849,0.0001) 

0.7193 

(0.1722,0.0000) 

0.8503 

(0.2779,0.0022) 

LOG of AADT2 

0.2390 

(0.0926,0.0099) 

0.2586 

(0.0975,0.0080) 

0.3294 

(0.1255,0.0087) 

SDR2 

-0.0003 

(0.0001,0.0403) 

-0.0005 

(0.0001,0.0018) 

PKTRUCK 

-0.0479 

(0.0110,0.0000) N/A4

PKTHRU2 

0.0249 

(0.0085,0.0034) 

0.0154 

(0.0082,0.0591) 

PKLEFT 

0.0229 

(0.0118,0.0525) N/A4

N/A4

PKLEFT1 

-0.0158 

(0.0083,0.0565) 

0.1100 

(0.0412,0.0076) 

MEDTYPE12

-0.4027 

(0.2084,0.0533) 

MICHIGAN3

0.4823 

(0.2645,0.0683) 

N/A4

LTLN1S (0 or 1) 

N/A4

N/A4

-0.4841 

(0.2311,0.0362) 

K 

0.4001 

(0.0958,0.0000) 

0.4382 

(0.0965,0.0000) 

0.4578 

(0.1307,0.0005) 

Pearson product-moment 

correlation coefficients 0.77 0.75 0.64 

MPB/yr 0.12 0.28 0.48 

MAD/yr 1.16 1.20 1.31 

1 The main model published in Vogt, 1999, (p. 116) 

2 Median Type 1 (painted) on major roads 

3 Indicator variable for Michigan 

4 N/A: not available 
191 

Table 170. Parameter Estimates for Recalibrated INJACC Type IV: Full Models 

Main Model Variant 1 

Original 

Main Model1

Applied to Full 

Model Data 

Variables 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Intercept 

-7.3927 

(2.1279,0.0005) 

-7.9801 

(2.0870,0.0001) 

-12.5296 

(2.9908,0.0001) 

LOG of AADT1 

0.5008 

(0.2186,0.0220) 

0.5670 

(0.2145,0.0082) 

0.9505 

(0.3284,0.0038) 

LOG of AADT2 

0.3027 

(0.1341,0.0240) 

0.3452 

(0.1213,0.0044) 

0.3237 

(0.1645,0.0491) 

SPD2 

0.0289 

(0.0145,0.0465) 

0.0262 

(0.0149,0.0795) 

0.0339 

(0.0179,0.0577) 

PKTRUCK 

-0.0520 

(0.0127,0.0000) N/A3

PKLEFT1 

0.0523 

(0.0128,0.0000) 

N/A3

0.0994 

(0.0433,0.0216) 

SDR2 

-0.0003 

(0.0002,0.0420) 

MEDTYPE12

N/A3

-0.5299 

(0.2560,0.0385) 

N/A3

K 

0.4671 

(0.1296,0.0003) 

0.5400 

(0.1345,0.0001) 

0.4308 

(0.1824,0.0182) 

Pearson product-moment 

correlation coefficients 0.71 0.70 0.60 

MPB/yr 0.05 -0.05 0.14 

MAD/yr 0.65 0.67 0.68 

1 INJACC Variant 1 Model; there is no main INJACC model in Vogt, 1999 

2 Median Type 1 (painted) on major roads 

3 N/A: not available 

3.4.5 Type V Models 

The data used to calibrate full models include the California and Michigan sites from the 

original study, additional years of accident data from the California and Michigan sites, 

and the Georgia sites. Some of California sites experienced changes in their design 

features during the 1996–98 period. For such sites, accidents during the 1996–98 period 

were ignored in the database, and only 1993–95 accident data were used. Summary 

statistics on the data are provided in section 3.2 of this report. 

Two models were developed for both TOTACC and INJACC. Again, the main model 

was selected by examining the Pearson product-moment correlation coefficient, 

overdispersion, MPB per year, and MAD per year. 

For TOTACC, major and minor AADTs, commercial driveways on major roads, speed 

limits on major roads, light, and horizontal curvature variables were found to be 

significant in the main model. Compared to the main model, Variant 1 in table 171 yields 

improvement in overdispersion, but not in other GOF measures. Variant 1 showed a 
192 

lower Pearson product-moment correlation coefficient than the main model, but MPB per 

year and MAD per year were higher. 

For INJACC, major and minor AADTs, presence of lighting, speed limits on major roads, 

and horizontal curve on minor roads within 244 m (800 ft) of intersection were 

significant variables in the main model. Variant 1 in table 172 was superior to the main 

model in terms of lower overdispersion and other GOF measures, with the exception of 

MPB per year. However, the model includes a Michigan indicator variable, which means 

more influence of the Michigan data on the model. Because the IHSDM requires the 

main model to be recalibrated to work in any State, the model with the State indicator 

was selected as a variant, not as the main model. 

For reference, a comparison between the Vogt full models applied to the recalibration 

data and the newly recalibrated models for TOTACC and INJACC also is given. As 

expected, there were some differences between the recalibrated models and the Vogt 

models. For TOTACC, the recalibrated main model included additional terms 

COMDRWY1, SPD1, LIGHT, and HEICOM compared to the Vogt model but did not 

include PKTRUCK, PKLEFT2, PROT_LT, and VEICOM, all of which were in the Vogt 

model. For the INJACC model, the recalibrated main model separated the safety effect of 

major and minor road AADTs. The main model included LIGHT, SPD1, and HEI2 but 

excluded PKLEFT2, PKTRUCK, PROT_LT, and VEICOM when compared to the Vogt 

model. The GOF as measured by MPB per year and MAD per year indicates that the 

recalibrated models for TOTACC and INJACC provide better GOF than the Vogt models. 

Pearson product-moment correlation coefficients were also higher for INJACC but were 

a little lower for TOTACC. The GOF as measured by K was not as good as that for the 

Vogt models. 

Tables 171 and 172 show the model results for TOTACC and INJACC, respectively. 
193 

Table 171. Parameter Estimates for Recalibrated TOTACC Full Models: Type V 

Main Model Variant 1 

Original 

Main Model1

Applied to Full 

Model Data 

Variables 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Intercept 

-5.1527 

(1.8653,0.0057) 

-5.4718 

(1.8686,0.0034) 

-6.9636 

(2.7911,0.0132) 

LOG of AADT1 

0.4499 

(0.1968,0.0223) 

0.4220 

(0.1976,0.0327) 

0.6199 

(0.2504,0.0133) 

LOG of AADT2 

0.2699 

(0.0767,0.0004) 

0.2913 

(0.0755,0.0001) 

0.3948 

(0.1737,0.0230) 

COMDRWY1 

0.0539 

(0.0304,0.0757) 

0.0494 

(0.0296,0.0948) 

SPD1 

0.0177 

(0.0090,0.0482) 

0.0229 

(0.0088,0.0092) 

LIGHT 

-0.2938 

(0.1837,0.1098) 

HEICOM 

-0.0288 

(0.0153,0.0597) 

N/A3

HI 

-0.0221 

(0.0116,0.0571) 

MEDTYPE12

-0.4941 

(0.2349,0.0354) 

N/A3

PKTRUCK 

0.0315 

(0.0143,0.0275) 

PKLEFT2 

-0.0142 

(0.0047,0.0023) 

PROT_LT (0=no, 1=yes) 

-0.6754 

(0.1824,0.0002) 

VEICOM 

N/A3

N/A3

0.1299 

(0.0450,0.0039) 

K 

0.4019 

(0.0765,0.0000) 

0.3954 

(0.0781,0.0000) 

0.1161 

(0.0323,0.0003) 

Pearson product-moment 

correlation coefficients 0.77 0.73 0.78 

MPB/yr -0.02 -0.03 -0.79 

MAD/yr 2.90 3.03 3.31 

1 The main model published in Vogt, 1999, (p. 122) 

2 Median Type 1 (painted) on major roads 

3 N/A: not available 
194 

Table 172. Parameter Estimates for Recalibrated INJACC Full Models: Type V 

Main Model Variant 1 

Original 

Main Model1

Applied to Full 

Model Data 

Variables 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Coeff. 

(s.e., p-value) 

Intercept 

-9.0707 

(1.9064,0.0000) 

-8.6196 

(1.7838,0.0000) 

-3.2562 

(2.9932,0.2767) 

LOG of AADT1 

0.6697 

(0.1899,0.0004) 

0.6875 

(0.1756,0.0001) 

LOG of AADT2 

0.2509 

(0.0929,0.0069) 

0.1731 

(0.0933,0.0636) 

N/A3

Log of (AADT1*AADT2) N/A3 N/A3

0.2358 

(0.1722,0.1707) 

LIGHT 

-0.3985 

(0.1702,0.0192) 

-0.4054 

(0.1641,0.0135) 

SPD1 

0.0397 

(0.0093,0.0000) 

0.0370 

(0.0091,0.0001) 

HEI2 

-0.0284 

(0.0126,0.0244) 

-0.0230 

(0.0124,0.0642) 

N/A3

PKLEFT2 

-0.0113 

(0.0062,0.0678) 

PKTRUCK 

N/A3

0.0323 

(0.0146,0.0267) 

MICHIGAN2

0.3499 

(0.1653,0.0343) N/A3

PROT_LT (0=no, 1=yes) 

-0.2943 

(0.1864,0.1144) 

VEICOM 

N/A3

N/A3

0.0822 

(0.0551,0.1358) 

K 

0.2360 

(0.0958,0.0138) 

0.2065 

(0.0918,0.0244) 

0.1630 

(0.0662,0.0138) 

Pearson product-moment 

correlation coefficients 0.68 0.70 0.43 

MPB/yr 0.00 -0.01 -1.02 

MAD/yr 0.98 0.94 1.40 

1 The main model published in Vogt, 1999, (p. 124) 

2 Indicator variable for Michigan 

3 N/A: not available 

3.5 ESTIMATION OF ACCIDENT MODIFICATION FACTORS 

This section discusses the derivation of AMFs for both total and injury (fatal and nonfatal 

injury) accidents. 

FHWA and its contractors have developed a new approach that combines historical 

accident data, regression analysis, before-and-after studies, and expert judgment to make 

safety performance predictions that are better than those obtained by any of the individual 

approaches. A recent report documents an accident prediction algorithm for 

implementing the new approach for two-lane rural highway sections that include road 
195 

segments and intersections.(3) Ongoing efforts aim to produce similar documents for other 

types of facilities. 

The accident prediction algorithm has been developed for incorporation in the IHSDM as 

the Crash Prediction Module, but is suitable for stand-alone applications. As indicated 

earlier, the structure of the accident prediction algorithm for the five types of rural atgrade intersections is as follows: 

Nint = Nb (AMF1 AMF2 ... AMFn) (15) 

where 

Nint = predicted number of total intersection-related accidents per year after application of 

AMFs; 

Nb = predicted number of total intersection-related accidents per year for base conditions; 

and 

AMF1 AMF2 ... AMFn = AMFs for various intersection features 

The accident algorithm report, referred to as the “Red Book,” provides AMFs for twolane rural roads and intersections.(3) An additional report provided AMFs for turning 

lanes at intersections.(5) As part of this project, the available data have been used to 

attempt to derive AMFs for these and any other variables at rural intersections to compare 

and refine the current AMFs. 

The AMFs provided in the “Red Book” are shown below in table 173. These AMFs apply 

to total intersection accidents (TOTACC). Also shown are the AMFs relevant to 

intersection types I, II, and V from Harwood et al.(5)
196 

Table 173. AMFs from Previous Studies 

AMF Type I Type II Type V 

SKEW exp(0.004SKEW) exp(0.0054)SKEW 1 

LT MAJ 

1.00 if none exist 

0.78 if at least one 

exists 

(0.56 if at least one 

exists) 

1.00 if none exist 

0.76 on one approach 

(0.72 on one approach) 

0.58 on both approaches 

(0.52 on both 

approaches) 

1.00 if none exist 

0.82 on one approach 

0.67 on both approaches 

RT MAJ 

1.00 if none exist 

0.95 on one approach 

(0.86 on one approach) 

0.90 on both approaches 

(0.74 on both approaches) 

1.00 if none exist 

0.975 on one approach 

(0.96 on one approach) 

0.95 on both approaches 

(0.92 on both 

approaches) 

SIGHT DISTANCE 

1.00 if sight distance is not limited 

1.05 if limited in 1 quadrants 

1.10 if limited in 2 quadrants 

1.15 if limited in 3 quadrants 

1.20 if limited in 4 quadrants 1 

Derivation of AMFs in this project was attempted in two ways. First, AMFs were inferred 

from the parameter estimates of the full models presented in section 3.4. Second, a 

relatively new and untested regression procedure that relates the difference between the 

observed number of crashes at a site and is predicted by a base model to the nonbase 

condition factors was applied. This procedure is explained in detail later in this section. 

3.5.1 AMFs Derived from Recalibration Full Models 

One approach to deriving AMFs is to apply a model using the estimated parameter values 

from only statistically significant variables in accident prediction models. This approach 

suffers from correlation between geometric variables and traffic, and the difference in 

accident experience between sites is possibly due to the substantial unexplained variation 

resulting from omitted factors. Nevertheless, AMFs derived in this manner from the full 

models of section 3.4 are presented in tables 174 and 175. 
197 

Table 174. AMFs Derived from Type I and II Full Models 

Type I Type II 

AMF Total Injury Total Injury 

Group A Data

HI11 exp(0.0263HI1) exp(0.0286HI1) 

Not 

calibrated exp(0.0408HI1) 

RT MAJ 1.19 Not calibrated

DRWY1 Not calibrated Not calibrated 1.13 1.09 

Group B Data

RT MAJ 0.88 0.87 0.86 0.85 

RT MIN 1.35 1.36 

LT MAJ 0.82 0.80 Not calibrated

MEDIAN Not calibrated Not calibrated

Not 

calibrated 0.72 1 As a continuous variable, the AMF for HI1 is a function and not a factor 
Table 175. AMFs Derived from Type III, IV, and V Full Models 

Type III Type IV Type V 

AMF Total Injury Total Injury Total 

COMDRWY1 

exp (0.0681COMDRWY1) 

exp (0.0627COMDRWY1) 

exp(0.0539 COMDRWY1) 

VEI1 exp(0.1081VEI1) 

Not calibrated

HAU exp(0.0101HAU) exp(0.0163HAU) MEDWIDTH1 

exp (-0.0106MEDWDTH1) 

MEDTYPE11 0.73 

Not calibrated

HAZRAT1 exp(0.1889HAZRAT1) 

Not calibrated

Not calibrated 2

PKTRUCK 

exp(-0.0253PKTRUCK) exp(-0.0479PKTRUCK) exp(-0.0520PKTRUCK)

PKTURN exp(0.0254PKTURN) 

Not calibrated

PKTHRU2 

exp(0.0249PKTHRU2) 

PKLEFT exp(0.0229PKLEFT) 

Not calibrated

PKLEFT1 

Not calibrated exp(0.0523PKLEFT1) 

SDR2 exp(-0.0003SDR2) 

Not calibrated

Not ca

LIGHT 0.75 0.67 HEICOM exp(-0.0288HEICOM) 

Not ca

HEI2 

Not calibrated

Not calibrated 

Not calibrated

Not calibrated

 exp(-0

 1 Medtype1: Painted 

198 
199

3.5.2 AMFs Derived from Regression Models 

Recalibration of AMFs was also undertaken using a relatively untested regression 

analysis procedure in which the following steps were taken: 

1. Suitable base conditions for qualifying the current AMFs were selected, i.e., for a 

turning lane AMF, the base condition is no turning lane. 

2. The AADT base models that meet all of the base conditions were estimated. 

3. The difference between a site’s accident count per year and the expected value per 

year was used as an estimate of the dependent variable, Y. 

4. Any factor (for example, left-turn lane on major road) that differs from the base 

conditions was specified as an independent variable. 

5. The β coefficient of a factor was estimated from a simple linear regression model. 

6. AMFs were estimated from the following equations: 

If perfect knowledge for base models and AMFs is available, Y in the accident prediction 

algorithm should be the observed Y. 

Y Y AMFs *

∧

= (16) 

 

Equation (16) can be rewritten as: 

Y AMFs

Y

∧ = (17) 

From steps 3 and 5: 

Y Y β ∧= − (18) 

Equations (17) and (18) can be combined to estimate an AMF: 

Y AMF

Y β = − (19) 

7. In the case that β coefficients in equation (19) are insignificant (at the 90 percent 

level in this research), it was assumed that these factors have no effect on the 

safety of the intersection. This offered a larger sample size to re-estimate the 

insignificant AMFs. 

8. The β coefficients of the insignificant AMFs were re-estimated by repeating step 

2 and subsequent steps. 

9. If the β coefficients became significant, the estimated coefficients were adopted 

as the relevant AMFs. If not, they were set to a value of 1. 
200

Types I and II 

For types I and II, the base conditions and base models described in section 3.3 and 

which were developed using the Group B dataset were used. AMFs derived from this 

procedure are shown in table 176. The base conditions include no turning lanes on major 

or minor road and no median on the major road. As mentioned, where AMFs were not 

estimated to be significantly different from 1, a value of 1 has been assigned. 

Table 176. AMFs Estimated from Regression Procedure 

Type I Type II 

AMF TOTACC INJACC TOTACC INJACC 

RT MIN 1.48 1.56 1 1 

RT MAJ 1 1 0.71 1 

LT MIN 1 1 1 1 

LT MAJ 1 1 0.71 0.42 

MEDIAN 1 1 0.77 0.52 

Few AMFs could be derived with statistically significant results. For Type I, the AMF for 

right-turn lane on the minor road increases the expected number of crashes from the base 

model. For Type II, right- and left-turn lanes on major and median on major are expected 

to reduce the expected number of crashes from the base model. 

Type III 

Unlike the case for Type I and II, for which the Group B dataset was applied, the Group 

A dataset was used to calibrate AMFs for Type III intersections because the Group B 

dataset does not provide sight distance and angle data. As a result, new base models had 

to be calibrated for the AMFs. 

The nominal or base condition for “intersection left-turn lane” is the presence of left-lane 

on the major-road approach because as many as 79.4 percent of the available sites have 

left-turn lanes. For “right-turn lane,” the absence of right-turn lane is the base condition. 

The base condition for intersection sight distance is the availability of adequate 

intersection sight distance along the major road in all quadrants of the intersection. The 

same definition regarding sight distance in a quadrant as described on page 48 of the 

Harwood et al. report was used to define adequate sight distance.(3) The base condition 

for intersection skew angle was plus or minus 5 degrees of skew to have more base sites 

and to accommodate any possible measurement errors. 

Table 177 shows the base conditions for Type III AMFs. Table 178 displays the base 

model estimated using the sites meeting all of the base conditions. Because the β

coefficient of log of AADT1 was quite insignificant, log of (AADT1 * AADT2) was 

used as the traffic variable. 
201

AMFs derived from this procedure are given in table 179. These AMFs apply to total 

accidents and total injury accidents. 

Table 177. Base Conditions for Type III Sites 

AMF Base Condition 

Frequency Meeting Base 

Conditions (Percent) 

Left lane on major road Presence of left lane 108 (79.4) 

Right lane on major road Absence of right lane 88 (64.7) 

Sight distance Adequate sight distance 104 (76.5) 

Intersection angle -5° ~ 5° 89 (65.4) 

Total1 All 28 (20.6) 1 Total means sites meeting all of the base conditions

Table 178. Base Model for Type III Sites 

TOTACC INJACC 

Variables Coeff. (s.e., p-value) Coeff. (s.e., p-value) 

Intercept 

-7.5583

(1.1313,0.0000)

-9.0573

(1.9821,0.0000)

Log (AADT1* AADT2)1

0.4909

(0.0740,0.0000)

0.5342

(0.1251,0.0000)

K 0.2045 0.3172

1 Logs of AADT1 and AADT2 were combined because the β coefficient of log of AADT1 was insignificant 

Table 179. AMFs for Type III Sites 

AMFs Recalibrated (TOTACC) Recalibrated (INJACC) 

Left lane on major road 0.71 (One approach) 1 (One approach) 

Right lane on major road 1 (One approach) 1 (One approach) 

Sight distance 1 1 

Intersection angle 

1+(0.016*SKEW1

)/ 

(0.982

+0.016*SKEW) 

1+(0.017*SKEW1

)/ 

(0.523

+0.017*SKEW) 1 SKEW = intersection skew angle (degrees), expressed as the absolute value of the difference 

 between 90 degrees and the actual intersection angle 2 0.98 = mean of the observed TOTACC accidents per year of the sites meeting no angle, no right 

lane, and presence of left lane 3 0.52 = mean of the observed INJACC accidents per year of the sites meeting no angle, no right 

lane, and presence of left lane 
202

Type IV 

As was the case for Type III, the Group A dataset was used to calibrate AMFs for Type 

IV intersections because the Group B dataset does not provide sight distance and angle 

data. New base models were calibrated for the AMFs. 

The base condition for “intersection left-turn lane” is the presence of left-lane on the 

major road approaches because as many as 72.6 percent of the available sites have leftturn lane on both approaches. For “intersection right-turn lane,” the absence of right-turn 

lane is the base condition. The base condition for intersection sight distance is the 

availability of adequate intersection sight distance along the major road in all quadrants 

of the intersection. As for Type III, the base condition for intersection skew angle was 

plus or minus 5 degrees of skew to have more base sites and to accommodate any 

possible measurement errors. The base conditions for Type IV AMFs are shown in table 

180. Table 181 represents the base model estimated using the sites meeting all of the 

base conditions. Since the β coefficient of log of AADT1 was quite insignificant, log of 

(AADT1 * AADT2) was used as the traffic volume variable. 

