The Calibrator: 

An SPF Calibration and Assessment Tool 

Updated User Guide 

FHWA-SA-17-016 Updated June 2018
THE CALIBRATOR—UPDATED USER GUIDE

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.

Any opinions, findings, and conclusions or recommendations, and translations thereof, 

expressed in this publication are those of the author(s) and do not necessarily reflect the views 

of the Federal Highway Administration.

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.
THE CALIBRATOR—UPDATED USER GUIDE

TECHNICAL DOCUMENTATION PAGE

1. Report No.

FHWA-SA-17-016

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

 

4. Title and Subtitle

The Calibrator—An SPF Calibration and Assessment Tool

Updated User Guide

5. Report Date

December 2016 (original)

June 2018 (updated)

6. Performing Organization Code

7. Author(s) 

Craig Lyon, Bhagwant Persaud, and Frank Gross

8. Performing Organization Report No.

9. Performing Organization Name and Address

VHB

8300 Boone Boulevard

Suite 700

Vienna, VA 22182

10. Work Unit No.

11. Contract or Grant No.

DTFH61-10-D-00022-T-13005

12. Sponsoring Agency Name and Address

Federal Highway Administration Office of Safety

1200 New Jersey Ave., SE

Washington, DC 20590

13. Type of Report and Period

Updated Final Report, June 2018 

14. Sponsoring Agency Code

FHWA

15. Supplementary Notes

The Contracting Officer’s Task Manager (COTM) was Stuart Thompson.

16. Abstract

This user guide provides background information on safety performance functions (SPFs) and the need for calibration. It also serves as a 

companion “how-to” manual for The Calibrator software tool. This is an updated user guide based on enhancements to The Calibrator, 

including the ability to calibrate SPFs based on calibration functions and dispersion functions.

INSTALLATION NOTE: The Calibrator was developed for Microsoft Excel versions 2007 and later, running on Windows Operating 

Systems with the SOLVER add-in installed. Since the file includes macros, there may be warnings about enabling macros or Trusting the 

document before using it. Other issues that users may encounter include Trust Center settings. Users can access the Trust Center by 

navigating to (File, Options, and Trust Center). In the Trust Center options, click on Macro Settings and adjust according to your 

organizations policy. Microsoft also releases updates that can occasionally break ActiveX/Macros. Refer to your IT department about 

resolutions/hotfixes for ActiveX controls.

17. Key Words:

Roadway, Safety, Data, Analysis, SPF, Performance, 

Function, Calibrate, Calibration

18. Distribution Statement

No restrictions.

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page) 

Unclassified

21. No. of Pages

103

22. Price

Form DOT F 1700.7 (8-72) Reproduction of completed pages authorized
THE CALIBRATOR—UPDATED USER GUIDE

ii

TABLE OF CONTENTS

1. Introduction......................................................................................................................... 1

2. Background on SPF Calibration...................................................................................... 3

Why Calibrate?........................................................................................................................................................... 3

Methodology for Calibration................................................................................................................................. 3

Guidance on Preparing Data for Calibration.................................................................................................. 6

Selecting Sites for Calibration.......................................................................................................................... 6

Dealing with Outliers.......................................................................................................................................... 7

Comparing the AADT Range of Calibration Data .................................................................................. 7

Minimum Sample Sizes............................................................................................................................................. 7

Multiple Calibration Factors.................................................................................................................................. 8

Interpretation of the Constant Calibration Factor...................................................................................... 9

3. Goodness-Of-Fit Measures .............................................................................................10

Mean Absolute Deviation.................................................................................................................................... 10

Modified R2................................................................................................................................................................ 10

Dispersion Parameter........................................................................................................................................... 11

Coefficient of Variation of the Calibration Factor..................................................................................... 11

Cumulative Residual Plots................................................................................................................................... 12

Akaike’s Information Criterion (AIC)............................................................................................................. 15

Schwarz Bayesian Information Criterion (BIC)........................................................................................... 15

Assessment Tables................................................................................................................................................. 16

Summary of SPF Assessment.............................................................................................................................. 17

Assessing the Acceptability of an SPF........................................................................................................ 17

Comparing Multiple SPFs................................................................................................................................ 17
THE CALIBRATOR—UPDATED USER GUIDE

iii

4. Issues in SPF Selection....................................................................................................19

Use of HSM or non-HSM SPFs and CMFs.................................................................................................... 19

Meeting the Data Requirements....................................................................................................................... 20

SPFs for Specific Conditions............................................................................................................................... 20

Desired Precision of Predictions...................................................................................................................... 21

5. Using the Calibrator........................................................................................................22

Importing Data......................................................................................................................................................... 23

Steps for Importing Data ................................................................................................................................ 24

Defining SPFs and CMFs....................................................................................................................................... 25

Steps for Defining SPFs.................................................................................................................................... 26

Steps for Selecting a Predefined SPF.......................................................................................................... 28

Steps for Defining CMFs................................................................................................................................. 29

Steps for Defining Dispersion Parameter................................................................................................. 30

Saving and Editing SPFs and CMFs............................................................................................................... 30

Calibration and Goodness-of-Fit Measures.................................................................................................. 30

Steps for Calibrating SPFs and Dispersion Parameters...................................................................... 30

CURE Plots and Assessment Tables............................................................................................................... 32

Steps for Creating CURE Plots and Assessment Tables.................................................................... 32

6. Examples.............................................................................................................................36

Example 1: SPF for Motorcycle Crashes on Urban Freeways.............................................................. 36

Example 2: SPF and CMFs for 3-Leg Stop-Controlled Intersections on Rural 2-Lane Roads.. 43

Example 3: HSM SPF and CMFs, AASHTOWare Safety AnalystTM SPF, and Custom SPF 

Applied to Rural 2-Lane Roads......................................................................................................................... 49

Appendix: Predefined SPFs....................................................................................................61

A.1. HSM Base Condition SPFs......................................................................................................................... 61
THE CALIBRATOR—UPDATED USER GUIDE

iv

A.1.1 Two-Lane Rural Road Chapter........................................................................................................ 61

A.1.2 Multi-Lane Rural Road Chapter....................................................................................................... 62

A.1.3 Urban and Suburban Arterials Chapter........................................................................................ 66

A.1.3 Freeway Chapter.................................................................................................................................... 74

A.2. AASHTOWare Safety AnalystTM SPFs.................................................................................................. 89

Segments............................................................................................................................................................... 89

Intersections ........................................................................................................................................................ 89

Technical Working Group.................................................................................................................................. 93

References..................................................................................................................................94
THE CALIBRATOR—UPDATED USER GUIDE

v 

LIST OF FIGURES

Figure 1. Chart. Calibration process....................................................................................................................... 4

Figure 2. Equation. Calibration factor..................................................................................................................... 4

Figure 3. Equation. Calibration function................................................................................................................ 5

Figure 4. Equation. Variable dispersion as linear function of length........................................................... 5

Figure 5. Equation. Variable dispersion as nonlinear function of length. .................................................. 5

Figure 6. Equation. Mean absolute deviation..................................................................................................... 10

Figure 7. Equation. Modified R2 value. ................................................................................................................. 10

Figure 8. Equation. Variance of negative binomial distribution.................................................................. 11

Figure 9. Equation. Dispersion parameter......................................................................................................... 11

Figure 10. Equation. Coefficient of variation of a constant calibration factor..................................... 11

Figure 11. Equation. Variance of calibration factor........................................................................................ 12

Figure 12. Equation. Variance of random walk. ............................................................................................... 13

Figure 13. Equation. Lower 95 percent confidence limit. ............................................................................ 13

Figure 14. Equation. Upper 95 percent confidence limit. ............................................................................ 13

Figure 15. Chart. Example CURE plot................................................................................................................. 14

Figure 16. Equation. Akaike’s Information Criterion (AIC). ....................................................................... 15

Figure 17. Equation. Schwarz Bayesian Information Criterion (BIC)...................................................... 15

Figure 18. Image. Example road segment database required for calibration. ...................................... 24

Figure 19. Image. Example of imported data..................................................................................................... 25

Figure 20. Image. Example of variable list for imported data..................................................................... 25

Figure 21. Image. Example of user-defined SPF and CMFs.......................................................................... 26

Figure 22. Image. Example of selection of predefined SPFs. ....................................................................... 28

Figure 23. Image. Example of selecting an SPF to calibrate from predefined SPFs............................ 31
THE CALIBRATOR—UPDATED USER GUIDE

vi

Figure 24. Image. Example of the solver results screen............................................................................... 31