The AMFs derived are shown in table 182. These AMFs apply to total accidents and total 

injury accidents. 

Table 180. Base Conditions for Type IV Sites 

AMFs Base Condition 

Frequency Meeting Base Conditions 

(Percent) 

Left-turn lane on major 

road 

Presence of left lane (both 

approach) 90 (72.6) 

Right-turn lane on 

major road Absence of right lane 69 (55.6) 

Sight distance Adequate sight distance 81 (65.3) 

Intersection angle -5° ~ 5° 75 (60.5) 

Total1 All 11 (8.9) 1 Total means sites meeting all of the base conditions 

Table 181. Base Model for Type IV Sites 

TOTACC INJACC 

Variables Coeff. (s.e., p-value) Coeff. (s.e., p-value) 

Intercept 

-12.1778

(6.6284,0.0662)

-14.2207

(7.1609,0.0470)

Log (AADT1* AADT2)1

0.8220

(0.4330,0.0576)

0.9261

(0.4677,0.0477)

K 0.5159 0.3871

1 Logs of AADT1 and AADT2 were combined because the β coefficient of log of AADT1 was 

 insignificant 
203

Table 182. AMFs for Type IV Sites 

Recalibrated (TOTACC) Recalibrated (INJACC) 

AMFs One Approach Both Approaches One Approach Both Approaches 

Left-turn lane on 

major road 1 1 0.86 0.74 

Right-turn lane on 

major road 1 1 1 1 

Sight Distance 1 1 

Intersection Angle 

1+(0.053*SKEW1)/ 

(1.432+0.053*SKEW) 

1+(0.048*SKEW1)/ 

(0.723+0.048*SKEW 1 SKEW = intersection skew angle (degrees), expressed as the absolute value of the difference 

 between 90 degrees and the actual intersection angle 2 0.43 = mean of the observed TOTACC accidents per year of the sites meeting no angle, no right 

lane, and presence of left lane 3 0.72 = mean of the observed INJACC accidents per year of the sites meeting no angle, no right 

lane, and presence of left lane 

Type V 

Because the Group B dataset does not provide sight distance and angle, the Group A 

dataset was used to recalibrate the current AMFs for Type V intersections, and new base 

models were calibrated for applying the AMFs. 

As many as 75 percent of the available sites have left-turn lane on both approaches. 

Therefore, the base condition for “intersection left-turn lane” is the presence of left-lane 

on the major road approaches. For “intersection right-turn lane,” the absence of right-turn 

lane is the base condition. The base condition for intersection skew angle was plus or 

minus 5 degrees of skew for the same reasons as those for Type III and IV. Sight distance 

was ignored for the base conditions to develop a base model because the number of sites 

with adequate sight distance was almost equal to the ones with sight distance limited in 

one or two quadrants. As a result, if one of the two sight distance levels was considered 

as a base condition, there would be insufficient sites for a base model. In addition, sight 

distance is believed to have no effect on safety because conflicting traffic movements are 

controlled by signals. The base conditions for Type V AMFs are shown in table 183. 

Table 184 represents the base model estimated using the sites meeting all of the base 

conditions. Because the β coefficient of log of AADT1 was insignificant, log of (AADT1 

* AADT2) was used to represent the traffic volume variable. 

No AMFs were statistically significant using this procedure for Type V sites. Therefore, a 

value of 1 was assigned, which indicates that the variable was not found to have a 

significant impact on the safety of the intersection. 
204

Table 183. Base Conditions for Type V Sites 

AMFs Base Condition 

Frequency Meeting Base Conditions 

(Percent) 

Left lane on major 

road 

Presence of left lane (both 

approach) 75 

Right lane on major 

road Absence of right lane 51 

Angle -5° ~ 5° 60 

Total1 All 22 1

 Total means sites meeting all of the base conditions 

Table 184. Base Model for Type V Sites 

TOTACC INJACC 

Variables Coeff. (s.e., p-value) Coeff. (s.e., p-value) 

Intercept 

-5.1864

(3.2780,0.1136)

-6.1265

(3.7145,0.0991)

Log (AADT1* AADT2)1

0.4001

(0.1969,0.0422)

0.3907

(0.2164,0.0710)

K 0.6499 0.4147

1 Log of AADT1 was insignificant, so logs of AADT1 and AADT2 were combined 

3.5.3 Summary of AMFs 

This research introduced two ways of deriving AMFs. One approach is to adopt the 

estimated parameter values from the statistically significant variables in the accident 

prediction models. The other approach uses a relatively untested regression procedure. 

Although in general the first approach is easier to apply, the second approach is 

recommended. This approach aims to attribute the difference between the observed 

number of crashes at a site and that predicted by a base model to the presence of non-base 

condition factors. This difference will explain a real effect of the presence of individual 

design features on safety. 

Tables 185 through 187 compare the AMFs from the “Red Book” and those derived here. 

The AMFs from Harwood et al. are also shown in brackets.(5) As mentioned, none of the 

variables investigated showed any significant impact on safety for Type V sites, resulting 

in AMFs of one for these variables. 

Compared to the previous works, for Types I and II, no AMF was estimated for SKEW. 

For right-turn lane on major roads, AMFs greater than one and less than one were 

estimated for Type II sites using the Group A dataset for the former and the Group B for 

the latter. 

Whereas the “Red Book” provides separate AMFs for right-and left-turn lanes on major 

roads at Type II intersections, turning lanes at most sits in this dataset were provided on 

both approaches and separate effects could not be detected for one versus two approaches. 

SKEW did not provide a significant AMF different from 1 in the new data. And very few 

sites had deficient sight distance so an AMF could not be estimated. 
205

For Type III and IV intersections, intersection angle (SKEW) was estimated as 

significant in the regression models. Right-turn lanes on major roads provided significant 

AMFs for Type IV intersections. For Type V intersections, no AMFs were found to be 

significantly different from 1. 

Table 185. Comparison of Type I–II AMFs for TOTACC 

“Red Book” and Harwood et al. (2002) Full Models Regression Models 

AMF 

Type I Type II Type I Type II Type I Type II 

SKEW exp(0.004SKEW) exp(0.0054SKEW) 

Not 

calibrated

Not 

calibrated 1 1 

RT MAJ 

1.00 if none exist 

0.95 on one approach 

(0.86 on one approach) 

0.90 on both approaches 

(0.74 on both approaches) 

 0.88 1.19,0.861 1 0.71 

LT MAJ 

1.00 if none exist 

0.78 if at least one 

exists 

(0.56 if at least one 

exists) 

1.00 if none exist 

0.76 on one approach 

(0.72 on one 

approach) 

0.58 on both 

approaches 

(0.52 on both 

approaches) 0.82 1 0.71 

1.05 if limited in 1 quadrants 

1.10 if limited in 2 quadrants 

1.15 if limited in 3 quadrants 

SIGHT 

DISTANCE 1.20 if limited in 4 quadrants 

Not 

calibrated

Not 

calibrated

Not 

calibrated

Not 

calibrated

RT MIN 1.35 1.48 1 

HI1 exp(0.0263)

Not 

calibrated

DRWY1 1.13 

Not 

calibrated

Not 

calibrated

MEDIAN 

Not calibrated Not calibrated

Not 

calibrated Not 

calibrated 1 0.77 1 Group A = 1.19, Group B = 0.86 
Table 186. Comparison of Type III–V AMFs for TOTACC 

“Red Book” and Harwood et al. 

(2002) AMFs Derived From Full Models AMFs Derived F

AMF Type 

III-IV Type V Type III Type IV Type V Type III 

SKEW 1 exp(0.010SKEW) 

1+(0.016*SKEW)/ (0.98+0.016*SKEW) 

1+(0(1.4

RT MAJ 

1.00 if none exist 0.975 on one approach (0.96 on one approach) 0.95 on both approaches (0.92 on both approaches) 1 1 

LT MAJ 

1.00 if none exist 0.82 on one approach0.67 on both approaches 0.71 1 

SIGHT DISTANCE 1 

Not calibrated Not calibrated

1 1 

COMDRWY1 exp 

(0.0681COMDRWY1) 

exp (0.0539 COMDRWY1) 

VEI1 exp(0.1081VEI1) MEDWIDTH1 

exp (-0.0106MEDWDTH1)

MEDTYPE1 0.73 

Not calibrated

PKTRUCK 

exp (-0.0479PKTRUCK) 

PKTHRU2 

exp (0.0249PKTHRU2) 

PKLEFT 

exp (0.0229PKLEFT) 

SDR2 exp(-0.0003SDR2) 

Not calibrated

LIGHT 0.75 HEICOM 

None 

provided 

Not calibrated

Not calibrated

exp (-0.0288HEICOM) 

Not calibrated

Not 

206 
Table 187. Comparison of AMFs for INJACC 

“Red 

Book” AMFs Derived From Full Models AMFs Derived Fro

AMF Type I - V Type I Type II Type III Type IV Type V Type I Type II T

SKEW 

Not calibrated Not 

calibrated exp(0.0163SKEW) 1 1 

1+(0.017(0.52+0

RT MAJ 0.87 0.85 1 1 1 LT MAJ 0.8 1 0.42 1 RT MIN 1.36 1.56 1 1 SIGHT DISTANCE Not calibrated

Not 

calibrated

1 

HI 

exp (0.0286) 

exp (0.0408) 

DRWY1 

1.09 

Not 

calibrated

Not 

calibrated

MEDIAN 0.72 

Not calibrated

1 0.52 

COMDRWY1 

exp (0.0627COMDRWY1)

HAZRAT1 

exp (0.1889HAZRAT1) 

Not calibrated

PKTRUCK 

exp (-0.0253PKTRUCK) 

exp (-0.0520PKTRUCK) 

PKTURN exp(0.0254PKTURN) Not calibratedPKLEFT1 

exp (0.0523PKLEF) 

SDR2 

Not calibrated

LIGHT 0.67 HEI2 

None provided 

Not calibrated

Not 

calibrated

Not calibrated

Not calibrated

exp (-0.0284HEI2)

Not 

calibrated

Not 

calibrated

Not cali

207 
208

3.6 SENSITIVITY ANALYSIS RESULTS 

A sensitivity analysis was performed to examine the estimated effect on safety of the AMFs 

derived from the full models and regression base models. The sensitivity analysis 

applies each AMF to the base model estimate for various levels of AADT. 

3.6.1 Type I Intersections 

The predicted TOTAL and INJURY accident frequencies per year for each AMF derived 

from the full models and regression base models are presented in tables 188 through 195. 

Type I TOTAL Accidents 

The AMFs derived for TOTAL accidents for Type I intersections are HI1, right-turn lanes on 

major, right-turn lane on minor, and left-turn lanes on major roads. The sensitivity test results 

for these AMFs are presented in tables 188 through 191. 

Table 188. Sensitivity of Safety to HI1 for Type I TOTAL Accidents Per Year

HI1 

Major Road AADT (veh/day) 

Minor Road 

AADT 

(veh/day) 0 5 10 20 

50 0.088 0.101 0.115 0.150

100 0.113 0.129 0.147 0.191

400 

 

 400 0.185 0.211 0.240 0.312

100 0.204 0.233 0.265 0.345

500 0.361 0.411 0.469 0.610

1,000 

 

 1,000 0.461 0.526 0.600 0.780

100 0.414 0.472 0.539 0.701

500 0.732 0.835 0.952 1.239

1,000 0.936 1.067 1.217 1.583

3,000 

 

 

 3,000 1.380 1.574 1.796 2.336

100 0.576 0.656 0.749 0.974

500 1.017 1.160 1.324 1.722

1,000 1.300 1.483 1.692 2.200

3,000 1.919 2.188 2.496 3.247

5,000 

 

 

 

 5,000 2.299 2.622 2.990 3.890

100 0.900 1.026 1.170 1.522

500 1.590 1.814 2.069 2.691

1,000 2.033 2.318 2.644 3.440

3,000 2.999 3.421 3.901 5.075

5,000 3.594 4.099 4.675 6.081

10,000 

 

 

 

 

 10,000 4.593 5.238 5.975 7.772

Note: Group B AADT base model was used. 

The AMF for HI1 was derived from full models. 
209

Table 189. Sensitivity of Safety to RT MAJ for Type I TOTAL Accidents Per Year

Major Road RT MAJ 

AADT 

(veh/day) 

Minor Road 

AADT 

(veh/day) No Right-Turn Lane on Major Road Presence of Right-Turn Lane on 

Major Road 

50 0.088 0.078

100 0.113 0.099

400 

 

 400 0.185 0.162

100 0.204 0.180

500 0.361 0.317

1,000 

 

 1,000 0.461 0.406

100 0.414 0.364

500 0.732 0.644

1,000 0.936 0.823

3,000 

 

 

 3,000 1.380 1.215

100 0.576 0.506

500 1.017 0.895

1,000 1.300 1.144

3,000 1.919 1.688

5,000 

 

 

 

 5,000 2.299 2.023

100 0.900 0.792

500 1.590 1.400

1,000 2.033 1.789

3,000 2.999 2.639

5,000 3.594 3.162

10,000 

 

 

 

 

 10,000 4.593 4.042

Note: Group B AADT base model was used. 

The AMF for RT MAJ was derived from full models. 
210

Table 190. Sensitivity of Safety to RT MIN for Type I TOTAL Accidents Per Year

RT MIN 

Presence of Right-Turn Lane on 

Minor Road Major Road AADT (veh/day) 

Minor Road 

AADT 

(veh/day) 

No Right-Turn Lane 

on Minor Road 

A B 

50 0.088 0.119 0.131

100 0.113 0.153 0.167

400 

 

 400 0.185 0.249 0.273

100 0.204 0.275 0.302

500 0.361 0.487 0.534

1,000 

 

 1,000 0.461 0.622 0.682

100 0.414 0.559 0.613

500 0.732 0.988 1.083

1,000 0.936 1.263 1.385

3,000 

 

 

 3,000 1.380 1.864 2.043

100 0.576 0.777 0.852

500 1.017 1.374 1.506

1,000 1.300 1.756 1.925

3,000 1.919 2.590 2.839

5,000 

 

 

 

 5,000 2.299 3.103 3.402

100 0.900 1.215 1.332

500 1.590 2.147 2.354

1,000 2.033 2.744 3.099

3,000 2.999 4.049 4.439

5,000 3.594 4.851 5.319

10,000 

 

 

 

 

 10,000 4.593 6.200 6.798

Note: Group B AADT base model was used. 

A: AMF derived from full models. 

B: AMF derived from regression models. 
211

Table 191. Sensitivity of Safety to LT MAJ for Type I TOTAL Accidents Per Year

Major Road LT MAJ 

AADT 

(veh/day) 

Minor Road 

AADT 

(veh/day) No Left-Turn Lane on Major Road Presence of Left-Turn Lane on Major 

Road 

50 0.088 0.073

100 0.113 0.093

400 

 

 400 0.185 0.151

100 0.204 0.167

500 0.361 0.296

1,000 

 

 1,000 0.461 0.378

100 0.414 0.340

500 0.732 0.600

1,000 0.936 0.767

3,000 

 

 

 3,000 1.380 1.132

100 0.576 0.472

500 1.017 0.834

1,000 1.300 1.066

3,000 1.919 1.573

5,000 

 

 

 

 5,000 2.299 1.885

100 0.900 0.738

500 1.590 1.304

1,000 2.033 1.667

3,000 2.999 2.459

5,000 3.594 2.947

10,000 

 

 

 

 

 10,000 4.593 3.766

Note: Group B AADT base model was used. 

The AMF for LT MAJ was derived from full models. 
212

Type I INJURY Accidents 

The AMFs derived for INJURY accidents for Type I intersections are HI1, right-turn lane on 

major, right-turn lanes on minor, and left-turn lanes on major roads. The sensitivity test 

results for these AMFs are presented in tables 192 through 195. 

Table 192. Sensitivity of Safety to HI1 for Type I INJURY Accidents Per Year

HI1 

Major Road AADT (veh/day) 

Minor Road 

AADT 

(veh/day) 0 5 10 20 

50 0.036 0.042 0.048 0.064

100 0.046 0.053 0.061 0.081

400

 

 400 0.073 0.084 0.097 0.129

100 0.082 0.095 0.109 0.145

500 0.142 0.163 0.188 0.251

1,000

 

 1,000 0.179 0.206 0.238 0.317

100 0.166 0.192 0.221 0.295

500 0.287 0.331 0.382 0.508

1,000 0.362 0.418 0.482 0.642

3,000

 

 

 3,000 0.526 0.606 0.700 0.931

100 0.231 0.266 0.307 0.409

500 0.398 0.459 0.530 0.705

1,000 0.503 0.581 0.670 0.892

3,000 0.730 0.842 0.971 1.293

5,000

 

 

 

 5,000 0.867 1.001 1.154 1.537

100 0.361 0.416 0.480 0.639

500 0.621 0.717 0.827 1.101

1,000 0.786 0.906 1.046 1.392

3,000 1.139 1.314 1.516 2.018

5,000 1.354 1.562 1.802 2.399

10,000

 

 

 

 

 10,000 1.712 1.975 2.278 3.033

 Note: Group B AADT base model was used. 

 The AMF for HI1 was derived from full models. 
213

Table 193. Sensitivity of Safety to RT MAJ for Type I INJURY Accidents Per Year

Major Road RT MAJ 

AADT 

(veh/day) 

Minor Road 

AADT 

(veh/day) No Right-Turn Lane on Major Road Presence of Right-Turn Lane on Major 

Road 

50 0.036 0.031

100 0.046 0.040

400 

 

 400 0.073 0.063

100 0.082 0.071

500 0.142 0.123

1,000 

 

 1,000 0.179 0.156

100 0.166 0.145

500 0.287 0.249

1,000 0.362 0.315

3,000 

 

 

 3,000 0.526 0.457

100 0.231 0.201

500 0.398 0.346

1,000 0.503 0.438

3,000 0.730 0.635

5,000 

 

 

 

 5,000 0.867 0.755

100 0.361 0.314

500 0.621 0.541

1,000 0.786 0.684

3,000 1.139 0.991

5,000 1.354 1.178

10,000 

 

 

 

 

 10,000 1.712 1.489

Note: Group B AADT base model was used. 

The AMF for RT MAJ was derived from full models. 
214

Table 194. Sensitivity of Safety to RT MIN for Type I INJURY Accidents Per Year 

RT MIN 

Presence of right-turn lane on minor 

road 

Major Road AADT 

(veh/day) 

Minor Road 

AADT (veh/day) No right-turn lane 

on minor road 

A B 

50 0.036 0.049 0.056

100 0.046 0.062 0.071

400 

 

 400 0.073 0.099 0.114

100 0.082 0.112 0.128

500 0.142 0.192 0.221

1,000 

 

 1,000 0.179 0.243 0.279

100 0.166 0.226 0.260

500 0.287 0.390 0.447

1,000 0.362 0.493 0.565

3,000 

 

 

 3,000 0.526 0.715 0.820

100 0.231 0.314 0.360

500 0.398 0.541 0.621

1,000 0.503 0.684 0.785

3,000 0.730 0.992 1.138

5,000 

 

 

 

 5,000 0.867 1.180 1.353

100 0.361 0.490 0.563

500 0.621 0.845 0.970

1,000 0.786 1.068 1.226

3,000 1.139 1.549 1.777

5,000 1.354 1.841 2.112

10,000 

 

 

 

 

 10,000 1.712 2.328 2.670

Note: Group B AADT base model was used. 

A: AMF derived from full models. 

B: AMF derived from regression models. 
215

Table 195. Sensitivity of Safety to LT MAJ for Type I INJURY Accidents Per Year

Major Road LT MAJ 

AADT 

(veh/day) 

Minor Road 

AADT 

(veh/day) No Left-Turn Lane on Major Road Presence of Left-Turn Lane on Major 

Road 

50 0.036 0.029

100 0.046 0.036

400 

 

 400 0.073 0.058

100 0.082 0.066

500 0.142 0.113

1,000 

 

 1,000 0.179 0.143

100 0.166 0.133

500 0.287 0.229

1,000 0.362 0.290

3,000 

 

 

 3,000 0.526 0.420

100 0.231 0.185

500 0.398 0.318

1,000 0.503 0.403

3,000 0.730 0.584

5,000 

 

 

 

 5,000 0.867 0.694

100 0.361 0.288

500 0.621 0.497

1,000 0.786 0.629

3,000 1.139 0.911

5,000 1.354 1.083

10,000 

 

 

 

 

 10,000 1.712 1.369

Note: Group B AADT base model was used. 

The AMF for LT MAJ was derived from full models. 
216

3.6.2 Type II Intersections 

The predicted TOTAL and INJURY accident frequencies per year for each AMF derived 

from the full models and regression base models are presented in tables 196 through 204. 

Type II TOTAL Accidents 

The AMFs derived for TOTAL accidents for Type II intersections are ND, right-turn lanes 

on major, left-turn lanes on major, and median on major roads. The sensitivity test results for 

these AMFs are presented in tables 196 through 199. 