Figure 25. Image. Example results from ‘Results’ tab.................................................................................... 32

Figure 26. Image. Example assessment creating CURE plots for two variables.................................. 33

Figure 27. Image. Example CURE plots from "Generate Graphs.".......................................................... 34

Figure 28. Image. Example assessment tables from "Generate Tables."................................................ 35

Figure 29. Equation. SPF for example 1.............................................................................................................. 36

Figure 30. Image. Information in ‘Define Variables’ tab for example 1. ................................................. 37

Figure 31. Image. Calibration results from example 1.................................................................................. 38

Figure 32. Chart. CURE plot for outside shoulder width for example 1.............................................. 39

Figure 33. Chart. CURE plot for inside shoulder width for example 1................................................. 39

Figure 34. Chart. CURE plot for median width for example 1................................................................. 40

Figure 35. Chart. CURE plot for motorcycle AADT for example 1....................................................... 40

Figure 36. Chart. CURE plot for fitted (calibrated) values for example 1............................................ 41

Figure 37. Image. CURE plot assessment results for example 1............................................................... 41

Figure 38. Image. Assessment table results for example 1.......................................................................... 42

Figure 39. Equation. SPF for example 2.............................................................................................................. 43

Figure 40. Image. Information in ‘Define Variables’ tab for example 2. ................................................. 44

Figure 41. Image. Calibration results from example 2.................................................................................. 45

Figure 42. Image. CURE plot for major road AADT for example 2....................................................... 46

Figure 43. Image. CURE plot for minor road AADT for example 2....................................................... 47

Figure 44. Image. CURE plot for fitted (calibrated) values for example 2............................................ 47

Figure 45. Image. CURE plot assessment results for example 2............................................................... 48

Figure 46. Image. Assessment table results for example 2.......................................................................... 48

Figure 47. Equation. SPF for example 3.............................................................................................................. 49
THE CALIBRATOR—UPDATED USER GUIDE

vii

Figure 48. Image. Variable list on ‘Define Variables’ tab for example 3................................................. 49

Figure 49. Image. Selecting predefined SPFs for example 3........................................................................ 51

Figure 50. Image. Selecting predefined HSM SPF for example 3............................................................... 52

Figure 51. Image. Editing predefined HSM SPF for example 3................................................................... 53

Figure 52. Image. Calibration results for example 3 (based on calibration factor). .......................... 54

Figure 53. Image. State X CURE plot for fitted (calibrated) values for example 3 (based on 

constant calibration factor)...................................................................................................................................... 55

Figure 54. Image. AASHTOWare Safety AnalystTM CURE plot for fitted (calibrated) values for 

example 3 (based on constant calibration factor). ......................................................................................... 55

Figure 55. Image. HSM CURE plot for fitted (calibrated) values for example 3 (based on 

constant calibration factor)...................................................................................................................................... 56

Figure 56. Image. Calibration results for example 3 (based on calibration function)....................... 56

Figure 57. Image. State X CURE plot for fitted (calibrated) values for example 3 (based on 

calibration function).................................................................................................................................................... 57

Figure 58. Image. AASHTOWare Safety AnalystTM CURE plot for fitted (calibrated) values for 

example 3 (based on calibration function)......................................................................................................... 57

Figure 59. Image. HSM CURE plot for fitted (calibrated) values for example 3 (based on 

calibration function).................................................................................................................................................... 58

Figure 60. Equation. SPF for segments (HSM-RUR2U-KABCO).............................................................. 61

Figure 61. Equation. SPF for three-leg STOP controlled intersections (HSM-RUR2-3STKABCO).......................................................................................................................................................................... 61

Figure 62. Equation. SPF for four-leg STOP controlled intersections (HSM-RUR2-4ST-KABCO).