Table 196. Sensitivity of Safety to DRWY1 for Type II TOTAL Accidents Per Year

Major Road DRWY1 

AADT 

(veh/day) 

Minor Road 

AADT 

(veh/day) 0 3 5 

50 0.056 0.064 0.072

100 0.082 0.093 0.105

400 

 

 400 0.175 0.198 0.223

100 0.158 0.179 0.202

500 0.380 0.429 0.485

1,000 

 

 1,000 0.554 0.626 0.707

100 0.346 0.391 0.442

500 0.831 0.939 1.061

1,000 1.212 1.369 1.548

3,000 

 

 

 3,000 2.204 2.491 2.815

100 0.498 0.563 0.636

500 1.196 1.351 1.527

1,000 1.744 1.971 2.227

3,000 3.173 3.585 4.051

5,000 

 

 

 

 5,000 4.190 4.735 5.350

100 0.816 0.922 1.042

500 1.960 2.215 2.503

1,000 2.859 3.230 3.650

3,000 5.200 5.876 6.639

5,000 6.867 7.760 8.769

10,000 

 

 

 

 

 10,000 10.016 11.318 12.789

Note: Group B AADT base model was used. 

The AMF for DRWY1 was derived from full models. 
217

Table 197. Sensitivity of Safety to RT MAJ for Type II TOTAL Accidents Per Year

RT MAJ 

Presence of Right-Turn Lane on Major

Road 

Major Road 

AADT 

(veh/day) 

Minor Road 

AADT 

(veh/day) No Right-Turn Lane on Major Road 

A B C 

50 0.056 0.067 0.049 0.040

100 0.082 0.098 0.071 0.058

400 

 

 400 0.175 0.208 0.151 0.124

100 0.158 0.188 0.136 0.112

500 0.380 0.452 0.327 0.270

1,000 

 

 1,000 0.554 0.659 0.476 0.393

100 0.346 0.412 0.297 0.246

500 0.831 0.989 0.715 0.590

1,000 1.212 1.442 1.042 0.860

3,000 

 

 

 3,000 2.204 2.623 1.896 1.565

100 0.498 0.592 0.428 0.353

500 1.196 1.423 1.028 0.849

1,000 1.744 2.076 1.500 1.238

3,000 3.173 3.775 2.728 2.252

5,000 

 

 

 

 5,000 4.190 4.986 3.603 2.975

100 0.816 0.971 0.702 0.579

500 1.960 2.332 1.686 1.392

1,000 2.859 3.402 2.459 2.030

3,000 5.200 6.188 4.472 3.692

5,000 6.867 8.172 5.906 4.876

10,000 

 

 

 

 

 10,000 10.016 11.919 8.614 7.111

Note: Group B AADT base model was used. 

A: AMF derived from full models, Group A data. 

B: AMF derived from full models, Group B data. 

C: AMF derived from regression models 
218

Table 198. Sensitivity of Safety to LT MAJ for Type II TOTAL Accidents Per Year

Major Road LT MAJ 

AADT 

(veh/day) 

Minor Road 

AADT 

(veh/day) No Left-Turn Lane on Major Road Presence of Left-Turn Lane on Major 

Road 

50 0.056 0.040 

100 0.082 0.058 

400 

 

 400 0.175 0.124 

100 0.158 0.112 

500 0.380 0.270 

1,000 

 

 1,000 0.554 0.393 

100 0.346 0.246 

500 0.831 0.590 

1,000 1.212 0.860 

3,000 

 

 

 3,000 2.204 1.565 

100 0.498 0.353 

500 1.196 0.8449

1,000 1.744 1.238 

3,000 3.173 2.252 

5,000 

 

 

 

 5,000 4.190 2.975 

100 0.816 0.579 

500 1.960 1.392 

1,000 2.859 2.030 

3,000 5.200 3.692 

5,000 6.867 4.876 

10,000 

 

 

 

 

 10,000 10.016 7.111 

Note: Group B AADT base model was used. 

The AMF for LT MAJ was derived from regression models. 
219

Table 199. Sensitivity of Safety to MEDIAN for Type II TOTAL Accidents Per Year

Major Road MEDIAN 

AADT 

(veh/day) 

Minor Road 

AADT 

(veh/day) No Median on Major Road Presence of Median on Major Road 

50 0.056 0.043

100 0.082 0.063

400 

 

 400 0.175 0.135

100 0.158 0.122

500 0.380 0.292

1,000 

 

 1,000 0.554 0.426

100 0.346 0.266

500 0.831 0.640

1,000 1.212 0.933

3,000 

 

 

 3,000 2.204 1.697

100 0.498 0.383

500 1.196 0.921

1,000 1.744 1.343

3,000 3.173 2.443

5,000 

 

 

 

 5,000 4.190 3.226

100 0.816 0.628

500 1.960 1.509

1,000 2.859 2.201

3,000 5.200 4.004

5,000 6.867 5.288

10,000 

 

 

 

 

 10,000 10.016 7.712

Note: Group B AADT base model was used. 

The AMF for MEDIAN was derived from regression models. 
220

Type II INJURY Accidents 

The AMFs derived for INJURY accidents for Type II intersections are HI1, DRWY1, rightturn lanes on major, left-turn lanes on major, and median on major roads. The sensitivity test 

results for these AMFs are presented in tables 200 through 204. 

Table 200. Sensitivity of Safety to HI1 for Type II INJURY Accidents Per Year

HI1 Major Road AADT (veh/day) Minor Road AADT 

(veh/day) 0 5 10 20 

50 0.033 0.040 0.049 0.074

100 0.049 0.060 0.073 0.110

400

 

 400 0.107 0.131 0.161 0.242

100 0.087 0.106 0.130 0.196

500 0.216 0.265 0.325 0.489

1,000

 

 1,000 0.321 0.394 0.483 0.726

100 0.173 0.212 0.259 0.390

500 0.431 0.529 0.649 0.975

1,000 0.640 0.785 0.962 1.447

3,000

 

 

 3,000 1.196 1.466 1.798 2.704

100 0.238 0.292 0.358 0.538

500 0.594 0.729 0.894 1.344

1,000 0.882 1.082 1.326 1.995

3,000 1.648 2.021 2.479 3.727

5,000

 

 

 

 5,000 2.204 2.703 3.315 4.985

100 0.368 0.451 0.553 0.831

500 0.919 1.127 1.382 2.078

1,000 1.363 1.672 2.050 3.083

3,000 2.548 3.124 3.831 5.761

5,000 3.407 4.178 5.124 7.705

10,000

 

 

 

 

 10,000 5.055 6.199 7.602 11.433

Note: Group B AADT base model was used. 

The AMF for HI1 was derived from full models. 
221

Table 201. Sensitivity of Safety to DRWY1 for Type II INJURY Accidents Per Year

Major Road DRWY1 

AADT 

(veh/day) 

Minor Road 

AADT 

(veh/day) 0 3 5 

50 0.033 0.036 0.039

100 0.049 0.053 0.058

400 

 

 400 0.107 0.117 0.127

100 0.087 0.094 0.103

500 0.216 0.236 0.257

1,000 

 

 1,000 0.321 0.350 0.381

100 0.173 0.188 0.205

500 0.431 0.470 0.512

1,000 0.640 0.697 0.760

3,000 

 

 

 3,000 1.196 1.303 1.421

100 0.238 0.259 0.283

500 0.594 0.648 0.706

1,000 0.882 0.961 1.048

3,000 1.648 1.797 1.958

5,000 

 

 

 

 5,000 2.204 2.403 2.619

100 0.368 0.401 0.437

500 0.919 1.001 1.092

1,000 1.363 1.486 1.620

3,000 2.548 2.777 3.027

5,000 3.407 3.714 4.048

10,000 

 

 

 

 

 10,000 5.055 5.510 6.006

Note: Group B AADT base model was used. 

The AMF for DRWY1 was derived from full models. 
222

Table 202. Sensitivity of Safety to RT MAJ for Type II INJURY Accidents Per Year

Major Road RT MAJ 

AADT 

(veh/day) 

Minor Road 

AADT 

(veh/day) No Right-Turn Lane on Major Road Presence of Right-Turn Lane on Major 

Road 

50 0.033 0.028

100 0.049 0.041

400 

 

 400 0.107 0.091

100 0.087 0.074

500 0.216 0.184

1,000 

 

 1,000 0.321 0.273

100 0.173 0.147

500 0.431 0.367

1,000 0.640 0.544

3,000 

 

 

 3,000 1.196 1.016

100 0.238 0.202

500 0.594 0.505

1,000 0.882 0.750

3,000 1.648 1.401

5,000 

 

 

 

 5,000 2.204 1.874

100 0.368 0.312

500 0.919 0.781

1,000 1.363 1.159

3,000 2.548 2.165

5,000 3.407 2.896

10,000 

 

 

 

 

 10,000 5.055 4.297

Note: Group B AADT base model was used. 

The AMF for RT MAJ was derived from full models. 
223

Table 203. Sensitivity of Safety to LT MAJ for Type II INJURY Accidents Per Year

Major Road LT MAJ 

AADT 

(veh/day) 

Minor Road 

AADT 

(veh/day) No Left-Turn Lane on Major Road Presence of Left-Turn Lane on Major 

Road 

50 0.033 0.014

100 0.049 0.020

400 

 

 400 0.107 0.045

100 0.087 0.036

500 0.216 0.091

1,000 

 

 1,000 0.321 0.135

100 0.173 0.072

500 0.431 0.181

1,000 0.640 0.269

3,000 

 

 

 3,000 1.196 0.502

100 0.238 0.100

500 0.594 0.250

1,000 0.882 0.370

3,000 1.648 0.692

5,000 

 

 

 

 5,000 2.204 0.926

100 0.368 0.154

500 0.919 0.386

1,000 1.363 0.573

3,000 2.548 1.070

5,000 3.407 1.431

10,000 

 

 

 

 

 10,000 5.055 2.123

Note: Group B AADT base model was used. 

The AMF for LT MAJ was derived from regression models. 
224

Table 204. Sensitivity of Safety to MEDIAN for Type II INJURY 

Accidents Per Year 

MEDIAN 

Presence of Median on Major Road 

Major Road 

AADT 

(veh/day) 

Minor Road 

AADT 

(veh/day) No Median on Major Road A B 

50 0.033 0.024 0.017

100 0.049 0.035 0.025

400 

 

 400 0.107 0.077 0.056

100 0.087 0.062 0.045

500 0.216 0.156 0.112

1,000 

 

 1,000 0.321 0.231 0.167

100 0.173 0.124 0.090

500 0.431 0.311 0.224

1,000 0.640 0.461 0.333

3,000 

 

 

 3,000 1.196 0.861 0.622

100 0.238 0.171 0.124

500 0.594 0.428 0.309

1,000 0.882 0.635 0.459

3,000 1.648 1.187 0.857

5,000 

 

 

 

 5,000 2.204 1.587 1.146

100 0.368 0.265 0.191

500 0.919 0.662 0.478

1,000 1.363 0.981 0.709

3,000 2.548 1.834 1.325

5,000 3.407 2.453 1.772

10,000 

 

 

 

 

 10,000 5.055 3.640 2.629

Note: Group B AADT base model was used. 

A: AMF derived from full models. 

B: AMF derived from regression models. 
225

3.6.3 Type III Intersections 

The predicted TOTAL and INJURY accident frequencies per year for each AMF derived 

from the full models and regression base models are presented in tables 205 through 215. 

Type III TOTAL Accidents 

The AMFs derived for TOTAL accidents for Type III intersections are intersection SKEW 

angle, commercial driveways on major road, vertical curves on major road, median width on 

major road, painted median type on major road, and major road left-turn lane. The sensitivity 

test results for these AMFs are presented in tables 205 through 210. 

Table 205. Sensitivity of Safety to Skew Angles for Type III TOTAL 

Accidents Per Year 

SKEW Angle (degrees) 

A B A B A B A B A B 

Major Road 

AADT 

(veh/day) 

Minor Road 

AADT 

(veh/day) 0 10 15 30 45 

50 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.01

100 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.02

400 

 

 400 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.03 0.02

100 0.03 0.03 0.04 0.04 0.04 0.04 0.05 0.04 0.05 0.05

500 0.05 0.05 0.06 0.06 0.06 0.06 0.07 0.07 0.08 0.07

1,000 

 

 1,000 0.06 0.06 0.07 0.07 0.07 0.07 0.08 0.08 0.09 0.09

100 0.11 0.11 0.12 0.13 0.13 0.13 0.15 0.15 0.17 0.16

500 0.17 0.17 0.18 0.19 0.19 0.20 0.23 0.22 0.26 0.24

1,000 0.20 0.20 0.22 0.23 0.23 0.24 0.27 0.26 0.31 0.28

3,000 

 

 

 3,000 0.26 0.26 0.29 0.30 0.31 0.31 0.36 0.35 0.41 0.37

100 0.19 0.19 0.21 0.22 0.23 0.23 0.26 0.26 0.30 0.28

500 0.29 0.29 0.32 0.33 0.34 0.35 0.39 0.39 0.46 0.41

1,000 0.35 0.35 0.38 0.40 0.40 0.42 0.47 0.46 0.55 0.49

3,000 0.46 0.46 0.51 0.52 0.53 0.55 0.62 0.61 0.72 0.65

5,000 

 

 

 

 5,000 0.52 0.52 0.58 0.60 0.61 0.63 0.71 0.70 0.82 0.74

100 0.41 0.41 0.46 0.47 0.48 0.49 0.56 0.55 0.65 0.59

500 0.62 0.62 0.69 0.71 0.72 0.74 0.84 0.83 0.98 0.89

1,000 0.74 0.74 0.82 0.85 0.86 0.89 1.00 0.99 1.17 1.06

3,000 0.98 0.98 1.09 1.12 1.14 1.17 1.33 1.30 1.55 1.40

5,000 1.12 1.12 1.24 1.27 1.30 1.34 1.51 1.48 1.76 1.59

10,000 

 

 

 

 

 10,000 1.33 1.33 1.47 1.52 1.55 1.59 1.80 1.77 2.10 1.90

Note: Group B AADT base model was used. 

A: AMF derived from full models. 

B: AMF derived from regression models. 
226

Table 206. Sensitivity of Safety to Commercial Driveways on Major Road forType III 

TOTAL Accidents Per Year 

Major Road AADT Commercial Driveways on Major Road (density) 

(veh/day) 

Minor Road AADT 

(veh/day) 0 5 10 15 

400 50 0.01 0.01 0.02 0.03

 100 0.01 0.02 0.02 0.03

 400 0.02 0.02 0.03 0.05

1,000 100 0.03 0.05 0.07 0.09

 500 0.05 0.07 0.10 0.14

 1,000 0.06 0.08 0.12 0.17

3,000 100 0.11 0.16 0.22 0.31

 500 0.17 0.23 0.33 0.46

 1,000 0.20 0.28 0.39 0.55

 3,000 0.26 0.37 0.52 0.73

5,000 100 0.19 0.27 0.38 0.54

 500 0.29 0.41 0.58 0.81

 1,000 0.35 0.49 0.69 0.96

 3,000 0.46 0.65 0.91 1.28

 5,000 0.52 0.74 1.03 1.45

10,000 100 0.41 0.58 0.82 1.15

 500 0.62 0.87 1.23 1.73

 1,000 0.74 1.04 1.47 2.06

 3,000 0.98 1.38 1.94 2.72

 5,000 1.12 1.57 2.21 3.10

 10,000 1.33 1.87 2.63 3.70

Note: Group B AADT base model was used. 

The AMF for CD on major road was derived from full models. 
227

Table 207. Sensitivity of Safety to Vertical Curves on Major Road (VEI1) for Type III 

TOTAL Accidents Per Year 

Major Road AADT VEI1 

(veh/day) 

Minor Road AADT 

(veh/day) 0 3 5 10 

400 50 0.01 0.01 0.02 0.03

 100 0.01 0.02 0.02 0.04

 400 0.02 0.02 0.03 0.05

1,000 100 0.03 0.05 0.06 0.10

 500 0.05 0.07 0.09 0.15

 1,000 0.06 0.08 0.10 0.18

3,000 100 0.11 0.15 0.19 0.33

 500 0.17 0.23 0.29 0.49

 1,000 0.20 0.27 0.34 0.59

 3,000 0.26 0.36 0.45 0.77

5,000 100 0.19 0.27 0.33 0.57

 500 0.29 0.40 0.50 0.86

 1,000 0.35 0.48 0.60 1.02

 3,000 0.46 0.64 0.79 1.35

 5,000 0.52 0.72 0.90 1.54

10,000 100 0.41 0.57 0.71 1.22

 500 0.62 0.86 1.07 1.83

 1,000 0.74 1.03 1.27 2.19

 3,000 0.98 1.36 1.68 2.89

 5,000 1.12 1.54 1.92 3.29

 10,000 1.33 1.84 2.29 3.93

Note: Group B AADT base model was used. 

The AMF for VEI1 was derived from full models. 
228

Table 208. Sensitivity of Safety to Median Width on Major Road (MEDWIDTH1) for 

Type III TOTAL Accidents Per Year 

Major Road AADT MEDWIDHT1 

(veh/day) 

Minor Road AADT 

(veh/day) 0 6 12 20 

400 50 0.01 0.01 0.01 0.01

 100 0.01 0.01 0.01 0.01

 400 0.02 0.02 0.02 0.01

1,000 100 0.03 0.03 0.03 0.03

 500 0.05 0.05 0.04 0.04

 1,000 0.06 0.06 0.05 0.05

3,000 100 0.11 0.10 0.10 0.09

 500 0.17 0.16 0.15 0.13

 1,000 0.20 0.19 0.17 0.16

 3,000 0.26 0.25 0.23 0.21

5,000 100 0.19 0.18 0.17 0.16

 500 0.29 0.27 0.26 0.24

 1,000 0.35 0.33 0.31 0.28

 3,000 0.46 0.43 0.40 0.37

 5,000 0.52 0.49 0.46 0.42

10,000 100 0.41 0.39 0.36 0.33

 500 0.62 0.58 0.55 0.50

 1,000 0.74 0.70 0.65 0.60

 3,000 0.98 0.92 0.86 0.79

 5,000 1.12 1.05 0.98 0.90

 10,000 1.33 1.25 1.17 1.08

Note: Group B AADT base model was used. 

The AMF for MEDWIDTH1 was derived from full models. 
229

Table 209. Sensitivity of Safety to Painted Median Type on Major Road (MEDTYPE1) 

for Type III TOTAL Accidents Per Year 

Major Road AADT Median Type on Major Road 

(veh/day) 

Minor Road AADT 

(veh/day) No Median Painted Median 

400 50 0.01 0.01

 100 0.01 0.01

 400 0.02 0.01

1,000 100 0.03 0.02

 500 0.05 0.04

 1,000 0.06 0.04

3,000 100 0.11 0.08

 500 0.17 0.12

 1,000 0.20 0.15

 3,000 0.26 0.19

5,000 100 0.19 0.14

 500 0.29 0.21

 1,000 0.35 0.25

 3,000 0.46 0.34

 5,000 0.52 0.38

10,000 100 0.41 0.30

 500 0.62 0.45

 1,000 0.74 0.54

 3,000 0.98 0.72

 5,000 1.12 0.82

 10,000 1.33 0.97

Note: Group B AADT base model was used. 

The AMF for MEDTYPE1 was derived from full models. 
230

Table 210. Sensitivity of Safety to Major Road Left-Turn Lane for Type III TOTAL 

 Accidents Per Year 

Major Road AADT Major Road Left-Turn Lane 

(veh/day) 

Minor Road AADT 

(veh/day) No Left-Turn Lane One Left-Turn Lane 

400 50 0.01 0.01

 100 0.01 0.01

 400 0.02 0.01

1,000 100 0.03 0.02

 500 0.05 0.04

 1,000 0.06 0.04

3,000 100 0.11 0.08

 500 0.17 0.12

 1,000 0.20 0.14

 3,000 0.26 0.19

5,000 100 0.19 0.14

 500 0.29 0.21

 1,000 0.35 0.25

 3,000 0.46 0.33

 5,000 0.52 0.37

10,000 100 0.41 0.29

 500 0.62 0.44

 1,000 0.74 0.53

 3,000 0.98 0.70

 5,000 1.12 0.79

 10,000 1.33 0.95

Note: Group B AADT base model was used. 

The AMF for Major Road Left-Turn Lane was derived from regression models. 
231

Type III INJURY Accidents 

The AMFs derived for INJURY accidents for Type III intersections are intersection SKEW 

angle, commercial driveways on major road, hazard rating on major road, peak truck 

percentage on major road, and peak turning percentage. The sensitivity test results for these 

AMFs are presented below. 