............................................................................................................................................................................................. 61

Figure 63. Equation. SPF for four-leg signalized intersections (HSM-RUR2-4SG-KABCO)........... 61

Figure 64. Equation. SPF for total crashes (HSM-RUR4U-KABCO). ...................................................... 62

Figure 65. Equation. SPF for KABC crashes (HSM-RUR4U-KABC). ...................................................... 62

Figure 66. Equation. SPF for KAB crashes (HSM-RUR4U-KAB)............................................................... 62

Figure 67. Equation. SPF for total crashes (HSM-RUR4D-KABCO)....................................................... 62
THE CALIBRATOR—UPDATED USER GUIDE

viii

Figure 68. Equation. SPF for KABC crashes (HSM-RUR4D-KABC). ...................................................... 62

Figure 69. Equation. SPF for KAB crashes (HSM-RUR4D-KAB). ............................................................. 63

Figure 70. Equation. SPF for total crashes (HSM-RUR4-3ST-KABCO). ................................................ 64

Figure 71. Equation. SPF for KABC crashes (HSM-RUR4-3ST-KABC).................................................. 64

Figure 72. Equation. SPF for KAB crashes (HSM-RUR4-3ST-KAB)......................................................... 64

Figure 73. Equation. SPF for total crashes (HSM-RUR4-4ST-KABCO). ................................................ 64

Figure 74. Equation. SPF for KABC crashes (HSM-RUR4-4ST-KABC).................................................. 64

Figure 75. Equation. SPF for KAB crashes (HSM-RUR4-4ST-KAB)......................................................... 64

Figure 76. Equation. SPF for total crashes (HSM-RUR4-4SG-KABCO). ............................................... 65

Figure 77. Equation. SPF for KABC crashes (HSM-RUR4-4SG-KABC)................................................. 65

Figure 78. Equation. SPF for KAB crashes (HSM-RUR4-4SG-KAB)........................................................ 65

Figure 79. Equation. SPF for MVNONDWY crashes.................................................................................... 66

Figure 80. Equation. SPF for KABC MVNONDWY crashes...................................................................... 66

Figure 81. Equation. SPF for PDO MVNONDWY crashes........................................................................ 66

Figure 82. Equation. SPF for SV crashes............................................................................................................. 68

Figure 83. Equation. SPF for KABC SV crashes............................................................................................... 68

Figure 84. Equation. SPF for PDO SV crashes.................................................................................................. 68

Figure 85. Equation. SPF for MVDWY crashes................................................................................................ 69

Figure 86. Equation. SPF for KABC MVDWY crashes. ................................................................................ 69

Figure 87. Equation. SPF for PDO MVDWY crashes.................................................................................... 69

Figure 88. Equation. SPF for MVINT crashes.................................................................................................... 72

Figure 89. Equation. SPF for KABC MVINT crashes..................................................................................... 72

Figure 90. Equation. SPF for PDO MVINT crashes........................................................................................ 72

Figure 91. Equation. SPF for SVINT crashes..................................................................................................... 73
THE CALIBRATOR—UPDATED USER GUIDE

ix

Figure 92. Equation. SPF for KABC SVINT crashes....................................................................................... 73

Figure 93. Equation. SPF for PDO SVINT crashes. ........................................................................................ 73

Figure 94. Equation. SPF for freeway KABC MV crashes............................................................................ 75

Figure 95. Equation. SPF for freeway PDO MV crashes............................................................................... 75

Figure 96. Equation. SPF for freeway KABC SV crashes.............................................................................. 76

Figure 97. Equation. SPF for freeway PDO SV crashes................................................................................ 76

Figure 98. Equation. SPF for ramp entrance KABC crashes....................................................................... 77

Figure 99. Equation. SPF for ramp entrance PDO crashes......................................................................... 77

Figure 100. Equation. SPF for ramp exit KABC crashes.............................................................................. 78

Figure 101. Equation. SPF for ramp exit PDO crashes................................................................................. 78

Figure 102. Equation. SPF for ramp segment KABC MV crashes............................................................. 79

Figure 103. Equation. SPF for ramp segment PDO MV crashes............................................................... 79

Figure 104. Equation. SPF for ramp segment KABC SV crashes. ............................................................. 81

Figure 105. Equation. SPF for ramp segment PDO SV crashes................................................................. 81

Figure 106. Equation. SPF for ramp terminal KABC MV crashes............................................................. 83

Figure 107. Equation. SPF for ramp terminal PDO MV crashes................................................................ 83

Figure 108. Equation. Safety AnalystTM SPF for segment total crashes................................................... 89

Figure 109. Equation. Safety AnalystTM SPF for segment KABC crashes. .............................................. 89

Figure 110. Equation. Safety AnalystTM SPF for intersection total crashes............................................ 89