Table 211. Sensitivity of Safety to Skew Angles for Type III INJURY Accidents Per 

 Year 

SKEW Angle (degrees) 

A B A B A B A B A B 

Major Road 

AADT 

(veh/day) 

Minor Road 

AADT 

(veh/day) 0 10 15 30 45 

50 0.002 0.002 0.002 0.002 0.002 0.003 0.003 0.003 0.004 0.003

100 0.002 0.002 0.003 0.003 0.003 0.003 0.004 0.003 0.005 0.004

400 

 

 400 0.003 0.003 0.004 0.004 0.004 0.004 0.005 0.005 0.007 0.005

100 0.008 0.008 0.009 0.010 0.010 0.010 0.013 0.012 0.016 0.012

500 0.012 0.012 0.014 0.015 0.015 0.016 0.019 0.018 0.025 0.019

1,000 

 

 1,000 0.014 0.014 0.017 0.018 0.018 0.019 0.023 0.021 0.030 0.023

100 0.033 0.033 0.039 0.042 0.043 0.044 0.054 0.050 0.069 0.053

500 0.051 0.051 0.060 0.064 0.065 0.068 0.083 0.076 0.106 0.081

1,000 0.061 0.061 0.072 0.076 0.078 0.082 0.100 0.092 0.128 0.098

3,000 

 

 

 3,000 0.082 0.082 0.097 0.102 0.105 0.109 0.134 0.123 0.171 0.131

100 0.066 0.066 0.077 0.082 0.084 0.087 0.107 0.098 0.137 0.105

500 0.101 0.101 0.119 0.126 0.129 0.134 0.164 0.151 0.210 0.161

1,000 0.121 0.121 0.143 0.151 0.155 0.161 0.197 0.181 0.252 0.193

3,000 0.162 0.162 0.191 0.202 0.207 0.215 0.264 0.242 0.337 0.258

5,000 

 

 

 

 5,000 0.185 0.185 0.218 0.231 0.237 0.246 0.302 0.277 0.386 0.296

100 0.166 0.166 0.195 0.206 0.212 0.220 0.270 0.248 0.345 0.264

500 0.254 0.254 0.299 0.316 0.324 0.337 0.414 0.379 0.528 0.405

1,000 0.305 0.305 0.359 0.380 0.389 0.405 0.497 0.456 0.635 0.486

3,000 0.408 0.408 0.480 0.508 0.521 0.542 0.665 0.610 0.849 0.650

5,000 0.467 0.467 0.549 0.582 0.596 0.620 0.761 0.698 0.972 0.745

10,000 

 

 

 

 

 10,000 0.561 0.561 0.660 0.699 0.716 0.745 0.915 0.839 1.168 0.895

Note: Group B AADT base model was used 

A: AMF derived from full models. 

B: AMF derived from regression models. 
232

Table 212. Sensitivity of Safety to Commercial Driveways on Major Road for 

 Type III INJURY Accidents Per Year 

Major Road AADT Commercial Driveways on Major Road (density) 

(veh/day) 

Minor Road AADT 

(veh/day) 0 5 10 15 

400 50 0.002 0.003 0.004 0.005

 100 0.002 0.003 0.004 0.006

 400 0.003 0.005 0.006 0.008

1,000 100 0.008 0.011 0.014 0.020

 500 0.012 0.016 0.022 0.030

 1,000 0.014 0.019 0.027 0.036

3,000 100 0.033 0.046 0.062 0.085

 500 0.051 0.070 0.096 0.131

 1,000 0.061 0.084 0.115 0.157

 3,000 0.082 0.112 0.154 0.210

5,000 100 0.066 0.090 0.123 0.169

 500 0.101 0.138 0.189 0.258

 1,000 0.121 0.166 0.227 0.310

 3,000 0.162 0.222 0.303 0.415

 5,000 0.185 0.254 0.347 0.475

10,000 100 0.166 0.227 0.310 0.424

 500 0.254 0.347 0.475 0.650

 1,000 0.305 0.417 0.571 0.781

 3,000 0.408 0.558 0.763 1.044

 5,000 0.467 0.639 0.874 1.196

 10,000 0.561 0.767 1.050 1.436

Note: Group B AADT base model was used 

The AMF for Commercial driveways on major road was derived from full models. 
233

Table 213. Sensitivity of Safety to Hazard Rating on Major Road (HAZRAT1) for 

 Type III INJURY Accidents Per Year 

Major Road AADT HAZRAT 

(veh/day) 

Minor Road AADT 

(veh/day) 1 3 5 7 

400 50 0.002 0.003 0.005 0.007

 100 0.002 0.004 0.006 0.009

 400 0.003 0.006 0.008 0.012

1,000 100 0.008 0.014 0.020 0.029

 500 0.012 0.021 0.030 0.044

 1,000 0.014 0.025 0.037 0.053

3,000 100 0.033 0.059 0.086 0.125

 500 0.051 0.090 0.131 0.192

 1,000 0.061 0.108 0.158 0.230

 3,000 0.082 0.145 0.211 0.308

5,000 100 0.066 0.116 0.169 0.247

 500 0.101 0.178 0.259 0.378

 1,000 0.121 0.213 0.311 0.454

 3,000 0.162 0.286 0.417 0.608

 5,000 0.185 0.327 0.477 0.696

10,000 100 0.166 0.292 0.426 0.622

 500 0.254 0.447 0.652 0.952

 1,000 0.305 0.537 0.784 1.144

 3,000 0.408 0.719 1.049 1.530

 5,000 0.467 0.823 1.200 1.751

 10,000 0.561 0.988 1.442 2.104

Note: Group B AADT base model was used 

The AMF for HAZRAT1 was derived from full models. 
234

Table 214. Sensitivity of Safety to Peak Truck Percentage (PKTRUCK) for Type III 

TOTAL Accidents Per Year 

Major Road AADT PKTURCK (percent) 

(veh/day) 

Minor Road AADT 

(veh/day) 0 5 10 15 

400 50 0.002 0.002 0.001 0.001

 100 0.002 0.002 0.002 0.002

 400 0.003 0.003 0.003 0.002

1,000 100 0.008 0.007 0.006 0.005

 500 0.012 0.010 0.009 0.008

 1,000 0.014 0.013 0.011 0.010

3,000 100 0.033 0.029 0.026 0.023

 500 0.051 0.045 0.040 0.035

 1,000 0.061 0.054 0.048 0.042

 3,000 0.082 0.072 0.064 0.056

5,000 100 0.066 0.058 0.051 0.045

 500 0.101 0.089 0.078 0.069

 1,000 0.121 0.107 0.094 0.083

 3,000 0.162 0.143 0.126 0.111

 5,000 0.185 0.163 0.144 0.127

10,000 100 0.166 0.146 0.129 0.113

 500 0.254 0.224 0.197 0.174

 1,000 0.305 0.269 0.237 0.209

 3,000 0.408 0.359 0.317 0.279

 5,000 0.467 0.411 0.362 0.319

 10,000 0.561 0.494 0.435 0.384

Note: Group B AADT base model was used. 

The AMF for PKTRUCK was derived from full models.. 
235

Table 215. Sensitivity of Safety to Peak Turning Percentage (PKTURN) for Type III 

TOTAL Accidents Per Year 

Major Road AADT PKTURN (percent) 

(veh/day) 

Minor Road AADT 

(veh/day) 0 10 20 30 

400 50 0.002 0.002 0.003 0.004

 100 0.002 0.003 0.004 0.005

 400 0.003 0.004 0.005 0.007

1,000 100 0.008 0.010 0.013 0.017

 500 0.012 0.015 0.020 0.025

 1,000 0.014 0.018 0.024 0.030

3,000 100 0.033 0.043 0.055 0.071

 500 0.051 0.066 0.085 0.109

 1,000 0.061 0.079 0.102 0.131

 3,000 0.082 0.106 0.136 0.176

5,000 100 0.066 0.085 0.109 0.141

 500 0.101 0.130 0.168 0.216

 1,000 0.121 0.156 0.201 0.259

 3,000 0.162 0.209 0.269 0.347

 5,000 0.185 0.239 0.308 0.397

10,000 100 0.166 0.214 0.275 0.355

 500 0.254 0.327 0.422 0.544

 1,000 0.305 0.393 0.507 0.653

 3,000 0.408 0.526 0.678 0.874

 5,000 0.467 0.602 0.776 1.000

 10,000 0.561 0.723 0.932 1.202

Note: Group B AADT base model was used. 

The AMF for PKTURN was derived from full models. 
236

3.6.4 Type IV Intersections 

The predicted TOTAL and INJURY accident frequencies per year for each AMF derived 

from the full models and regression base models are presented in tables 216 through 224. 

Type IV TOTAL Accidents 

The AMFs derived for TOTAL accidents for Type IV intersections are intersection SKEW 

angle, right sight distance from minor road, peak truck percentage, peak through percentage 

on minor road, and peak left-turn percentage. The sensitivity test results for these AMFs are 

presented in tables 216 through 220. 

Table 216. Sensitivity of Safety to Skew Angles for Type IV TOTAL Accidents PerYear 

Major Road SKEW Angle (degrees) 

AADT 

(veh/day) 

Minor Road 

AADT 

(veh/day) 0 10 15 30 45 

400 50 0.01 0.01 0.01 0.01 0.01

 100 0.01 0.01 0.01 0.01 0.01

 400 0.02 0.02 0.02 0.02 0.02

1,000 100 0.02 0.03 0.03 0.04 0.04

 500 0.06 0.07 0.07 0.08 0.09

 1,000 0.08 0.10 0.11 0.12 0.13

3,000 100 0.10 0.13 0.13 0.15 0.16

 500 0.23 0.29 0.31 0.35 0.37

 1,000 0.32 0.41 0.44 0.49 0.52

 3,000 0.57 0.72 0.77 0.87 0.92

5,000 100 0.19 0.24 0.26 0.29 0.31

 500 0.44 0.55 0.59 0.66 0.71

 1,000 0.62 0.79 0.84 0.95 1.01

 3,000 1.09 1.39 1.48 1.67 1.78

 5,000 1.42 1.80 1.93 2.17 2.31

10,000 100 0.46 0.59 0.63 0.71 0.75

 500 1.06 1.35 1.44 1.62 1.72

 1,000 1.51 1.92 2.05 2.31 2.46

 3,000 2.66 3.38 3.61 4.06 4.32

 5,000 3.46 4.39 4.69 5.27 5.62

 10,000 4.93 6.27 6.69 7.53 8.02

Note: Group B AADT base model was used. 

The AMF for Intersection SKEW angle was derived from regression base models. 
237

Table 217. Sensitivity of Safety to Right Sight Distance from Minor Road (SDR2) for 

Type IV TOTAL Accidents Per Year 

Major Road AADT SDR2 

(veh/day) 

Minor Road AADT 

(veh/day) 0 500 1,000 1500 

400 50 0.005 0.005 0.003 0.002

 100 0.007 0.006 0.005 0.003

 400 0.015 0.013 0.010 0.006

1,000 100 0.024 0.021 0.015 0.010

 500 0.055 0.048 0.035 0.022

 1,000 0.079 0.068 0.050 0.032

3,000 100 0.099 0.085 0.063 0.040

 500 0.226 0.195 0.144 0.092

 1,000 0.323 0.278 0.206 0.131

 3,000 0.567 0.488 0.362 0.231

5,000 100 0.191 0.164 0.121 0.077

 500 0.435 0.375 0.278 0.177

 1,000 0.622 0.535 0.396 0.253

 3,000 1.093 0.940 0.697 0.444

 5,000 1.420 1.222 0.906 0.577

10,000 100 0.463 0.399 0.296 0.188

 500 1.059 0.912 0.675 0.431

 1,000 1.512 1.301 0.964 0.615

 3,000 2.658 2.288 1.695 1.081

 5,000 3.455 2.974 2.203 1.405

 10,000 4.932 4.245 3.145 2.005

Note: Group B AADT base model was used. 

The AMF for SDR2 was derived from full models. 
238

Table 218. Sensitivity of Safety to Peak Truck Percentage (PKTRUCK) for Type III 

TOTAL Accidents Per Year 

Major Road AADT PKTRUCK 

(veh/day) 

Minor Road AADT 

(veh/day) 0 5 10 15 

400 50 0.005 0.004 0.003 0.003

 100 0.007 0.006 0.005 0.004

 400 0.015 0.012 0.009 0.007

1,000 100 0.024 0.019 0.015 0.012

 500 0.055 0.043 0.034 0.027

 1,000 0.079 0.062 0.049 0.038

3,000 100 0.099 0.078 0.061 0.048

 500 0.226 0.178 0.140 0.110

 1,000 0.323 0.254 0.200 0.157

 3,000 0.567 0.447 0.351 0.277

5,000 100 0.191 0.150 0.118 0.093

 500 0.435 0.343 0.270 0.212

 1,000 0.622 0.489 0.385 0.303

 3,000 1.093 0.860 0.677 0.533

 5,000 1.420 1.118 0.880 0.692

10,000 100 0.463 0.365 0.287 0.226

 500 1.059 0.834 0.656 0.516

 1,000 1.512 1.190 0.937 0.737

 3,000 2.658 2.092 1.646 1.296

 5,000 3.455 2.719 2.140 1.684

 10,000 4.932 3.882 3.055 2.404

Note: Group B AADT base model was used. 

The AMF for PKTRUCK was derived from full models. 
239

Table 219. Sensitivity of Safety to Peak Through Percentage on Minor Road 

(PKTHRU2) for Type IV TOTAL Accidents Per Year 

Major Road AADT PKTHRU2 

(veh/day) 

Minor Road AADT 

(veh/day) 0 10 20 30 

400 50 0.005 0.007 0.009 0.011

 100 0.007 0.010 0.012 0.016

 400 0.015 0.020 0.025 0.032

1,000 100 0.024 0.031 0.040 0.051

 500 0.055 0.071 0.091 0.117

 1,000 0.079 0.101 0.130 0.166

3,000 100 0.099 0.127 0.163 0.209

 500 0.226 0.290 0.372 0.477

 1,000 0.323 0.414 0.531 0.681

 3,000 0.567 0.728 0.934 1.198

5,000 100 0.191 0.244 0.313 0.402

 500 0.435 0.558 0.716 0.919

 1,000 0.622 0.797 1.023 1.312

 3,000 1.093 1.401 1.798 2.306

 5,000 1.420 1.822 2.337 2.998

10,000 100 0.463 0.595 0.763 0.978

 500 1.059 1. 359 1.743 2.236

 1,000 1.512 1.939 2.488 3.191

 3,000 2.658 3.409 4.373 5.610

 5,000 3.455 4.432 5.685 7.293

 10,000 4.932 6.327 8.116 10.410

Note: Group B AADT base model was used. 

The AMF for PKTHRU2 was derived from full models. 
240

Table 220. Sensitivity of Safety to Peak Left-Turn Percentage (PKLEFT) for Type IV 

TOTAL Accidents Per Year 

Major Road AADT PKLEFT 

(veh/day) 

Minor Road AADT 

(veh/day) 0 10 20 30 

400 50 0.005 0.007 0.008 0.010

 100 0.007 0.009 0.012 0.015

 400 0.015 0.019 0.024 0.030

1,000 100 0.024 0.030 0.038 0.048

 500 0.055 0.069 0.087 0.110

 1,000 0.079 0.099 0.125 0.157

3,000 100 0.099 0.124 0.156 0.197

 500 0.226 0.284 0.357 0.449

 1,000 0.323 0.406 0.510 0.642

 3,000 0.567 0.713 0.897 1.128

5,000 100 0.191 0.240 0.301 0.379

 500 0.435 0.547 0.688 0.865

 1,000 0.622 0.781 0.983 1.235

 3,000 1.093 1.374 1.727 2.172

 5,000 1.420 1.786 2.245 2.823

10,000 100 0.463 0.583 0.733 0.921

 500 1.059 1.332 1.674 2.105

 1,000 1.512 1.901 2.390 3.005

 3,000 2.658 3.342 4.202 5.283

 5,000 3.455 4.344 5.462 6.868

 10,000 4.932 6.202 7.797 9.804

Note: Group B AADT base model was used. 

The AMF for PKLEFT was derived from full models. 
241

Type IV INJURY Accidents 

The AMFs derived for INJURY accidents for Type IV intersections are intersection SKEW 

angle, major right-turn lane, peak truck percentage, and peak left-turn percentage. The 

sensitivity test results for these AMFs are presented in tables 221 through 224. 

Table 221. Sensitivity of Safety to Skew Angles for Type IV INJURY 

Accidents Per Year 

Major Road SKEW Angle (degrees) 

AADT 

(veh/day) 

Minor Road 

AADT 

(veh/day) 0 10 15 30 45 

400 50 0.003 0.004 0.004 0.004 0.005

 100 0.004 0.005 0.006 0.006 0.006

 400 0.007 0.010 0.010 0.012 0.012

1,000 100 0.012 0.016 0.017 0.019 0.020

 500 0.024 0.034 0.036 0.040 0.042

 1,000 0.033 0.046 0.050 0.055 0.058

3,000 100 0.046 0.064 0.069 0.077 0.081

 500 0.095 0.134 0.143 0.159 0.167

 1,000 0.131 0.183 0.196 0.218 0.229

 3,000 0.215 0.301 0.323 0.359 0.376

5,000 100 0.087 0.122 0.131 0.145 0.153

 500 0.181 0.253 0.271 0.301 0.317

 1,000 0.248 0.347 0.372 0.413 0.433

 3,000 0.408 0.571 0.611 0.679 0.713

 5,000 0.514 0.719 0.771 0.857 0.899

10,000 100 0.208 0.291 0.311 0.346 0.363

 500 0.431 0.603 0.646 0.718 0.754

 1,000 0.590 0.826 0.884 0.983 1.032

 3,000 0.970 1.359 1.456 1.617 1.698

 5,000 1.223 1.713 1.835 2.039 2.141

 10,000 1.675 2.345 2.513 2.792 2.932

Note: Group B AADT base model was used. 

The AMF for Intersection SKEW angle was derived from regression base models. 
242

Table 222. Sensitivity of Safety to Major Right-Turn Lane for Type IV INJURY 

Accidents Per Year 

Right-Turn Lane on Major Road 

Major Road 

AADT (veh/day) 

Minor Road 

AADT (veh/day) No Right Turn 

Right-Turn Lane on 

One Approach 

Right-Turn Lane on Two 

Approaches 

400 50 0.003 0.002 0.002

 100 0.004 0.003 0.003

 400 0.007 0.006 0.005

1,000 100 0.012 0.010 0.009

 500 0.024 0.021 0.018

 1,000 0.033 0.028 0.024

3,000 100 0.046 0.040 0.034

 500 0.095 0.082 0.071

 1,000 0.131 0.112 0.097

 3,000 0.215 0.185 0.159

5,000 100 0.087 0.075 0.065

 500 0.181 0.156 0.134

 1,000 0.248 0.213 0.183

 3,000 0.408 0.351 0.302

 5,000 0.514 0.442 0.380

10,000 100 0.208 0.178 0.154

 500 0.431 0.370 0.319

 1,000 0.590 0.507 0.436

 3,000 0.970 0.835 0.718

 5,000 1.223 1.052 0.905

 10,000 1.675 1.441 1.240

Note: Group B AADT base model was used. 

The AMF for Major Right-Turn Lane was derived from full models. 
243

Table 223. Sensitivity of Safety to Peak Truck Percentage (PKTRUCK) for Type IV 

INJURY Accidents Per Year 

Major Road AADT PKTRUCK 

(veh/day) 

Minor Road AADT 

(veh/day) 0 5 10 15 

400 50 0.003 0.002 0.002 0.001

 100 0.004 0.003 0.002 0.002

 400 0.007 0.005 0.004 0.003

1,000 100 0.012 0.009 0.007 0.005

 500 0.024 0.019 0.014 0.011

 1,000 0.033 0.025 0.020 0.015

3,000 100 0.046 0.035 0.027 0.021

 500 0.095 0.074 0.057 0.044

 1,000 0.131 0.101 0.078 0.060

 3,000 0.215 0.166 0.128 0.099

5,000 100 0.087 0.067 0.052 0.040

 500 0.181 0.139 0.108 0.083

 1,000 0.248 0.191 0.147 0.114

 3,000 0.408 0.314 0.242 0.187

 5,000 0.514 0.396 0.306 0.236

10,000 100 0.208 0.160 0.123 0.095

 500 0.431 0.332 0.256 0.197

 1,000 0.590 0.455 0.351 0.270

 3,000 0.970 0.748 0.577 0.445

 5,000 1.223 0.943 0.727 0.561

 10,000 1.675 1.292 0.996 0.768

Note: Group B AADT base model was used. 

The AMF for PKTRUCK was derived from full models. 
244

Table 224. Sensitivity of Safety to Peak Left-Turn Percentage (PKLEFT) for Type IV 

INJURY Accidents Per Year 

Major Road AADT PKLEFT 

(veh/day) 

Minor Road AADT 

(veh/day) 0 10 20 30 

400 50 0.003 0.005 0.008 0.013

 100 0.004 0.006 0.011 0.018

 400 0.007 0.012 0.020 0.033

1,000 100 0.012 0.020 0.033 0.056

 500 0.024 0.041 0.069 0.116

 1,000 0.033 0.056 0.094 0.159

3,000 100 0.046 0.078 0.131 0.221

 500 0.095 0.161 0.272 0.458

 1,000 0.131 0.221 0.372 0.628

 3,000 0.215 0.363 0.612 1.033

5,000 100 0.087 0.147 0.248 0.419

 500 0.181 0.305 0.515 0.869

 1,000 0.248 0.418 0.705 1.189

 3,000 0.408 0.688 1.160 1.957

 5,000 0.514 0.867 1.463 2.468

10,000 100 0.208 0.350 0.591 0.997

 500 0.431 0.726 1.226 2.068

 1,000 0.590 0.995 1.678 2.831

 3,000 0.970 1.637 2.762 4.660

 5,000 1.223 2.064 3.482 5.875

 10,000 1.675 2.826 4.768 8.044

Note: Group B AADT base model was used. 