Figure 111. Equation. Safety AnalystTM SPF for intersection KABC crashes........................................ 89
THE CALIBRATOR—UPDATED USER GUIDE

x 

LIST OF TABLES

Table 1. Example of categorical variable assessment..................................................................................... 16

Table 2. Summary of GOF measures for ranking SPFs................................................................................. 18

Table 3. Comparison of multiple SPFs (based on calibration factor)...................................................... 59

Table 4. Comparison of multiple SPFs (based on calibration function). ................................................ 60

Table 5. Coefficients for multiple-vehicle non-driveway segment SPFs................................................. 67

Table 6. Coefficients for single-vehicle segment SPFs................................................................................... 68

Table 7. Coefficients for multiple-vehicle driveway-related segment SPFs. ......................................... 70

Table 8. Coefficients for multiple-vehicle intersection SPFs. ..................................................................... 72

Table 9. Coefficients for single-vehicle intersection SPFs............................................................................ 73

Table 10. Coefficients for multiple-vehicle freeway segment SPFs.......................................................... 75

Table 11. Coefficients for single-vehicle freeway segment SPFs............................................................... 76

Table 12. Coefficients for ramp entrance speed-change lane SPFs. ........................................................ 77

Table 13. Coefficients for ramp exit speed-change lane SPFs.................................................................... 78

Table 14. Coefficients for multiple-vehicle ramp segment SPFs. .............................................................. 79

Table 15. Coefficients for single-vehicle ramp segment SPFs. ................................................................... 81

Table 16. Coefficients for ramp terminal SPFs................................................................................................. 83

Table 17. Coefficients for AASHTOWare Safety AnalystTM SPFs........................................................... 90
THE CALIBRATOR—UPDATED USER GUIDE

xi 

LIST OF ACRONYMS

AADT Annual average daily traffic

AADTMAJ Average annual daily traffic on major road

AADTMIN Average annual daily traffic on minor road

AASHTO American Association of State Highway and Transportation Officials

AIC Akaike’s Information Criterion 

BIC Bayesian Information Criterion

CMF Crash Modification Factor

CURE Cumulative residuals

CV Coefficient of variation

DCMF Development of Crash Modification Factors

FHWA Federal Highway Administration

GOF Goodness-of-fit

HSM Highway Safety Manual

k Dispersion

KABCO Refers to a scale that is used to represent injury severity in crash 

reporting: K is fatal injury, A is serious injury, B is minor injury, C is 

possible injury, and O is property damage only.

MAD Mean absolute deviation

NCHRP National Cooperative Highway Research Program

ODOT Oregon Department of Transportation

PDO Property damage only

SPF Safety Performance Function

V Variance

V(C) Variance of the calibration factor
THE CALIBRATOR—UPDATED USER GUIDE

1 

1. INTRODUCTION

Safety Performance Functions (SPFs) and Crash Modification Factors (CMFs) are integral parts 

of the Highway Safety Manual (HSM) methods for estimating the expected number of crashes 

for a given site. SPFs and CMFs are available from a number of sources, including the HSM, CMF 

Clearinghouse, AASHTOWare Safety AnalystTM, and State-specific reports. While SPFs and 

CMFs are widely available, they are produced using data from specific locations and times. For 

various theoretical and practical reasons, SPFs and CMFs may not be directly transferable 

across jurisdictions or over time within the same jurisdiction. As such, SPFs and CMFs may not 

be nationally applicable in their raw form. For example, SPFs and CMFs are intended for 

application under certain conditions, including factors related to how the crash data are coded. 

If data for a given time and place do not meet the same standard or if the conditions differ from 

those used to develop the SPF or CMF, then it is necessary to calibrate the SPFs and/or CMFs.

The Calibrator is a spreadsheet-based tool to help users assess SPF and CMF compatibility and 

applicability, and to calibrate SPFs and CMFs for application in a different time or place. The 

tool is applicable to all SPFs or predictions from the combination of SPFs and CMFs as is 

consistent with the HSM Part C Predictive Method. The tool provides the option of calculating 

a single calibration factor or calculating a unique factor for each site based on a calibration 

function for each SPF or SPF and CMF combination. The tool also provides various goodnessof-fit measures and an assessment of how the predictions are performing over the range of all 

variables in the SPF and CMFs applied.