The AMF for PKLEFT was derived from full model 
245

3.6.5 Type V Intersections 

The predicted TOTAL and INJURY accident frequencies per year for each AMF derived 

from the full models and regression base models are presented in tables 225 through 229. 

Type V TOTAL Accidents 

The AMFs derived for TOTAL accidents for Type IV intersections are commercial 

driveways on major road, horizontal curve combinations on major and minor roads, and light. 

The sensitivity test results for these AMFs are presented in tables 225 through 227. 

Table 225. Sensitivity of Safety to Commercial Driveways on Major Road for Type V 

TOTAL Accidents Per Year 

Major Road AADT Commercial Driveways on Major Road (density) 

(veh/day) 

Minor Road AADT 

(veh/day) 0 5 10 15 

400 50 0.72 0.94 1.24 1.62

 100 0.82 1.07 1.40 1.84

 400 1.05 1.38 1.80 2.36

1,000 100 1.29 1.69 2.22 2.90

 500 1.73 2.27 2.97 3.89

 1,000 1.96 2.57 3.37 4.41

3,000 100 2.24 2.94 3.84 5.03

 500 3.00 3.93 5.15 6.74

 1,000 3.40 4.46 5.84 7.64

 3,000 4.16 5.44 7.13 9.33

5,000 100 2.90 3.79 4.96 6.50

 500 3.88 5.08 6.65 8.70

 1,000 4.40 5.76 7.54 9.87

 3,000 5.37 7.03 9.20 12.05

 5,000 5.89 7.71 10.09 13.22

10,000 100 4.10 5.36 7.02 9.19

 500 5.49 7.18 9.40 12.31

 1,000 6.22 8.14 10.66 13.96

 3,000 7.59 9.94 13.02 17.04

 5,000 8.33 10.91 14.28 18.70

 10,000 9.45 12.37 16.20 21.21

Note: Group A AADT base model was used. 

The AMF for Commercial driveways on major road was derived from full models. 
246

Table 226. Sensitivity of Safety to Horizontal Curve Combinations on Major and 

 Minor Roads (HEICOM) for Type III TOTAL Accidents Per Year 

Major Road AADT HEICOM 

(veh/day) 

Minor Road AADT 

(veh/day) 0 3 5 10 

400 50 0.72 0.66 0.62 0.54

 100 0.82 0.75 0.71 0.61

 400 1.05 0.96 0.91 0.79

1,000 100 1.29 1.19 1.12 0.97

 500 1.73 1.59 1.50 1.30

 1,000 1.96 1.80 1.70 1.47

3,000 100 2.24 2.06 1.94 1.68

 500 3.00 2.75 2.60 2.25

 1,000 3.40 3.12 2.95 2.55

 3,000 4.16 3.81 3.60 3.12

5,000 100 2.90 2.66 2.51 2.17

 500 3.88 3.56 3.36 2.91

 1,000 4.40 4.03 3.81 3.30

 3,000 5.37 4.92 4.65 4.02

 5,000 5.89 5.40 5.10 4.42

10,000 100 4.10 3.76 3.55 3.07

 500 5.49 5.03 4.75 4.11

 1,000 6.22 5.71 5.39 4.66

 3,000 7.59 6.96 6.57 5.69

 5,000 8.33 7.64 7.21 6.25

 10,000 9.45 8.67 8.18 7.08

Note: Group A AADT base model was used. 

The AMF for HEICOM was derived from full models. 
247

Table 227. Sensitivity of Safety to Light for Type IV TOTAL Accidents Per Year 

Major Road AADT Presence of Light 

(veh/day) 

Minor Road AADT 

(veh/day) No Yes 

400 50 0.72 0.54

 100 0.82 0.61

 400 1.05 0.79

1,000 100 1.29 0.97

 500 1.73 1.30

 1,000 1.96 1.47

3,000 100 2.24 1.68

 500 3.00 2.25

 1,000 3.40 2.55

 3,000 4.16 3.12

5,000 100 2.90 2.17

 500 3.88 2.91

 1,000 4.40 3.30

 3,000 5.37 4.03

 5,000 5.89 4.42

10,000 100 4.10 3.07

 500 5.49 4.11

 1,000 6.22 4.67

 3,000 7.59 5.69

 5,000 8.33 6.25

 10,000 9.45 7.09

Note: Group A AADT base model was used. 

The AMF for LIGHT was derived from full models. 
248

Type V INJURY Accidents 

The AMFs derived for INJURY accidents for Type V intersections are horizontal curves on 

minor roads and light on intersections. The sensitivity test results for these AMFs are 

presented in tables 228 to 229. 

Table 228. Sensitivity of Safety to Horizontal Curves on Minor Road (HEI2) for Type 

IV TOTAL Accidents Per Year 

Major Road AADT HEI2 

(veh/day) 

Minor Road AADT 

(veh/day) 0 3 5 10 

400 50 0.35 0.32 0.30 0.26

 100 0.41 0.38 0.36 0.31

 400 0.58 0.53 0.50 0.43

1,000 100 0.52 0.47 0.45 0.39

 500 0.76 0.70 0.66 0.57

 1,000 0.90 0.82 0.78 0.67

3,000 100 0.67 0.62 0.58 0.51

 500 0.99 0.91 0.86 0.74

 1,000 1.17 1.07 1.01 0.88

 3,000 1.52 1.39 1.32 1.14

5,000 100 0.76 0.70 0.66 0.57

 500 1.12 1.02 0.97 0.84

 1,000 1.32 1.21 1.14 0.99

 3,000 1.71 1.57 1.49 1.29

 5,000 1.94 1.78 1.68 1.46

10,000 100 0.90 0.82 0.78 0.67

 500 1.32 1.21 1.14 0.99

 1,000 1.56 1.43 1.35 1.17

 3,000 2.02 1.86 1.76 1.52

 5,000 2.29 2.10 1.98 1.72

 10,000 2.70 2.48 2.34 2.03

Note: Group A AADT base model was used. 

The AMF for HEI2 was derived from full models. 
249

Table 229. Sensitivity of Safety to Light for Type IV TOTAL Accidents Per Year 

Major Road AADT Presence of Light 

(veh/day) 

Minor Road AADT 

(veh/day) No Yes 

400 50 0.35 0.24

 100 0.41 0.28

 400 0.58 0.39

1,000 100 0.52 0.35

 500 0.76 0.51

 1,000 0.90 0.60

3,000 100 0.67 0.45

 500 0.99 0.66

 1,000 1.17 0.78

 3,000 1.52 1.02

5,000 100 0.76 0.51

 500 1.12 0.75

 1,000 1.32 0.88

 3,000 1.71 1.15

 5,000 1.94 1.30

10,000 100 0.90 0.60

 500 1.32 0.88

 1,000 1.56 1.04

 3,000 2.02 1.36

 5,000 2.29 1.53

 10,000 2.70 1.81

Note: Group A AADT base model was used. 

The AMF for LIGHT was derived from full models. 

3.7 SUMMARY, DISCUSSION, AND CONCLUSIONS 

In summarizing and discussing the model recalibration exercise, it is important not to lose 

sight of the fundamental purpose of the statistical models that are the focus of this research. 

Because the models are required for use in the IHSDM accident prediction algorithm, the 

recalibration efforts were focused on this application. In this sense, the research reflected 

here represents a different perspective from the original calibration by Vogt since, at that 

time, the algorithm was not developed and the calibration philosophy was somewhat 

different. Models with a comprehensive set of regression parameters were to be used directly 

for predicting the expected number of accidents at intersections and for deriving AMFs for 

the five types of intersection crash models examined in this research. To remind the reader, 

the five intersection types examined are: 

• Type I: Three-legged stop controlled intersections of two-lane roads. 

• Type II: Four-legged stop controlled intersections of two-lane roads. 

• Type III: Three-legged stop controlled intersections with two lanes on the minor and 

four lanes on major roads. 

• Type IV: Four-legged stop controlled intersections with two lanes on the minor and 

four lanes on major roads. 

• Type V: Signalized intersections of two-lane roads. 
250

The accident prediction algorithm enables the number of total intersection-related accidents 

per year to be estimated by multiplying the predicted number of such accidents for base 

conditions by AMFs for various features specific to an intersection. The Harwood et al. “Red 

Book” presented base models and AMFs for three- and four-legged intersections of two-lane 

rural roads with STOP control, and four-legged signalized intersections of two-lane roads. 

These base models were the best of available accident prediction models developed in the 

earlier Vogt FHWA projects and included only variables that were statistically significant at 

the 15 percent level. Those projects also developed full models with additional variables with 

the intention of using the variable coefficients to estimate AMFs for use in IHSDM. The full 

models, along with several variants, are presented in two FHWA reports. Vogt and Bared 

present models for three- and four-legged intersections of two-lane roads, while Vogt 

documents models for three other types of rural intersections: three- and four-legged stop 

controlled with four lanes on the major and two on the minor, and signalized intersections of 

two-lane roads.(1,2) 

Understanding what was required for the recalibration effort is an improvement of the base 

models and AMFs to be used in the IHSDM accident prediction algorithm—including 

possible enhancements to model functional forms, addition or exclusion of variables, and 

updated parameter estimates. This requirement guided the approach. At the same time, full 

models were developed in keeping with the original intent of the project and with the 

expectation that it may be possible to derive AMFs similar to what were accomplished in the 

earlier FHWA work. 

The discussion provided here focuses primarily on summarizing and briefly discussing the 

results of the recalibration detailed in the body of this report, and translating these results into 

meaningful observations and conclusions. The reader interested in additional details, such as 

sources of published results for the earlier models and comparison tables, should refer to the 

earlier sections of this report. Descriptions of all variable abbreviations and definitions used 

in this report can be found at the beginning of this document. 

3.7.1 Model Recalibration 

For the five intersection types previously described, statistical models were developed for 

total accidents (TOTACC) and injury (fatal + nonfatal injury) accidents (INJACC) within 

76.25 m (250 ft) of the intersection center. For each intersection type, two fundamental 

classes of statistical models were developed—models using AADT as the sole predictor of 

crashes (referred as base or AADT models) and models containing a fairly comprehensive set 

of predictor variables (referred as full models). There are two levels for each class. Not all 

levels were calibrated for all model Types (I to V). These details of the models calibrated and 

data used are summarized in table 230. 
251

Table 230. Summary of Models Recalibrated and Data Used 

Model Site Types and Data Used 

Description Types I and II Type III Type IV Type V 

Group A Sites:

Full Model with 

variables in project 

data 

Minnesota 

Georgia 

California project 

Michigan 

Georgia 

California project 

Michigan 

Georgia 

California project 

Michigan 

Georgia 

Group B Sites: 

AADT Model for 

all sites, including 

California HSIS* 

California HSIS 

Minnesota 

Georgia 

California HSIS 

Michigan 

Georgia

California HSIS 

Michigan 

Georgia 

California HSIS 

Michigan 

Georgia 

Group B Sites: 

Full Model with 

variables from 

California HSIS 

California HSIS 

Minnesota 

Georgia Not calibrated Not calibrated Not calibrated

Subset of Group B 

Sites: 

AADT Model for 

sties meeting base 

conditions for 

project data plus 

California HSIS* 

California HSIS 

Minnesota 

Georgia 

California HSIS 

Michigan 

Georgia

California HSIS 

Michigan 

Georgia Not calibrated 

Subset of Group A 

Sites: 

AADT Model for 

sites meeting base 

conditions for 

project data Not calibrated 

California project 

Michigan 

Georgia 

California project 

Michigan 

Georgia 

California project 

Michigan 

Georgia * The California project data for Types II, IV, and V were not used. 

AADT Models Overview 

The AADT statistical models include AADT as the sole predictor variable and are proposed 

for consideration as base models to be used in IHSDM. The reasoning behind this apparently 

simplistic approach is that models with AADT as the only predictor are more likely to be 

transferable across jurisdictions than models that include other variables. This is an appealing 

feature, considering that the models are calibrated on data from three States within the United 

States; however, the likely application is to apply them for forecasting crashes across the 

entire country. This research strongly supported their use. 

Two types of AADT models are presented for Type I and II sites, and three types for Type III, 

IV, and V sites. First, models were calibrated using all available data from the HSIS 

California database, original sites from Minnesota and Michigan, and Georgia validation data. 

Second, models were developed for a subset of these sites that met specified conditions for 

possible use as base models in the IHSDM accident prediction algorithm. For Types III, IV, 

and V sites, additional AADT models were calibrated from a dataset that met the base 

conditions of the significant variables in the full models. These AADT-only models were 

calibrated on data from the original sites (intersections) from California, Michigan, and the 

sites used for the Georgia validation data. 
252

Full Models Overview 

Statistical models with relatively comprehensive sets of predictor variables were also 

developed. Unlike their AADT counterparts, these models include many variables, with the 

intent to explain as much of variation in crash occurrence as possible, given the available set 

of potential explanatory variables. 

For Types I and II, full models were developed using two groups of data. The first, Group A, 

was comprised of the sites from Minnesota and Georgia and consisted of many variables, 

including horizontal and vertical curvature. The California sites were not in this group 

because many of the variables were not available. Group B consisted of the Minnesota, 

Georgia, and California HSIS sites, but fewer variables were available for modeling. 

For Types III, IV, and V, the data used to calibrate full models consisted of the California 

and Michigan sites from the original study, including the additional years of accident data, 

and the Georgia sites. There was no equivalent to Group B of the Types I and II models 

because there were very few HSIS sites, and these had almost no variables of interest. 

Type I Model Results 

Type I AADT Models (see table 134 and table 135)

The recalibrated models for total accidents represent improvements to the one reported in 

Harwood et al. (such a model was not presented in the Vogt reports).(3) The β coefficient of 

the log of major road AADT is about two times that for minor road AADT, which seems to 

be a reasonable expectation on the basis of other models reported in the literature. The CURE 

plots confirmed the superiority of the chosen model form, which testifies to the 

reasonableness of the calibrated models. For the TOTACC model, the base condition model 

(calibrated from data that met specified base conditions) was estimated with a lower overall 

overdispersion parameter than the model using all sites. This was expected, because the base 

condition sites should be more homogeneous in their design characteristics. For the INJACC 

model the overdispersion was similar for the two AADT models. 

Type I Full Models (see table 160, table 161, and table 162) 

Full models were developed using two groups of data. The first, Group A, was comprised of 

the sites from Minnesota and Georgia and consisted of many variables, including horizontal 

and vertical curvature. The second, Group B, added California HSIS sites, which resulted in 

fewer variables being available for modeling. Two model variants are reported. One includes 

a State indicator term and the other does not. 

For the Group A models, when a State indicator variable was used in the models, the only 

geometric variable that proved to be significant was HI1. Without the State indicator, more 

geometric variables were statistically significant. This effect suggests that geometric 

variables are correlated with State of origin, with certain States possessing intersections that 

systematically share geometric traits. There were some similarities and differences between 

the recalibrated models and the Vogt and Bared models. For total accidents, posted speed 

limit on major roads and the angle variable HAU were not included in the recalibrated model, 

while right-turn lanes on minor roads and left-turn lanes on major roads were included. For 
253

injury accidents, right-turns on major roads, posted speed on major, number of driveways on 

major roads, and the angle variable HAU were not included while left-turn lanes on major 

roads was included. The GOF as measured by the overdispersion parameter was improved 

over the Vogt and Bared models, just one of numerous GOF measures. 

For both of the Group B models, with and without the State indicator variable, right-turn 

lanes on minor roads and left-turn lanes on major roads are significant in addition to rightturn lanes on major roads. 

Type II Model Results 

Type II AADT Models (see table 135 and table 139) 

Unlike the case for Type I models, the recalibrated Type II models for total accidents have 

more overdispersion than models reported in Harwood et al. (such a model was not presented 

in the Vogt reports).(3) In particular, the models do a poorer job for the Georgia and 

California sites. Nevertheless, the β coefficient of the log of major road AADT is about 20–

30 percent higher than that for minor road AADT, which appears to be reasonable. For both 

the TOTACC and INJACC models, the base condition models were estimated with a lower 

overdispersion than the model using all sites, again not surprising, because the base condition 

sites should be more homogeneous in their design characteristics. 

Type II Full Models (see table 163, table 164, table 165, and table 166) 

As was the case for Type I, full models were developed using two groups of data. The first, 

Group A, was comprised of sites from Minnesota and Georgia and included variables such as 

horizontal and vertical curvature. The second, Group B, added California HSIS sites, which 

resulted in fewer variables being available for modeling. Two model variants were reported. 

As for Type I, one included a State indicator term and the other did not. 

For the Group A models, there were some similarities and differences between the 

recalibrated models and the Vogt and Bared models. For the recalibrated models, significant 

geometric variables at approximately the 10 percent level of significance or better for 

TOTACC included right-turn lane on major roads and the number of driveways for the model 

l variant, including a State indicator variable, and number of driveways and the vertical 

curvature variable VCI1 for the variant without the State indicator variable. The Vogt and 

Bared model also included the angle variable HAU, the major road posted speed, and the 

horizontal curvature variable HI1, although these last two were of low significance. For the 

INJACC models, number of driveways and horizontal curvature within 76.25 m (250 ft) of 

the intersection center were significant at the 10 percent level or better for both the State 

indicator and non-State indicator variants. The Vogt model included roadside hazard rating 

as a significant variable and others that were not significant. The GOF as measured by the 

overdispersion parameter was not as good as that for the Vogt and Bared model. 

In the case of the Group B models, for TOTACC, significant variables (in addition to major 

and minor road AADTs) include right-turn lanes on major roads for the variant with the State 

indicator variable, and right- and left-turn lanes on major roads for the variant without the 

State indicator variable. For INJACC, medians and right-turn lanes on major roads were 

significant for both the State indicator and non-State indicator variants. Again, the GOF for 
254

all of the Group B models, as measured by the overdispersion parameter, was not as good as 

that for the Vogt and Bared model. 

Type III Model Results 

Type III AADT Models (see table 142, table 143, and table 145)

Unlike models for Type I and II intersections, a State indicator variable was insignificant for 

all models. The recalibrated models for TOTACC and INJACC generally have better GOF 

measures than comparable models from the earlier FHWA research. As expected, the GOF 

statistics were better for the models using base condition sites than for models using all sites. 

For the Group A models, for TOTACC, the β coefficient of the log of major road AADT is 

about three to four times that for minor road AADT, which, once again, is reasonable. For 

INJACC, the AADT variable effect was captured as the product of the major and minor 

AADTs as opposed to the TOTACC model, which specified these variables as separate terms. 

In the case of the Group B models, for both TOTACC and INJACC, the β coefficient of the 

log of major road AADT is significantly larger than that for minor road AADT, which is in 

accord with reasonable expectations. 

Type III Full Models (see table 167 and table 168) 

Two models each are reported for TOTACC and INJACC. The main model was selected 

based on the highest Pearson product-moment correlation coefficient, lowest overdispersion, 

MPB per year, and MAD per year. The other model was the one judged to be next best in 

terms of these measures. 

For TOTACC, major and minor AADTs, crest curve rates on major roads, intersection angle, 

commercial driveways on major roads, median width on major roads, and painted medians 

on major roads were found to be significant in the main model. Of these, only median widths 

on major roads and the AAADT variables were included in the Vogt model, but that model 

did have a driveway variable DRWY1 instead of COMDRWY1. State indicator variables 

were statistically insignificant in the recalibration. 

 

For INJACC, major and minor AADTs, roadside hazard ratings on major roads, intersection 

angles, commercial driveways on major roads, peak turning percentages, and peak truck 

percentages were found to be significant in the main model. None of these were included in 

the Vogt model, which had an angle variable HAU as the only geometric variable. Like 

TOTACC, State indicator variables were again statistically insignificant in the recalibration. 

The recalibrated models for both TOTACC and INJACC produce better GOF measures than 

the Vogt’s models, except for the overdispersion parameter. 
255

Type IV Model Results 

Type IV AADT Models (see table 148, table 149, and table 151) 

Unlike models for Type I and II intersections, a State indicator variable was not statistically 

significant for all models. The recalibrated models for TOTACC and INJACC resulted in 

generally improved GOF measures than comparable models from the previous FHWA 

research. 

For the Group A models, the small sample size was insufficient to provide good coefficients 

and p-values for a model with specified base conditions. For the TOTACC model using all 

sites, the β coefficient of the log of major road AADT is about one and one half times that for 

minor road AADT, conforming to expectations. The AADT variable effect for the INJACC 

model was captured as the product of the major and minor AADTs, as opposed to the 

TOTACC model, which specified these variables as separate terms. 

In the case of the Group B models, as seems reasonable, the β coefficient of the log of major 

road AADT is significantly larger than that for minor road AADT for both TOTACC and 

INJACC. As expected, the GOF statistics were improved for the models using base condition 

sites compared to models using all sites. 

Type IV Full Models (see table 170)

Two models were presented for both TOTACC and INJACC. Again, the main model was 

selected based on the highest Pearson product-moment correlation coefficient, lowest 

overdispersion, MPB per year, and MAD per year. 

For TOTACC, major and minor road AADTs, peak left-turn percentages, peak through 

percentages on minor roads, peak truck percentages, and right-side sight distances on minor 

roads were found to be significant in the main model. By contrast, the Vogt main model 

included only a peak left-turn percentage on major road variable PKLEFT1 and a left-turn 

lane on major road variable LTN1S in addition to the AADT variables. The main model 

showed the lowest overdispersion among candidate models and indicated the best GOF 

results. The State indicator variable was statistically insignificant in the main model, but for 

the variant model, a Michigan indicator variable was found to be significant, indicating more 

influence of the Michigan data on the model. 

For INJACC, major and minor road AADTs, peak left-turn percentages on major roads, peak 

truck percentages, and speed limits on minor roads were significant in the main model. The 

Vogt model contained a speed limit on minor road variable SPD2 and a peak left-turn 

percentage on major road variable PKLEFT1 in addition to the AADT variables. The variant 

model yields an improvement in overdispersion and Pearson product-moment correlation 

coefficient, but not in MPB per year and MAD per year. State indicator variables were 

statistically insignificant. 

The recalibrated models for TOTACC and INJACC generally provide better GOF measures 

than Vogt’s models. The overdispersion values of the recalibrated models were lower than 

Vogt’s for TOTACC but slightly higher for INJACC. 
256

Type V Model Results 

Type V AADT Models (see table 154, table 155, and table 156)

Statistical models could not be calibrated for specified base conditions due to lack of data. 

Unlike the case for the other model types, the Vogt report does not provide AADT-only 

models for Type V. Therefore, a comparison between the Vogt models and the newly 

calibrated AADT models for TOTACC and INJACC could not be done. 

For the Group A models, for TOTACC, the β coefficient of the log of major road AADT is 

about two to three times greater than that for minor road AADT, which is reasonable. As was 

the case for the Type III and IV models, for the INJACC model, the AADT variable effect 

was captured as the product of the major and minor AADTs as opposed to the TOTACC 

model, which specified these variables as separate terms. 

In the case of the Group B models, the main Type V TOTACC and INJACC models 

calibrated using all sites have a β coefficient of the log of major road AADT, in accord with 

expectations, about two to three times that for minor road AADT. 

Type V Full Models (see table 171 and table 172)

Two models were developed for both TOTACC and INJACC. Again, the main model was 

selected based on the highest Pearson product-moment correlation coefficient, lowest 

overdispersion, MPB per year, and MAD per year. 

For TOTACC, major and minor AADTs, commercial driveways on major roads, speed limits 

on major roads, presence of lighting, and horizontal curvature variables were found to be 

significant in the main model. By contrast, the Vogt main model included a completely 

different set of non-AADT variables: peak truck percentage PKTRUCK, peak left-turn 

percentage on minor road PKLEFT2, protected left lane PROT_LT, and vertical curvature 

VEICOM. The variant model provides an improvement over the main model in 

overdispersion and Pearson product-moment correlation, but not in MPB per year and MAD 

per year. 

For INJACC, major and minor AADTs, peak left-turn percentages on minor roads, peak 

truck percentages, presence of lighting, and speed limits on major roads were significant 

variables in the main model. Again, the Vogt main model had a completely different set of 

non-AADT variables: peak left-turn percentage on minor road PKLEFT2, peak truck 

percentage PKTRUCK, protected left lane PROT_LT, and vertical curvature VEICOM. In 

addition, the AADT variable effect was captured as the product of the major minor AADTs, 

as opposed to specifying these variables as separate terms in the recalibrated model. 

Although the recalibrated model variant was superior to the main model in terms of lower 

overdispersion and better fit to the data, it does include a Michigan indicator variable, which 

means more influence of the Michigan data on the model. Because the IHSDM requires the 

main model to be recalibrated to work in any State, the model with the State indicator was 

selected as a variant and not as the main model, similar to what was done for Types I and II. 

The recalibrated models for both TOTACC and INJACC provide a better GOF measures 

than Vogt’s models, except for the overdispersion parameter. 
257

3.7.2 Summary of AMFs 

Several strategies for assessing and recalibrating the AMFs corresponding with the five 

intersection models were explored, including: 

1. An attempt, similar to the technique used by Vogt, to infer AMFs from full models. 

2. Implementation of a relatively untested regression analysis procedure. The dependent 

variable was the difference between a site’s observed accident count and its AADTbased model prediction. Independent variables were factors at the site that differed 

from conditions assumed in base or AADT model. 

Tables 231, 232, 233, and 234 compare the AMFs from the “Red Book,” those from 

Harwood et al.’s 2002 report, and those derived during the course of this research. None of 

the variables used showed any significant impacts on safety for Type V sites. In general, the 

AMF estimates developed were of the same direction of effect and reasonably close in 

magnitude to those provided by Harwood et al. in 2000 and 2002. 

Whereas the “Red Book” provides separate AMFs for major road right-and left-turn lanes at 

Type II intersections, sites in this dataset had turning lanes on both approaches, and separate 

effects could not be detected for one versus two approaches. It is believed that a SKEW AMF 

significantly different than 1 was not supported by the data. There were only few sites with 

deficient sight distance, so an AMF could not be estimated for the effect of this variable. 

For Type III and IV intersections, SKEW was estimated as statistically significant in the 

regression models. Right-turn lanes on major roads provided statistically significant AMFs 

for Type IV intersections. For Type V intersections, no variables showed any statistically 

significant impacts on safety in the regression model. 
Table 231. Comparison of Type III–V AMFs for TOTACC 

AMF “Red Book” AMFs Derived From Full Models AMFs Derived From 

Type III-IV Type V Type III Type IV Type V Type III T

SKEW 1 exp(0.0101SKEW)

1+(0.016*SKEW)/ (0.98+0.016*SKEW)

1+(0.053(1.43+0.

RT MAJ 

1.00 if none exist 0.975 on one approach(0.96 on one approach)0.95 on both approaches (0.92 on both approaches) 1 1 

LT MAJ 

1.00 if none exist 0.82 on one approach 0.67 on both approaches 0.71 1 

SIGHT DISTANCE 1 

Not calibrated

Not calibrated

Not calibrated

1 1 

COMDRWY1 exp 

(0.0681COMDRWY1) 

exp (0.0539 COMDRWY1) 

VEI1 exp(0.1081VEI1) MEDWIDTH1 

exp (-0.0106MEDWDTH1) 

MEDTYPE1 0.73 

Not calibrated

PKTRUCK 

exp (-0.0479PKTRUCK)

PKTHRU2 

exp (0.0249PKTHRU2) 

PKLEFT 

exp (0.0229PKLEFT) 

SDR2 exp(-0.0003SDR2) 

Not calibrated

LIGHT 0.75 HEICOM 

None provided 

Not calibrated

Not calibrated

Not calibrated

exp (-0.0288HEICOM) 

Not calibrated

258 
259

Table 232. Comparison of Type I–II AMFs for TOTACC 

“Red Book” Full Models Regression Models 

AMF 

Type I Type II Type I Type II Type I Type II 

SKEW exp(0.004SKEW) exp(0.0054SKEW) 

Not 

calibrated

Not 

calibrated 1 1 

RT MAJ 

1.00 if none exist 

0.95 on one approach 

(0.86 on one approach) 

0.90 on both approaches 

(0.74 on both approaches) 

 0.88 1.19,0.861 1 0.71 

LT MAJ 

1.00 if none exist 

0.78 if at least one 

exists 

(0.56 if at least one 

exists) 

1.00 if none exist 

0.76 on one approach 

(0.72 on one 

approach) 

0.58 on both 

approaches 

(0.52 on both 

approaches) 0.82 

Not 

calibrated 

1 0.71 

1.05 if limited in 1 quadrants 

1.10 if limited in 2 quadrants 

1.15 if limited in 3 quadrants 

SIGHT 

DISTANCE 1.20 if limited in 4 quadrants 

Not 

calibrated

Not 

calibrated

Not 

calibrated

Not 

calibrated

RT MIN Not calibrated Not calibrated 1.35 

Not 

calibrated 1.48 1 

HI1 Not calibrated Not calibrated exp(0.0263)

Not 

calibrated

Not 

calibrated

Not 

calibrated

DRWY1 Not calibrated Not calibrated

Not 

calibrated 1.13 

Not 

calibrated

Not 

calibrated

MEDIAN Not calibrated Not calibrated

Not 

calibrated

Not 

calibrated 1 0.77 1 Group A = 1.19, Group B = 0.86 
Table 233. Comparison of Type III–V AMFs for TOTACC 

“Red Book” AMFs Derived From Full Models AMFs Derived Fro

AMF Type III-IV Type V Type III Type IV Type V Type III SKEW 1 exp(0.0101SKEW) 

1+(0.016*SKEW)/

(0.98+0.016*SKEW)

1+

(1.43

RT MAJ 

1.00 if none exist 0.975 on one approach (0.96 on one approach) 0.95 on both approaches (0.92 on both approaches) 1 

LT MAJ 

1.00 if none exist 0.82 on one approach 0.67 on both approaches 0.71 

SIGHT DISTANCE 1 

Not calibrated

Not calibrated

Not calibrated

1 

COMDRWY1 exp 

(0.0681COMDRWY1)

exp (0.0539 COMDRWY1) 

VEI1 exp(0.1081VEI1) MEDWIDTH1 

exp (-0.0106MEDWDTH1) 

MEDTYPE1 0.73 

Not calibrated

PKTRUCK 

exp (-0.0479PKTRUCK) 

PKTHRU2 

exp (0.0249PKTHRU2) 

PKLEFT 

exp (0.0229PKLEFT) 

SDR2 exp(-0.0003SDR2) 

Not calibrated

LIGHT 0.75 HEICOM 

None provided 

Not calibrated

Not calibrated

Not calibrated

exp (-0.0288HEICOM) 

Not calibrated

260 
261 

Table 234. Comparison of AMFs for INJACC 

“Red 

Book” AMFs Derived From Full Models AMFs Derived From Regr

AMF Type I-V Type I Type II Type III Type IV Type V Type I Type II Type III 

SKEW 

Not 

calibrated 

Not 

calibrated exp(0.0163SKEW) 1 1 

1+(0.017SKEW)/ (0.52+0.017SKEW)

1+(0(0.72

RT MAJ 0.87 0.85 1 1 1 

0.86 0.74 

LT MAJ 0.8 1 0.42 1 1 RT MIN 1.36 1.56 1 1 1 SIGHT DISTANCE 

Not 

calibrated

Not 

calibrated

1 1 

HI1 

exp (0.0286) 

exp (0.0408) 

DRWY1 

1.09 

Not 

calibrated

Not 

calibrated

MEDIAN 0.72 

Not calibrated

1 0.52 

COMDRWY1 

exp (0.0627COMDRWY1)

HAZRAT1 

exp (0.1889HAZRAT1) 

Not calibrated

PKTRUCK 

exp (-0.0253PKTRUCK) 

exp (-0.0520PKTRUCK) 

PKTURN exp(0.0254PKTURN) Not calibratedPKLEFT1 

exp (0.0523PKLEFT1) 

SDR2 

Not calibrated

LIGHT 0.67 HEI2 

None provided 

Not 

calibrated

Not 

calibrated

Not calibrated Not calibrated

exp (-0.0284HEI2)

Not 

calibrated

Not 

calibrated

Not calibrated Not c
262

3.7.3 Conclusions and Recommendations 

Extensive work was conducted as part of this effort to examine the appropriateness and 

defensibility of various models in the IHSDM. Numerous GOF indices were used to assess 

the models, as described in previous sections. Based on these extensive analyses, and 

practical issues of concern, several conclusions and recommendations can be drawn with 

respect to full models, AADT models, and AMFs. These are made in the context of IHSDM 

and general applications. 

IHSDM Application 

For IHSDM model development, it is recommended that there be a continuation of the 

current approach whereby AMFs are applied to base model accident predictions to account 

for factors for intersections under consideration that are different from the base condition. 

For base models, those calibrated with AADT as the only explanatory variable are 

recommended. For these models, the main considerations for recommendation surround the 

issues of variable selection, GOF, and the most defensible and representative data set from 

which models were estimated. Because previous AADT models were not directly calibrated 

as AADT-only, and instead were created by substituting constants for the non-AADT 

variables in the calibrated models, models estimated in previous efforts should be replaced 

with improved versions described in this report. Two sets of AADT models are 

recommended for both total and injury accidents. The first were calibrated using all available 

data and the second for a subset of sites meeting base condition criteria. If these base 

condition criterion are not known, or the appropriate AMFs not available, the models 

calibrated using all sites should be used. Specifically, the models shown in table 235 are 

recommended for use in the IHSDM: 

Table 235. AADT Models Recommended for Use in IHSDM 

Model Table Numbers Further Notes on Selection 

Type I 134, 135 Only Group B data models available. 

Type II 138, 139 Only Group B data models available. 

Type III 142, 143 Group B selected due to larger sample size. 

Type IV 148, 149 Group B selected due to larger sample size. 

Type V 154, 155, 157 Only Group A data models available. 

For AMFs, the main consideration is logical appeal. It is important to recognize that AMFs 

derived from expert opinion lack the conventional statistical variability measures associated 

with statistically derived AMFs. Also important is that expert derived AMFs were borne out 

of a perceived need among respected safety professionals that statistical information on 

empirically derived AMFs is unreliable. Combined with the fact that the research team had 

difficulty producing sufficient sample sizes for testing and/or validating AMFs, the following 

recommendations regarding AMFs are made: 

1. Expert opinion derived AMFs should be used in the IHSDM in the short term. 
263

2. Continued studies should be undertaken to: a) develop analytical methods for 

obtaining AMFs under observational study conditions; and b) accrue data to help 

validate and/or recalibrate and refine AMFs in support of the IHSDM. 

General Applications of Full Models 

Although this research was focused on IHSDM applications, useful byproducts are the full 

crash prediction models that have been calibrated. These models are appropriate for crash 

prediction applications such as network screening and safety treatment evaluation. In these 

applications, crash prediction models are most relevant to ongoing and planned Highway 

Safety Manual projects and to the FHWA initiative known as SafetyAnalyst that consists of 

software tools to help manage site-specific safety improvements. 

The overriding concerns for full models surround the selection of variables in the models, the 

intuitive appeal and agreement with engineering expectations, and the GOF criterion. Some 

of the main considerations in this regard include whether or not to include indicator variables 

for individual State effects (as opposed to a single constant term) and the appeal of individual 

model variables. It is generally believed that individual State effect models should be used if 

the individual States (e.g., California) were the target of crash forecasts. If crashes in States 

other than those identified are to be forecast, then models without State effects should be 

applied. Considering these factors, the full models shown in table 236 are recommended as 

“best available” statistical models: 

Table 236. Full Models Recommended for Use in Crash Prediction 

Model Table Numbers Further Notes on Selection 

Type I 159, 160 Group B not selected due to few available 

variables. 

Type II 163, 164 Group B not selected due to few available 

variables. 

Type III 167 main model, 168 main model Only Group A available. 

Type IV 169 main model, 170 main model Only Group A available. 

Type V 171 main model, 172 main model Only Group A available. 

265 

APPENDIX A: ALL MODELS IN THE REPORTS OF 

RELEVANCE 

Table 237. All Models in the Reports of Relevance 

Validation 

Number (V) 

Model 

Reference Reference Equation/Table 

Dependent 

Variable1 Remarks 

1, 5 1 1 Table 35, p. 115 A (TOT) Final Model 

2 1 1 Table 36, p. 116 A (INJ) Final Model 

3 1 1 Table 31, p. 111 A (TOT) Interim Model 

4 1 1 Table 34, p. 114 A (TOT) Interim Model 

5, 1 1 3 Eq. 52, p. 134 A (TOT) Full Model 

6 1 3 Eq. 53, p. 136 A (TOT) 

Recommended 

Base Model 

7 1 3 Eq. 54, p. 137 B (TOT) Full Model 

8 1 3 Eq. 55, p. 138 B (TOT) 

Alternative 

Base Model 

9, 14 2 1 Table 35, p. 115 A (TOT) Final Model 

10 2 1 Table 37, p. 117 A (INJ) Final Model 

11 2 1 Table 32, p. 112 A (TOT) Interim Model 

12 2 1 Table 34, p. 114 A (TOT) Interim Model 

13 2 1 Table 34, p. 114 A (TOT) Interim Model 

14, 9 2 3 Eq. 58, p. 140 A (TOT) Full Model 

15 2 3 Eq. 59, p. 141 A (TOT) 

Alternative 

Base Model 

16 2 3 Eq. 60, p. 142 B (TOT) Full Model 

17 2 3 Eq. 61, p. 143 B (TOT) 

Base Model 

Recommended 

18 3 2 Table 28, p. 111 C (TOT) ADT ONLY 

19 3 2 Table 28, p. 111 C (TOT) Main Model 

20 3 2 Table 28, p. 111 C (TOT) Variant 

21 3 2 Table 30, p. 113 C (INJ) ADT ONLY 

22 3 2 Table 30, p. 113 C (INJ) Variant 1 

23 3 2 Table 30, p. 113 C (INJ) Variant 2 

24 3 2 Table 29, p. 112 B (TOT) ADT ONLY 

25 3 2 Table 29, p. 112 B (TOT) Main Model 

26 3 2 Table 29, p. 112 B (TOT) Variant 1 

27 3 2 Table 29, p. 112 B (TOT) Variant 2 

28 3 2 Table 29, p. 112 B (TOT) Variant 3 
266 

Table 237. All Models in the Reports of Relevance (Continued) 

Validation 

Number (V) 

Model 

Reference Reference Equation/Table 

Dependent 

Variable1

 Remarks 

29 4 2 Table 32, p. 116 C (TOT) ADT ONLY 

30 4 2 Table 32, p. 116 C (TOT) Main Model 

31 4 2 Table 32, p. 116 C (TOT) Variant 1 

32 4 2 Table 32, p. 116 C (TOT) Variant 2 

33 4 2 Table 32, p. 116 C (TOT) Variant 3 

34 4 2 Table 34, p. 118 C (INJ) ADT ONLY 

35 4 2 Table 34, p. 118 C (INJ) Variant 1 

36 4 2 Table 33, p. 117 B (TOT) ADT ONLY 

37 4 2 Table 33, p. 117 B (TOT) Main Model 

38 4 2 Table 33, p. 117 B (TOT) Variant 1 

39 4 2 Table 33, p. 117 B (TOT) Variant 2 

40 4 2 Table 33, p. 117 B (TOT) Variant 3 

41 4 2 Table 34, p. 118 B (INJ) ADT only 

42 4 2 Table 34, p. 118 B (INJ) Variant 1 

43, 54 5 2 Table 35, p. 122 C (TOT) Main 

44, 53 5 2 Table 35, p. 122 C (TOT) Variant 1 

45 5 2 Table 35, p. 122 C (TOT) Variant 2 

46 5 2 Table 35, p. 122 C (TOT) Variant 3 

47 5 2 Table 37, p. 124 C (INJ) Main 

48, 56 5 2 Table 36, p. 123 B (TOT) Main 

49, 55 5 2 Table 36, p. 123 B (TOT) Variant 1 

50, 57 5 2 Table 36, p. 123 B (TOT) Variant 2 

51, 58 5 2 Table 36, p. 123 B (TOT) Variant 3 

52 5 2 Table 36, p. 123 B (INJ) Main 

53, 44 5 3 Eq. 63, p. 145 C(TOT) Full 

54, 43 5 3 Eq. 64, p. 146 C(TOT) Full 

55, 49 5 3 Eq. 65, p. 146 B (TOT) Full 

56, 48 5 3 Eq. 66, p. 146 B (TOT) Full 

57, 50 5 3 Eq. 67, p. 146 B (TOT) Full 

58, 51 5 3 Eq. 68, p. 148 B (TOT) 

Full 

Recommended 1A = Police definition of intersection related; B = Accidents generally considered to be intersection- 

 related (BMI); C = Total number occurring at intersection 
267 

APPENDIX B: MODELS VALIDATED 

Table 238. Models Validated 

Validation 

Number 

(V) 

Model 

Reference Reference Equation/Table 

Dependent 

Variable 

Validation 

Tasks Remarks 

1, 5 1 1 Table 35, p. 115 A (TOT) All Final Model 

2 1 1 Table 36, p. 116 A (INJ) All Final Model 

5, 1 1 3 Eq. 52, p. 134 A (TOT) See V1 Full Model 

6 1 3 Eq. 53, p. 136 A (TOT) Algo. 

Recommended 

Base Model 

9, 14 2 1 Table 35, p. 115 A (TOT) All Final Model 

10 2 1 Table 37, p. 117 A (INJ) All Final Model 

14, 9 2 3 Eq. 58, p. 140 A (TOT) See V9 Full Model 

17 2 3 Eq. 61, p. 143 B (TOT) Algo. 