The audience for the tool and this user guide are road safety practitioners responsible for 

developing new SPFs or calibrating existing SPFs to data from their jurisdiction. The tool is 

intended to automate the calibration process and provide information to users that will allow 

them to assess the suitability of one or more SPFs or to compare between alternate SPFs. 

Specifically, the tool can help users to complete the following:

• Assess the performance of the HSM Predictive Method as a whole on local data.

• Assess the performance of the uncalibrated HSM Part C SPFs on local data.

• Assess the performance of SPFs and CMFs from other sources on local data.

• Calibrate existing SPFs to local data using the HSM calibration procedure.

• Calibrate the dispersion parameter of an existing SPF to local data.

• Compare the performance of multiple SPFs.

• Identify the most appropriate SPFs and CMFs to apply from a list of alternatives. 

Note: The tool is NOT for developing original SPFs, creating the required datasets for calibration, or 

calibrating standalone CMFs.

This user guide provides directions for using the tool and illustration of its application through 

screenshots and examples using real data. It is intended to accompany the application of the 

tool. To facilitate that application, the user guide provides a brief background on the theory of 

SPF calibration, goodness-of-fit measures, and SPF selection. The guide draws on content from 
THE CALIBRATOR—UPDATED USER GUIDE

2 

the following six key resources, and users of the tool are encouraged to read the first three 

prior to using the tool.

1. The Highway Safety Manual, First Edition, Volume 2, Appendix A.

(1) This 

appendix addresses the calibration of the Part C predictive SPFs.

2. User’s Guide to Develop Highway Safety Manual Safety Performance 

Function Calibration Factors.

(2)

This project provides guidance for assessing the 

quality of a calibration factor. Relevant content includes guidance on preparing for 

calibration and on collecting data, a discussion of minimum sample sizes for reliable 

calibration factors, and guidance on when to split up the calibration dataset and estimate 

separate factors, for example, for different regions or terrain types.

3. Safety Performance Function Decision Guide: SPF Calibration vs. SPF 

Development.

(3) This guidebook discusses the factors that need to be considered 

while making the decision of whether to calibrate an existing SPF or develop a new SPF.

4. Safety Performance Function Development Guide: Developing JurisdictionSpecific SPFs.

(4) This guidebook provides the state of the knowledge on what data, 

expertise, tools, and other resources are required to develop jurisdiction-specific SPFs. 

5. The Art of Regression Modeling in Road Safety.

(5) This book provides instruction 

on how to fit and assess a multivariable statistical SPF to cross-sectional safety data using 

a simple spreadsheet.

6. Estimation of Calibration Functions for Predicting Crashes on Rural TwoLane Roads in Arizona.

(6) This paper discusses the development of a calibration 

function. 
THE CALIBRATOR—UPDATED USER GUIDE

3 

2. BACKGROUND ON SPF CALIBRATION

WHY CALIBRATE?

As stated in the User’s Guide to Develop Highway Safety Manual Safety Performance Function 

Calibration Factors, the use of SPFs in any jurisdiction calls for a calibration of such SPFs, and for 

the replacement of any default crash distributions applied to local and current conditions.(2)

Calibration is required because SPFs are developed using data associated with a single or select 

group of jurisdictions and for a specific time period. If applied to another jurisdiction, or to 

another time period, the predictions may be biased. The purpose of calibration is to ensure that 

this bias is tolerably small. The bias may arise from differences in several factors, including the 

following: 

• Crash reporting practices (e.g., minimum reporting thresholds). 

• Socio-demographic characteristics of the driving population. 

• Weather. 

• Roadway maintenance practices. 

• Other factors affecting crash risk, which are not represented in the SPF and which may 

differ by location or over time.

For the same reason, it is appropriate to replace any default crash distributions and adjustment 

factors, such as those found in the HSM, using jurisdiction-specific data for the same years as 

the jurisdiction-specific SPF calibration factors.(1)

Since the publication of the HSM, several State transportation departments have engaged in 

projects to develop calibration factors for HSM SPFs using their own data, such as Oregon, 

Illinois, Virginia, Washington, Louisiana, and Missouri.(2) The results of a study by the Oregon 

Department of Transportation (ODOT) highlighted the critical need to calibrate SPFs. The use 

of uncalibrated SPFs from Part C of the HSM would have over-estimated total crashes for most 

facilities in Oregon. The estimates would have been biased by 25 percent in the case of rural 

two-lane roadway segments and more than 80 percent for four-legged signalized intersections 

on rural multilane highways. Biases in uncalibrated SPFs may lead to suboptimal decisions when 

selecting sites for investigation, identifying safety strategies, or evaluating design alternatives.