Base Model 

Recommended 

19 3 2 Table 28, p. 111 C (TOT) All Main Model 

22 3 2 Table 30, p. 113 C (INJ) All Variant 1 

23 3 2 Table 30, p. 113 C (INJ) All Variant 2 

25 3 2 Table 29, p. 112 B (TOT) All Main Model 

30 4 2 Table 32, p. 116 C (TOT) All Main Model 

35 4 2 Table 34, p. 118 C (INJ) All Variant 1 

37 4 2 Table 33, p. 117 B (TOT) All Main Model 

42 4 2 Table 34, p. 118 B (INJ) All Variant 1 

43, 54 5 2 Table 35, p. 122 C (TOT) All Main 

44, 53 5 2 Table 35, p. 122 C (TOT) All Variant 1 

47 5 2 Table 37, p. 124 C (INJ) All Main 

48, 56 5 2 Table 36, p. 123 B (TOT) All Main 

51, 58 5 2 Table 36, p. 123 B (TOT) See V58 Variant 3 

52 5 2 Table 36, p. 123 B (INJ) All Main 

58, 51 5 3 Eq. 68, p. 148 B (TOT) Algo. Full Recommended

269 

APPENDIX C: DESCRIPTIVE STATISTICS FOR FULL 

DATASETS BY STATE 

TYPE I 

Table 239. Summary Statistics for Type I Sites by State 

Variables 

Number of 

Sites Mean Median Minimum Maximum 

Minnesota 270 0.5368 0.3571 0 3.86 

Georgia 116 1.2716 1.0000 0 6.00 

TOTACC per 

year 

California 1432 0.5669 0.3750 0 6.75 

Minnesota 270 0.2085 0.1429 0 1.57 

Georgia 116 0.4741 0.5000 0 2.50 

INJACC per 

year 

California 1432 0.2600 0.1250 0 4.13 

Minnesota 270 3981 2611 401 22067 

Georgia 116 3593 2950 420 16900 

AADT1 

California 1432 6590 5097 450 35750 

Minnesota 270 536 339 101 4608 

Georgia 116 639 430 300 6480 

AADT2 

California 1432 472 210 100 10001 

Minnesota 270 139 (51.5%) 

Georgia 116 3 (2.6%) 

RT MAJ 

California 1432 121 (8.4%) 

Minnesota 270 4 (1.5%) 

Georgia 116 4 (3.4%) 

RT MIN 

California 1432 40 (2.8%) 

Minnesota 270 45 (16.7%) 

Georgia 116 3 (2.6%) 

LT MAJ 

California 1432 388 (27.1%) 

Minnesota 270 0 (0%) 

Georgia 116 1 (0.9%) 

LT MIN 

California 1432 13 (0.9%) 

Minnesota 270 0 (0%) 

Georgia 116 3 (2.6%) 

MEDIAN 

California 1432 77 (5.4%) 

Minnesota 270 unknown 

Georgia 116 flat 48 (41.4%) 

rolling 58 (50%) 

mountainous 10 (8.6%) 

TERRAIN 

California 1432 flat 520 (36.3%) 

rolling 489 (34.1%) 

mountainous 423 (29.5%) 
270 

Table 239. Summary Statistics for Type I Sites by State (Continued) 

Variables 

Number 

of Sites Mean Median Minimum Maximum 

Minnesota 270 52.54 55.00 25 55 

Georgia 116 46.89 45.00 25 55 

SPD1 

California 1432 unknown 

Minnesota 270 1.29 1.00 0 8 

Georgia 116 1.57 1.00 0 7 

DRWY1 

California 1432 unknown 

Minnesota 270 2.13 2.00 1.00 4.00 

Georgia 116 3.56 3.50 1.50 7.00 

HAZRAT1 

California 1432 unknown 

Minnesota 270 -0.80 0.00 -90 85 

Georgia 116 -2.97 0.00 -65 60 

HAU 

California 1432 unknown 

Minnesota 270 unknown 

Georgia 116 1.02 0.35 0.00 7.00 

SHOULDER1 

California 1432 5.05 4.50 0.00 16.00 

Minnesota 270 0.1088 0.0000 0.0000 1.0200 

Georgia 116 1.3337 0.8855 0.0000 14.0000 

VCI1 

California 1432 unknown 

Minnesota 270 1.2689 0.0000 0.0000 29.0000 

Georgia 116 2.5545 0.6435 0.0000 23.2900 

HI1 

California 1432 unknown 
271 

TYPE II 

Table 240. Summary Statistics for Type II Sites by State 

Variable and Abbreviation 

Number 

of Sites Mean Median Minimum Maximum 

Minnesota 250 0.5406 0.3571 0 7.07 

Georgia 108 1.1806 0.5000 0 6.00 

TOTACC per year 

California 748 1.0132 0.6250 0 7.13 

Minnesota 250 0.2509 0.1429 0 3.14 

Georgia 108 0.6574 0.5000 0 3.50 

INJACC per year 

California 748 0.5110 0.3750 0 4.75 

Minnesota 250 2605 1983 419 14141 

Georgia 108 3181 2100 420 12300 

AADT1 

California 748 6784 5620 407 38126 

Minnesota 250 395 258 100 3209 

Georgia 108 644 430 100 7460 

AADT2 

California 748 562 310 100 6700 

Minnesota 250 130 (52%) 

Georgia 108 3 (2.8%) 

RT MAJ 

California 748 62 (8.3%) 

Minnesota 250 1 (0.4%) 

Georgia 108 2 (1.9%) 

RT MIN 

California 748 23 (3.1%) 

Minnesota 250 0 (0%) 

Georgia 108 6 (5.6%) 

LT MAJ 

California 748 217 (29%) 

Minnesota 250 0 (0%) 

Georgia 108 0 (0%) 

LT MIN 

California 748 1 (0.1%) 

Minnesota 250 0 (0%) 

Georgia 108 1 (0.9%) 

MEDIAN 

California 748 36 (4.8%) 
272 

Table 240. Summary Statistics for Type II Sites by State (Continued) 

Variable and Abbreviation Number of 

Sites 

Mean Median Minimum Maximum 

Minnesota 250 unknown 

Georgia 108 flat 52 (48.1%) 

rolling 52 (48.1%) 

mountainous (3.7%) 

TERRAIN 

California 748 flat 468 (62.6%) 

rolling 186 (24.9%) 

mountainous (12.6%) 

Minnesota 250 53.75 55.00 30 55 

Georgia 108 49.17 55.00 30 55 

SPD1 

California 748 unknown 

Minnesota 250 0.66 0.00 0 6 

Georgia 108 1.21 1.00 0 6 

DRWY1 

California 748 unknown 

Minnesota 250 2.04 2.00 1 6 

Georgia 108 3.41 3.00 1 6 

HAZRAT1 

California 748 unknown 

Minnesota 250 0.75 0.00 -120 150 

Georgia 108 -0.52 -0.25 -58 50 

HAU 

California 748 unknown 

Minnesota 250 unknown 

Georgia 108 0.73 0.50 0.00 2.30 

SHOULDER1 

California 748 6.10 6.00 0.00 16.00 

Minnesota 250 0.1350 0.0300 0.0000 2.1000 

Georgia 108 1.1089 0.9045 0.0000 7.5000 

VCI1 

California 748 unknown 

Minnesota 250 0.55 0.00 0.00 9.00 

Georgia 108 1.69 0.58 0.00 14.60 

HI1 

California 748 unknown 
273 

TYPE III 

Table 241. Summary Statistics for Type III Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) 

Variables State No. of Sites Mean Median Minimum Maximum 

CA 60 1.2 0.7 0.0 4.5 

MI 24 2.1 1.2 0.2 10.6 

GA 52 1.2 0.8 0.0 6.0 

TOTACC per Year 

 

 

 

 Total 136 1.4 0.8 0.0 10.6 

CA 60 0.6 0.3 0.0 3.7 

MI 24 0.5 0.4 0.0 2.0 

GA 52 0.5 0.5 0.0 4.0 

INJACC per Year 

 

 

 

Total 136 0.6 0.3 0.0 4.0 

CA 60 13484 12082 2360 33333 

MI 24 11635 11958 6817 23716 

GA 52 13100 12200 6500 28601 

AADT1 

 

 

 

Total 136 13011 12100 2360 33333 

CA 60 500 190 20 3001 

MI 24 835 779 15 2957 

GA 52 892 430 80 9490 

AADT2 

 

 

 

 Total 136 709 430 15 9490 

Total 136

CA 21(15.4%)

MI 24(17.6%)

GA 24(17.6%)

No Median 

 

 

 Total 69(50.7%)

CA 24(17.6%)

MI 0(0%)

GA 21(15.4%)

Painted 

 

 

 Total 45(33.1%)

CA 9(6.6%)

MI 0(0%)

GA 5(3.7%)

Curbed 

 

 

 Total 14(10.3%)

CA 6(4.4%)

MI 0(0%)

GA 2(1.5%)

MEDTYPE 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Other 

 

 

 Total 8(5.9%)

CA 60 5.2 2.5 0.0 36.0 

MI 24 0.0 0.0 0.0 

GA 52 27.0 20.0 0.0 63.0 

MEDWDTH1 

 

 

 Total 136 12.6 6.0 0.0 63.0 

CA 60 -2.0 0.0 -45.0 55.0 

MI 24 3.8 0.0 0.0 50.0 

GA 52 4.1 0.0 -65.0 90.0 

HAU 

 

 

Total 136 1.3 0.0 -65.0 90.0 
274 

Table 241. Summary Statistics for Type III Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) (Continued) 

Variables State No. of Sites Mean Median Minimum Maximum 

 Total 136

CA 2(1.5%)

MI 14(10.3%)

GA 0(0.0%)

1 

 

 

 Total 16(11.8%)

CA 29(21.3%)

MI 8(5.9%)

GA 21(15.4%)

2 

 

 

 Total 58(42.6%)

CA 12 (8.8%)

MI 1(0.7%)

GA 13(9.6%)

3 

 

 

 Total 26(19.1%)

CA 9(6.6%)

MI 1(0.7%)

GA 15(11.0%)

4 

 

 

 Total 25(18.4%)

CA 6(4.4%)

MI 0(0.0%)

GA 2(1.5%)

5 

 

 

 Total 8(5.9%)

CA 1(0.7%)

MI 0(0.0%)

GA 1(0.7%)

6 

 

 

 Total 2(1.5%)

CA 1(0.7%)

MI 0(0.0%)

GA 0(0.0%)

Total 1(0.7%)

MI unknown

HAZRAT1 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7 

 

 

 GA 2(4.0%)

CA 60 1.5 0.0 0.0 14.0

MI 24 2.9 2.0 0.0 11.0

GA 52 0.7 0.0 0.0 9.0

COMDRWY1 

 

 

 Total 136 1.5 0.0 0.0 14.0

CA 60 1.0 0.0 0.0 6.0

MI 24 1.7 1.0 0.0 7.0

GA 52 0.8 0.0 0.0 5.0

RESDRWY1 

 

 

 Total 136 1.0 0.0 0.0 7.0

CA 60 2.5 0.0 0.0 15.0

MI 24 4.6 5.0 0.0 11.0

GA 52 1.5 1.0 0.0 9.0

DRWY1 

 

 

 Total 136 2.5 1.0 0.0 15.0

 
275 

Table 241. Summary Statistics for Type III Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) (Continued) 

Variables State No. of Sites Mean Median Minimum Maximum 

CA 60 53.3 55.0 30.0 65.0

MI 24 43.1 40.0 30.0 55.0

GA 52 55.8 55.0 45.0 65.0

SPD1 

 

 

 Total 136 52.5 55.0 30.0 65.0

CA 60 34.2 35.0 15.0 35.0

MI 24 25.0 25.0 15.0 35.0

GA 52 37.1 35.0 25.0 55.0

SPD2 

 

 

 Total 136 33.7 35.0 15.0 55.0

 Total 136

CA 43(31.6%)

MI 9(6.6%)

GA 45(33.1%)

0 

 

 

 Total 97(71.3%)

CA 17(12.5%)

MI 15(11.0%)

GA 7(5.1%)

LIGHT 

 

 

 

 

 

 

 

 

1 

 

 

 Total 39(28.7%)

Total 136

CA 24(17.6%)

MI 24(17.6%)

GA 35(25.7%)

Flat 

 

 

 Total 83(61.0%)

CA 29(21.3%)

MI 0(0.0%)

GA 13(9.6%)

Rolling 

 

 

 Total 42(30.9%)

CA 7(5.1%)

MI 0(0.0%)

GA 4(2.9%)

TERRAIN1 

 

 

 

 

 

 

 

 

 

 

 

 

Mountainous 

 

 

 Total 11(8.1%)

Total 52

CA unknown

MI unknown

Flat 

 

 GA 24(17.6%)

CA unknown

MI unknown

Rolling 

 

 GA 21(15.4%)

CA unknown

MI unknown

TERRAIN2 

 

 

 

 

 

 

 

 

 

Mountainous 

 

 GA 7(5.1%)
276 

Table 241. Summary Statistics for Type III Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) (Continued) 

Variables State No. of Sites Mean Median Minimum Maximum 

Total 136

CA 44(32.4%)

MI 24(17.6%)

GA 40(29.4%)

0 

 

 

 Total 108(79.4%)

CA 16(11.8%)

MI 0(0.0%)

GA 12(8.8%)

RTLN1 

 

 

 

 

 

 

 

 

1 

 

 

 Total 28(20.6%)

Total 136

CA 15(11.0%)

MI 24(17.6%)

GA 9(6.6%)

0 

 

 

 Total 48(35.3%)

CA 45(33.1%)

MI 0(0.0%)

GA 43(31.6%)

LTLN1 

 

 

 

 

 

 

 

 

1 

 

 

 Total 88(64.7%)

Total 136

CA 55(40.4%)

MI 19(14.0%)

GA 43(31.6%)

0 

 

 

 Total 117(86.0%)

CA 5(3.7%)

MI 5(3.7%)

GA 9(6.6%)

RTLN2 

 

 

 

 

 

 

 

 

1 

 

 

 Total 19(14.0%)

Total 136

CA 57(41.9%)

MI 24(17.6%)

GA 50(36.8%)

0 

 

 

 Total 131(96.3%)

CA 3(2.2%)

MI 0(0.0%)

GA 2(1.5%)

LTLN2 

 

 

 

 

 

 

 

 

1 

 

 

 Total 5(3.7%)

CA 60 1.52 0.00 0.00 14.29

MI 24 1.36 0.00 0.00 9.15

GA 52 0.90 0.00 0.00 6.30

HI1 

 

 

 

 Total 136 1.26 0.00 0.00 14.29

CA 60 2.17 0.00 0.00 14.29

MI 24 3.21 0.00 0.00 26.63

GA 52 1.28 0.88 0.00 6.30

HEI1 

 

 

 

 Total 136 2.01 0.73 0.00 26.63
277 

Table 241. Summary Statistics for Type III Sites by State: California (CA), Michigan 

(MI), and Georgia (GA) (Continued) 

Variables State No. of Sites Mean Median Minimum Maximum 

CA 60 1.35 0.85 0.00 5.85 

MI 24 0.51 0.48 0.00 1.37 

GA 52 0.76 0.85 0.00 2.75 

GRADE1 

 

 

 Total 136 1.00 0.70 0.00 5.90 

CA 60 0.88 0.14 0.00 6.71 

MI 24 0.78 0.00 0.00 5.83 

GA 52 1.03 1.12 0.00 2.83 

VEI1 

 

 

 

 Total 136 0.90 0.60 0.00 6.70 

CA 60 9.53 7.91 1.18 28.16 

MI 24 8.21 7.59 2.93 16.63 

GA unknown 

PKTRUCK 

 

 

 

 Total 84 9.15 7.79 1.18 28.16 

CA 60 6.55 3.50 0.46 53.09 

MI 24 6.99 5.87 0.27 18.87 

GA unknown 

PKTURN 

 

 

 

 Total 84 6.68 4.28 0.27 53.09 

CA 60 3.15 1.73 0.23 25.97 

MI 24 3.59 3.20 0.13 11.17 

GA unknown 

PKLEFT 

 

 

 

 Total 84 3.28 2.16 0.13 25.97 

CA 60 1.44 0.62 0.00 21.29 

MI 24 1.54 0.97 0.00 5.95 

GA unknown 

PKLEFT1 

 

 

 

Total 84 1.47 0.69 0.00 21.29 

CA 60 55.44 60.77 0.00 100.00 

MI 24 54.97 58.70 0.00 100.00 

GA unknown 

PKLEFT2 

 

 

 

 Total 84 55.31 60.29 0.00 100.00 

CA 60 1553 2000 500 2000 

MI 24 1519 2000 600 2000 

GA 52 1470 1715 560 2000 

SD1 

 

 

 

 Total 136 1515 2000 500 2000 

CA 60 1364 1365 40 2000 

MI 24 1486 1800 400 2000 

GA 52 1448 1533 170 2000 

SDL2 

 

 

 

Total 136 1418 1510 40 2000 

CA 60 1380 1424 80 2000 

MI 24 1408 1350 500 2000 

GA 52 1493 1865 510 2000 

SDR2 

 

 

 Total 136 1428 1555 80 2000 
278 

TYPE IV 

Table 242. Summary Statistics for Type IV Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) 

Variables State No. of Sites Mean Median Minimum Maximum

CA 54 1.4 0.8 0.0 7.2 

MI 18 3.1 2.2 0.0 10.8 

GA 52 2.1 2.0 0.0 6.5 

TOTACC per year 

 

Total 124 2.0 1.4 0.0 10.8 

CA 54 0.8 0.5 0.0 5.7 

MI 18 1.0 0.9 0.0 3.2 

GA 52 1.0 1.0 0.0 4.5 

INJACC per year 

 

Total 124 0.9 0.5 0.0 5.7 

CA 54 13847 11199 3150 73799 

MI 18 10707 10550 5967 19384 

GA 52 12631 12850 5300 25799 

AADT1 

 

Total 124 12881 11496 3150 73799 

CA 54 441 301 21 1850 

MI 18 913 733 254 2018 

GA 52 706 463 300 2990 

AADT2 

 

Total 124 621 430 21 2990 

 

Total 124

CA 13(10.5%)

MI 18(14.5%)

GA 39(31.5%)

No Median 

 

 

 Total 70(56.5%)

CA 17(13.7%)

MI 0(0.0%)

GA 10(8.1%)

Painted 

 

 

 Total 27(21.8%)

CA 22(17.7%)

MI 0(0.0%)

GA 3(2.4%)

Curbed 

 

 

 Total 22(17.7%)

CA 2(1.6%)

MI 0(0.0%)

GA 0(0.0%)

MEDTYPE 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Other 

 

 

 Total 5(4.0%)

 
279 

 Table 242. Summary Statistics for Type IV Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) (Continued) 

Variables State No. of Sites Mean Median Minimum Maximum

CA 54 5.0 4.6 0.0 36 

MI 18 0 0 0 0 

GA 52 33.1 40.0 0.0 60 

MEDWDTH1 

 

Total 124 16.1 6.5 0 60 

CA 54 0.8 0.0 -20.0 22.5 

MI 18 1.1 0.0 -20.0 30.0 

GA 52 2.40 1.25 -50.0 55.0 

HAU 

 

Total 124 1.5 0.0 -50.0 55.0 

Total 124

CA 13(10.5%)

MI 8(6.5%)

GA 3(2.4%)

1 

 

 

 Total 24(19.4%)

CA 20(16.1%)

MI 9(7.3%)

GA 14(11.3%)

2 

 

 

 Total 43(34.7%)

CA 11(8.9%)

MI 1(0.8%)

GA 20(16.1%)

3 

 

 

 Total 32(25.8%)

CA 8(6.5%)

MI 0(0.0%)

GA 13(10.5%)

4 

 

 

 Total 21(16.9%)

CA 1(0.8%)

MI 0(0.0%)

GA 1(0.8%)

5 

 

 

 Total 2(1.6%)

CA 1(0.8%)

MI 0(0.0%)

GA 1(0.8%)

6 

 

 

 Total 2(1.6%)

CA 0(0.0%)

MI 0(0.0%)

GA 0(0.0%)

HAZRAT1 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7 

 

 

 Total 0(0.0%)

CA 54 0.7 0.0 0.0 12.0 

MI 18 1.3 0.5 0.0 7.0 

GA 52 0.3 0.0 0.0 2.0 

COMDRWY1 

 

Total 124 0.6 0 0 12 

 
280 

Table 242. Summary Statistics for Type IV Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) (Continued) 

Variables State No. of Sites Mean Median Minimum Maximum

CA 54 0.6 0.0 0.0 6.0 

MI 18 2.5 2 0 7 

GA 52 0.2 0.0 0.0 2.0 

RESDRWY1 

Total 124 0.7 0 0 7 

CA 54 1.3 0.0 0.0 15.0 

MI 18 3.8 4.0 0.0 9.0 

GA 52 0.4 0.0 0.0 3.0 

DRWY1 

 

 Total 124 1.3 0 0 15 

CA 54 56.4 55.0 25 65 

MI 18 45.3 42.5 35 55 

GA 52 58.4 55.0 45 65 

SPD1 

 

 Total 124 55.6 55 25 65 

CA 54 35.0 35.0 25 50 

MI 18 28.2 25.0 25 45 

GA 52 36.6 35.0 25 55 

SPD2 

 

Total 124 34.7 35.0 25 55 

Total 124

CA 36(29.0%)

MI 4(3.2%)

GA 47(37.9%)

0 

 

 

 Total 87(70.2%)

CA 18(14.5%)

MI 14(11.3%)

GA 5(4.0%)

LIGHT 

 

 

 

 

 

 

 

 

1 

 

 

 Total 37(29.8%)

 Total 124

CA 32(25.8%)

MI 18(14.5%)

GA 40(32.3%)

Flat 

 

 

 Total 90(72.6%)

CA 13(10.5%)

MI 0(0.0%)

GA 12(9.7%)

Rolling 

 

 

 Total 25(20.2%)

CA 9(7.3%)

MI 0(0.0%)

GA 0(0.0%)

TERRAIN1 

 

 

 

 

 

 

 

 

 

 

 

 

Mountainous 

 

 

 Total 9(7.3%)
281 

Table 242. Summary Statistics for Type IV Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) (Continued) 