METHODOLOGY FOR CALIBRATION

The calibration of an SPF includes two components: the estimation of a calibration factor or 

function and the estimation of the dispersion parameter or function. A calibration factor serves

as a multiplier to adjust the original SPF estimate. For example, a calibration factor of 1.25 

would increase the original SPF estimate by 25 percent, indicating that the uncalibrated SPF is 

under-predicting crashes. A calibration function is an equation that provides a unique calibration 

factor for each site, the values of which are dependent on the site-specific variables included in 

the equation. The calibrated dispersion parameter is applicable if the SPF was developed using a 

negative binomial error distribution assumption. The dispersion parameter is required for use 

of the Empirical Bayes procedure presented in the HSM. A dispersion function is an equation 
THE CALIBRATOR—UPDATED USER GUIDE

4 

that provides a unique dispersion parameter for each site, the values of which are dependent on 

the site-specific variables included in the equation.

Figure 1 shows the five-step procedure for calibrating an SPF. 

Figure 1. Chart. Calibration process. 

To compute a calibration factor, first apply the existing SPF to estimate the predicted crashes 

for each site in the calibration dataset. Then, sum both the observed and predicted crashes 

over all sites. Figure 2 shows the equation for computing the calibration factor. Finally, apply the 

calibration factor as a multiplier to the existing SPF for application (i.e., SPFcalibrated = C * 

SPFexisting). 

Figure 2. Equation. Calibration factor. 

Where: 

C = estimate of calibration factor for SPF of a given facility type.
THE CALIBRATOR—UPDATED USER GUIDE

5 

To compute a calibration function, fit a negative binomial regression model to the calibration 

data with the observed crashes as the dependent variable and the uncalibrated SPF estimates 

for each site as the predictor variable. In so doing, estimate the two parameters, a and b, as 

shown in Figure 3. 

Figure 3. Equation. Calibration function.

It is also logical to calibrate the dispersion parameter as this not only indicates how well the 

calibrated SPF fits the data, but also facilitates the use of the Empirical Bayes methodology. The 

dispersion parameter may be a constant value or a function of site characteristics. In the HSM

first edition, all dispersion parameters are either constant or a function of segment length. The 

form (i.e., constant or function) and value of the dispersion parameter are typically provided 

with the existing SPF. The discussion to follow will refer to the dispersion parameter as f(k), 

indicating that it is a function which may or may not be a constant.

Calibrating the dispersion parameter occurs through a maximum likelihood procedure, which 

determines the most likely dispersion parameter value that maximizes the negative binomial 

likelihood function (5). The spreadsheet tool can calibrate a constant dispersion parameter, k, or 

one that varies by length (for road segments). Figure 4 shows the equation for a variable 

dispersion parameter that is a linear function of length. Figure 5 shows the equation for a 

variable dispersion parameter that is a nonlinear function of length.

Figure 4. Equation. Variable dispersion as linear function of length. 

Figure 5. Equation. Variable dispersion as nonlinear function of length.

Where:

k, c, and d = estimated parameter. 

length = length of road segment. 

While analysts can select any of the optional dispersion parameter forms within The Calibrator 

when estimating a calibration factor or calibration function, it is suggested to use the same 

dispersion parameter form as the existing SPF. If the SPF of interest uses a dispersion 

parameter form other than one of those provided, then it is suggested to use a constant 

dispersion parameter form. At the time of this publication, The Calibrator software includes 

dispersion parameter forms to accommodate all SPFs included in the HSM first edition and 

AASHTOWare Safety AnalystTM.
THE CALIBRATOR—UPDATED USER GUIDE

6 

GUIDANCE ON PREPARING DATA FOR CALIBRATION

The development of calibration factors requires data for observed crashes, exposure (traffic 

volume), and any roadway characteristics included in the SPF or that define the facility types to 

which the SPF pertains (e.g., four-legged, rural, signalized intersections). To use the 

spreadsheet-based calibration tool, the data are required to be in a specified format prior to 

importing into the tool. The section titled, Using the Tool, provides further details on the 

required data format. 