Variables State No. of Sites Mean Median Minimum Maximum

 Total 124

CA 27(21.8%)

MI 18(14.5%)

GA 24(19.4%)

0 

 

 

 Total 69(55.6%)

CA 7(5.6%)

MI 0(0.0%)

GA 13(10.5%)

1 

 

 

 Total 20(16.1%)

CA 20(16.1%)

MI 0(0.0%)

GA 15(12.1%)

RTLN1 

 

 

 

 

 

 

 

 

 

 

 

 

2 

 

 

 Total 35(28.2%)

Total 124

CA 4(3.2%)

MI 18(14.5%)

GA 7(5.6%)

0 

 

 

 Total 29(23.4%)

CA 4(3.2%)

MI 0(0.0%)

GA 1(0.8%)

1 

 

 

 Total 5(4.0%)

CA 46(37.1%)

MI 0(0.0%)

GA 44(35.5%)

LTLN1 

 

 

 

 

 

 

 

 

 

 

 

 

2 

 

 

 Total 90(72.6%)

 Total 124

CA 33(26.6%)

MI 12(9.7%)

GA 27(21.8%)

0 

 

 

 Total 72(58.1%)

CA 7(5.6%)

MI 3(2.4%)

GA 3(2.4%)

1 

 

 

 Total 13(10.5%)

CA 14(11.3%)

MI 3(2.4%)

GA 22(17.7%)

RTLN2 

 

 

 

 

 

 

 

 

 

 

 

 

2 

 

 

 Total 39(31.5%)
282 

Table 242. Summary Statistics for Type IV Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) (Continued) 

Variables State No. of Sites Mean Median Minimum Maximum

Total 124

CA 52(41.9%)

MI 18(14.5%)

GA 52(41.9%)

0 

 

 

 Total 122(98.4%)

CA 2(1.6%)

MI 0(0.0%)

GA 0(0.0%)

1 

 

 

 Total 2(1.6%)

CA 0(0.0%)

MI 0(0.0%)

GA 0(0.0%)

LTLN2 

 

 

 

 

 

 

 

 

 

 

 

 

2 

 

 

 Total 0(0.0%)

CA 54 1.24 0.00 0.00 7.07

MI 18 0.83 0.00 0.00 7.33

GA 52 0.62 0.29 0.00 2.50

HI1 

 

Total 124 0.92 0 0 7.33

CA 54 1.47 0.00 0.00 7.07

MI 18 15.65 0.00 0.00 233.33

GA 52 0.88 0.72 0.00 3.49

HEI1 

 

Total 124 3.28 0.6 0 233.33

CA 54 1.19 0.67 0.00 5.80

MI 18 0.32 0.00 0.00 2.25

GA 52 0.89 0.85 0.00 2.30

GRADE1 

 

Total 124 0.94 0.71 0.00 5.80

CA 54 0.5 0.0 0.0 3.7 

MI 18 1.3 0.0 0.0 12.5 

GA 52 1.09 1.05 0.00 2.79

VEI1 

 

 Total 124 0.87 0.35 0 12.5 

CA 54 0.4 0.0 0.0 3.1 

MI 18 1.1 0.0 0.0 12.5 

GA 52 0.71 0.45 0.00 3.23

VI1 

 

Total 124 0.62 0 0 12.5 

CA 54 0.1 0.0 0.0 3.1 

MI 18 1.04 0.00 0.00 12.50

GA 52 0.50 0.00 0.00 2.57

VCI1 

 

Total 124 0.43 0 0 12.5 
283 

Table 242. Summary Statistics for Type IV Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) (Continued) 

Variables State No. of Sites Mean Median Minimum Maximum

CA 54 0.3 0.0 0.0 3.2 

MI 18 1.12 0.00 0.00 12.50 

GA 52 0.80 0.56 0.00 2.57 

VCEI1 

Total 124 0.63 0 0 12.5 

CA 54 11.99 8.92 2.22 37.25 

MI 18 7.83 7.94 1.75 13.13 

GA unknown 

PKTRUCK 

 

Total 72 10.95 8.36 1.75 37.25 

CA 54 7.93 4.87 0.00 48.52 

MI 18 14.10 9.53 4.54 32.55 

GA unknown 

PKTURN 

 

Total 72 9.47 6.56 0 48.52 

CA 54 4.05 2.54 0.00 25.26 

MI 18 7.04 4.75 2.14 16.76 

GA unknown 

PKLEFT 

 

 Total 72 4.8 3.08 0 25.26 

CA 54 2.25 1.02 0.00 13.96 

MI 18 4.36 3.10 0.83 11.56 

GA unknown 

PKLEFT1 

 

Total 72 2.78 1.51 0 13.96 

CA 54 39.78 37.12 0.00 100.00 

MI 18 36.22 34.10 13.61 58.65 

GA unknown 

PKLEFT2 

 

Total 72 38.89 36.66 0 100 

CA 54 95.27 97.71 67.77 100.00 

MI 18 91.85 94.51 79.20 98.26 

GA unknown 

PKTHRU1 

 

 Total 72 94.41 96.95 67.77 100 

CA 54 15.44 8.26 0.00 68.09 

MI 18 16.45 18.19 0.96 39.39 

GA unknown 

PKTHRU2 

 

 Total 72 15.69 10.82 0 68.09 

CA 54 1431 1519 400 2000 

MI 18 1430 1310 580 2000 

GA 52 1356 1301 639 2000 

SD1 

 

Total 124 1399 1332 400 2000 
284 

Table 242. Summary Statistics for Type IV Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) (Continued) 

Variables State No. of Sites Mean Median Minimum Maximum

CA 54 1382 1470 324 2000

MI 18 1286 1203 394 2000

GA 52 1254 1182 579 2000

SDL2 

 

Total 124 1314 1262 324 2000

CA 54 1384 1470 215 2000

MI 18 1356 1255 479 2000

GA 52 1263 1206 540 2000

SDR2 

 

Total 124 1329 1354 215 2000
285 

TYPE V 

Table 243. Summary Statistics for Type V Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) 

Variables State No. of Sites Mean Median Minimum Maximum

CA 18 5.2 5.3 1.3 10.7 

MI 31 8.1 8.0 2.0 14.8 

GA 51 4.8 3.5 0.0 26.5 

TOTACC per year 

 

 

 

 Total 100 5.9 5.3 0 26.5 

CA 18 2.0 1.8 0.3 4.0 

MI 31 2.6 2.5 0.0 6.5 

GA 51 1.2 0.5 0.0 6.5 

INJACC per year 

 

 

 

 Total 100 1.8 1.5 0 6.5 

CA 18 13095 12650 7340 25132 

MI 31 9007 8435 4917 17483 

GA 51 7798 7400 430 15200 

AADT1 

 

 

 

 Total 100 9126 8700 430 25132 

CA 18 3642 3026 940 10280 

MI 31 4796 4434 1961 12478 

GA 51 2749 2200 420 10400 

AADT2 

 

 

 

 Total 100 3544 3100 420 12478 

 

Total 100

CA 0

MI 22

GA 11

Pretimed 

 

 

 Total 33

CA 17

MI 4

GA 24

Actuated 

 

 

 Total 45

CA 1

MI 5

GA 16

SIGTYPE 

 

 

 

 

 

 

 

 

 

 

 

 

Semiactuated 

 

 

 Total 22
286 

Table 243. Summary Statistics for Type V Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) (Continued) 

Variables State No. of Sites Mean Median Minimum Maximum

 Total 100 

CA 12 

MI 31 

GA 44 

No Median 

Total 87 

CA 5 

MI 0 

GA 7 

Painted 

Total 12 

CA 1 

MI 0 

GA 0 

MEDTYPE 

 

 

 

 

 

 

 

 

 

 

 

 

Other 

Total 1 

 CA 18 3 0 0 13 

MEDWIDTH1 MI 31 0 0 0 0 

 GA 51 1.5 0 0 13 

 Total 100 1.3 0 0 13 

 CA 18 3.33 0 -10 30 

HAU MI 31 -3.06 0 -45 40 

 GA 51 0.82 0 -45 35 

 Total 100 0.07 0 -45 40 

 Total 100 

1 CA 3 

 MI 7 

 GA 2 

 Total 12 

2 CA 5 

 MI 15 

 GA 9 

 Total 29 

3 CA 6 

 MI 8 

 GA 13 

 Total 27 

4 CA 2 

 MI 1 

 GA 13 

 Total 16 

5 CA 1 

 MI 0 

 GA 12 

HAZRAT1 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 Total 13 
287 

Table 243. Summary Statistics for Type V Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) (Continued) 

Variables State No. of Sites Mean Median Minimum Maximum 

 6 CA 1 

HAZRAT1 MI 0 

 GA 2 

 Total 3 

 7 CA 0 

 MI 0 

 GA 0 

 Total 0 

CA 18 1.6 1 0 6 

MI 31 2.9 3 0 11 

GA 51 2.9 2 0 9 

COMDRWY1 

 

 

 Total 100 2.6 2 0 11 

CA 18 0.3 0 0 5 

MI 31 0.9 0 0 6 

GA 51 0.4 0 0 4 

RESDRWY1 

 

 Total 100 0.5 0 0 6 

 CA 18 1.9 1 0 7 

DRWY1 MI 31 3.8 3 0 15 

 GA 51 3.2 3 0 9 

 Total 100 3.2 3 0 15 

 CA 18 50.8 55 35 65 

SPD1 MI 31 47.4 50 30 55 

 GA 51 41.8 45 25 55 

 Total 100 45.2 45 25 65 

 CA 18 45 45 30 55 

SPD2 MI 31 43.1 45 25 55 

 GA 51 38.1 35 20 55 

 Total 100 40.9 40 20 55 

LIGHT Total 100 

 0 CA 1 

 MI 9 

 GA 19 

 Total 29 

 1 CA 17 

 MI 22 

 GA 32 

 Total 71 
288 

Table 243. Summary Statistics for Type V Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) (Continued) 

Variables State No. of Sites Mean Median Minimum Maximum 

Total 100

CA 11

MI 25

GA 23

Flat 

 

 

 Total 59

CA 5

MI 6

GA 27

Rolling 

 

 

 Total 38

CA 2

MI 0

GA 1

TERRAIN1 

 

 

 

 

 

 

 

 

 

 

 

 

Mountainous 

 

 

 Total 3

Total 100

CA 1

MI 27

GA 42

0 

 

 

 Total 70 

CA 17

MI 4

GA 9

PROTLT1 

 

 

 

 

 

 

 

 

1 

 

 

 Total 30 

 Total 100

CA 7

MI 14

GA 30

0 

 

 

 Total 51 

CA 3

MI 5

GA 13

1 

 

 

 Total 21 

CA 8

MI 12

GA 8

RTLN1 

 

 

 

 

 

 

 

 

 

 

 

 

2 

 

 

 Total 28 
289 

Table 243. Summary Statistics for Type V Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) (Continued) 

Variables State No. of Sites Mean Median Minimum Maximum 

 Total 100

CA 0

MI 7

GA 16

0 

 

 

 Total 23

CA 0

MI 1

GA 1

1 

 

 

 Total 2 

CA 18

MI 23

GA 34

LTLN1 

 

 

 

 

 

 

 

 

 

 

 

 

2 

 

 

 Total 75

 Total 100

CA 12

MI 14

GA 33

0 

 

 

 Total 59

CA 3

MI 7

GA 10

1 

 

 

 Total 20

CA 3

MI 10

GA 8

RTLN2 

 

 

 

 

 

 

 

 

 

 

 

 

2 

 

 

 Total 21

 Total 100

CA 8

MI 9

GA 28

0 

 

 

 Total 45

CA 0

MI 3

GA 2

1 

 

 

 Total 5

CA 10

MI 19

GA 21

LTLN2 

 

 

 

 

 

 

 

 

 

 

 

 

2 

 

 

 Total 50
290 

Table 243. Summary Statistics for Type V Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) (Continued) 

Variables State No. of Sites Mean Median Minimum Maximum 

CA 18 2.10 1.65 0.00 9.82 

MI 31 6.38 0.00 0.00 94.87 

GA 51 3.13 0.65 0.00 49.90 

HEI 

 

 

 

 Total 100 3.95 0.61 0.00 94.87 

CA 18 4.40 0.00 0.00 36.41 

MI 31 0.89 0.00 0.00 12.22 

HEI2 GA 51 2.85 0.00 0.00 19.00 

 Total 100 2.52 0.00 0.00 36.41 

CA 18 1.22 0.00 0.00 9.82 

MI 31 3.31 0.00 0.00 60.00 

GA 51 1.78 0.00 0.00 49.90 

HI1 

 

 

 

 Total 100 2.15 0.00 0.00 60.00 

CA 18 3.25 1.48 0.00 19.16 

MI 31 3.63 0.00 0.00 47.44 

GA 51 1.70 0.00 0.00 27.05 

HI2 

 

 

 

 Total 100 2.58 0.00 0.00 47.44 

CA 18 2.46 0.00 0.00 18.72 

MI 31 1.93 0.00 0.00 30.00 

GA 51 2.99 1.09 0.00 32.54 

HEICOM 

 

 

 

 Total 100 2.56 0.58 0.00 32.54 

CA 18 2.23 0.79 0.00 10.72 

MI 31 3.47 0.00 0.00 42.05 

GA 51 1.74 0.00 0.00 32.54 

HICOM 

 

 

 

 Total 100 2.36 0 0 42.05 

CA 18 0.88 0.58 0.00 3.45 

MI 31 0.80 0.83 0.00 3.31 

GA 51 1.56 1.45 0.00 4.98 

GRADE1 

 

 

 

 Total 100 1.20 1.00 0.00 4.98 

CA 18 1.01 0.59 0.00 5.30 

MI 31 1.00 0.71 0.00 4.00 

GA 51 1.99 1.65 0.00 7.79 

GRADE2 

 

 

 

 Total 100 1.50 1.28 0.00 7.79 

CA 18 1.40 0.46 0.00 11.97 

MI 31 1.43 0.94 0.00 6.83 

GA 51 1.48 1.45 0.00 4.98 

VEI1 

 

 

 

 Total 100 1.45 1.19 0.00 11.97 
291 

Table 243. Summary Statistics for Type V Sites by State: California (CA), 

 Michigan (MI), and Georgia (GA) (Continued) 

Variables State No. of Sites Mean Median Minimum Maximum 

CA 18 2.41 0.71 0.00 11.53 

MI 31 1.65 0.65 0.00 13.50 

GA 51 1.90 1.65 0.00 7.79 

VEI2 

 

 

 

 Total 100 1.91 1.39 0.00 13.50 

CA 18 2.03 1.33 0.00 8.13 

MI 31 1.87 1.62 0.00 6.75 

GA 51 1.69 1.60 0.00 4.79 

VEICOM 

 

 

 

 Total 100 1.81 1.59 0.00 8.13 

CA 18 1.38 0.00 0.00 10.79 

MI 31 0.66 0.00 0.00 4.77 

VCEI1 GA 51 1.26 1.15 0.00 5.18 

 Total 100 1.10 0.45 0.00 10.79 

CA 18 1.72 0.17 0.00 12.13 

MI 31 1.24 0.31 0.00 14.00 

GA 51 1.66 1.41 0.00 8.40 

VCEI2 

 

 

 

 Total 100 1.54 0.90 0.00 14.00 

CA 18 1.55 0.82 0.00 6.07 

MI 31 0.95 0.47 0.00 7.00 

GA 51 1.46 1.30 0.00 5.08 

VCEICOM 

 

 

 

 Total 100 1.32 1.03 0.00 7.00 

CA 18 7.36 6.43 2.69 15.45 

MI 31 9.89 8.37 2.97 45.43 

GA unknown 

PKTRUCK 

 

 

 

 Total 49 8.96 7.71 2.69 45.43 

CA 18 30.74 29.90 7.07 72.66 

MI 31 38.48 35.29 26.00 61.03 

GA unknown 

PKTURN 

 

 

 

 Total 49 35.64 34.48 7.07 72.66 

CA 18 15.80 14.51 4.20 37.07 

MI 31 19.54 19.09 11.88 31.58 

GA unknown 

PKLEFT 

 

 

 

 Total 49 18.17 17.97 4.2 37.07 

CA 18 13.83 11.36 1.78 43.23 

MI 31 15.66 16.32 4.60 36.67 

GA unknown 

PKLEFT1 

 

 

 

 Total 49 14.99 13.15 1.78 43.23 
292 

Table 243. Summary Statistics for Type V Sites by State: California (CA), 

Michigan (MI), and Georgia (GA) (Continued) 

Variables State No. of Sites Mean Median Minimum Maximum

CA 18 28.90 25.21 2.59 68.57 

MI 31 27.80 24.88 9.91 75.73 

GA unknown 

PKLEFT2 

 

 

 

 Total 49 28.21 24.88 2.59 75.73 

CA 18 74.49 80.83 18.01 96.73 

MI 31 69.27 70.37 44.40 85.33 

GA unknown 

PKTHRU1 

 

 

 

 Total 49 71.19 73.77 18.01 96.73 

CA 18 44.68 39.17 9.34 84.09 

MI 31 43.44 45.78 8.45 73.14 

GA unknown 

PKTHRU2 

 

 

 

 Total 49 43.9 41.99 8.45 84.09 

CA 18 1482 2000 267 2000 

MI 31 1447 1500 522 2000 

GA 51 1175 1086 235 2000 

SD1 

 

 

 

 Total 100 1314 1246 235 2000 

CA 18 1420 1750 390 2000 

MI 31 1389 1212 509 2000 

GA 51 1033 961 224 2000 

SD2 

 

 

 

 Total 100 1213 1091 224 2000 

CA 18 815 454 188 2000 

MI 31 814 615 200 2000 

GA 51 735 709 122 2000 

SDL1 

 

 

 

 Total 100 774 673 122 2000 

CA 18 1011 787 269 2000 

MI 31 1041 850 253 2000 

GA 51 794 739 142 2000 

SDL2 

 

 

 

 Total 100 910 750 142 2000 
293 

APPENDIX D: CURE PLOTS FOR TYPE I, II, III, IV, AND V 

AADT MODELS 

Figure 23. CURE Plot for Type I TOTACC AADT Model 

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 5000 10000 15000 20000 25000 30000 35000 40000

Major AADT

Cumulative Residuals

Adj Cum Resi

Standard Deviation

Standard Deviation
294 

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 5000 10000 15000 20000 25000 30000 35000 40000 45000

Major AADT

Cumulative Residuals

Adj Cum Resi

Standard Deviation

Standard Deviation

Figure 24. CURE Plot for Type II TOTACC AADT Model 

-25

-20

-15

-10

-5

0

5

10

15

20

25

0 10000 20000 30000 40000 50000 60000 70000 80000

Major AADT

Cumulative Residuals

Adj Cum Residuals

Standard Deviation

Standard Deviation

Figure 25. CURE Plot for Type III TOTACC AADT Model 
295 

-30

-20

-10

0

10

20

30

0 10000 20000 30000 40000 50000 60000 70000 80000

Major AADT

Cumulative Residuals

Adj Cum Residuals

Standard Deviation

Standard Deviation

Figure 26. CURE Plot for Type IV TOTACC AADT Model 

-40

-30

-20

-10

0

10

20

30

40

0 5000 10000 15000 20000 25000 30000

Major AADT

Cumulative Residuals

Adj Cum Residuals

Standard Deviation

Standard Deviation

Figure 27. CURE Plot for Type V TOTACC AADT Model 

297 

REFERENCES 

1. Vogt A. and Bared, J. Accident Prediction Models for Two-Lane Rural Roads: Segments 

and Intersections. FHWA-RD-98-133. October 1998. 

2. Vogt A. Crash Models For Rural Intersections: Four-Lane by Two-Lane Stop-Controlled 

and Two-Lane by Two-Lane Signalized. FHWA-RD-99-128. October 1999. 

3. Harwood, D.W., Council, F.M., Hauer, E., Hughes, W.E., and Vogt A. Prediction of the 

Expected Safety Performance of Rural Two-Lane Highways. FHWA-RD-99-207. 

December 2000. 

4. Oh, Jutaek, C. Lyon, S. Washington, B. Persaud, and J. Bared. Validation of the FHWA 

Crash Models for Rural Intersections: Lessons Learned. Journal of the Transportation 

Research Board. National Academy Press, Washington D.C., No 1840. pp 41-49. 2003. 

5. Harwood, D.W., Bauer, K.M., Potts, J.B., Torbic, D.J., Richard, K.R., Kohlman Rabbani, 

K.R., Hauer, E. and Elefteriadou, L. Safety Effectiveness of Intersection Left- and RightTurn Lanes. FHWA-RD-02-089. July 2002. 

6. Zegeer, C.V., Reinfurt, D.W., Hummer, J., Herf, L., and Hunter, W. Safety Effects of 

Cross-Section Design for Two-Lane Roads. Transportation Research Record 1195, 

Transportation Research Board, 1988. 

7. American Association of State Highway and Transportation Officials, A Policy on 

Geometric Design of Highways and Streets, Fourth Edition, 2001. 

8. Hauer, E. Reestimation of Models for Two-Lane Rural Road Segments. (draft). January 

2001. 

9. Hauer, E., and Bamfo, J. “Two Tools for Finding What Function Links the Dependent 

Variable to the Explanatory Variables.” In Proceedings of the ICTCT 1997 Conference, 

Lund, Sweden, 1997. 
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