There are three key aspects of data preparation: 1) selecting sites for calibration, 2) dealing 

with outliers, and 3) comparing the range of calibration data. The following sections provide an 

overview of these three aspects of data preparation. The tool itself does not directly 

accomplish these aspects and thus the content provided here is merely to illuminate the issues 

involved.

Selecting Sites for Calibration

The SPF Decision Guide: SPF Calibration vs. SPF Development discusses the development of a 

calibration dataset.(3) Step 2 of that process is the selection of sites for calibration. The guide 

indicates that sites should represent the intended application of the SPF(s). Two applications 

include network screening and before-after studies.

• Network Screening: If the intended application of the calibrated SPF is for network 

screening, then the calibration dataset should represent the network considered for

screening. Further, analysts may desire multiple calibration factors to account for 

regional or jurisdictional differences in data. This decision depends on the variation in 

terrain, climate, crash reporting practices, driver population, animal population, and 

other factors among the regions or jurisdictions. 

• Before-After Study: If the analyst intends to use the calibrated SPF in a before-after 

study or an analysis that only applies to a select group of sites defined by specific 

characteristics of interest, then the calibration dataset should only comprise those sites. 

For example, if the calibrated SPF is to be used in an empirical Bayes before-after study 

of installing centerline rumble strips on curves on two-lane rural roads, then the original 

SPF and reference group used for SPF calibration should include curves without 

centerline rumble strips on two-lane rural roads. The reference sites used for 

calibration should match the treated sites on other characteristics such as traffic 

volume, lane width, and roadside conditions. 

Randomization is another consideration in selecting appropriate sites for the calibration dataset. 

In general, it is preferred to use all sites within the population to calibrate network-level SPFs 

such as those in AASHTOWare Safety AnalystTM. Network-level SPFs require limited data (i.e., 

observed crashes, traffic volume, and segment length), which are typically available for all sites 

across the network. To calibrate SPFs from Part C of the HSM, and others that require detailed

data, it is often necessary to use a sample because the detailed data are not available on a 

network-wide basis. The aspect of selecting sites randomly is important because calibration 

factors will likely differ for various subsets of the facility type. For example, the calibration 
THE CALIBRATOR—UPDATED USER GUIDE

7 

factors will likely differ for subsets from different regions or subsets with different traffic 

volume ranges. Since the dependence of the calibration factor to these elements is unknown, 

the only way to ensure a sample is representative is to select units by some random process. 

Dealing with Outliers

Outliers can influence the calibration estimates and result in misleading or incorrect findings. As 

such, users should perform basic data quality checks before calibration. Quality checks include

plotting the data (e.g., X-Y plots, boxplots, and distribution plots) and calculating distributional 

statistics for each variable (dependent and independent). Values of predictor variables that are 

far outside the range of typical values for that variable could be considered leverage points and 

should be investigated. Looking at crash rates (e.g., crashes per million vehicle miles traveled) 

across specific groups of segments will highlight unusual crash rates and crash counts. Analysts 

should exclude extreme observations from the data unless they can verify and correct obvious 

errors. Hauer proposes a method to identify outliers that involves looking for a vertical “jump” 

in the cumulative residuals (CURE) plot.(7) Users are also encouraged to read the SPF 

Development Guide: Developing Jurisdiction-Specific SPFs prior to calibrating an existing SPF. While

it focuses on developing original SPFs, it discusses the elimination of outliers and other data 

quality control issues that would bias the estimates if not accounted for.(4) 

Comparing the AADT Range of Calibration Data

Another important consideration during data assembly is the range of traffic volumes and other 

variables used in the initial development of the SPFs. Applying SPFs to sites with variables 

significantly outside the range of those in the existing SPF may not provide reliable results. As 

such, analysts should assemble sufficient data in the desired range. If traffic volumes for local 

sites are significantly outside the range volumes applicable to the existing SPFs, then an agency 

may consider developing their own SPFs. As an approximation, and an alternative to developing 

jurisdiction-specific SPFs, an agency may consider developing separate calibration factors, one 

for the data within the range of the original SPF and another for the data outside of this range. 

For example, if the existing SPF represents sites with traffic volumes between 10,000 and 

20,000 vehicles per day, but some of the sites in question represent traffic volumes less than 

10,000, then the analyst may develop two separate calibration factors; one for sites with 

volumes less than 10,000 and a second for sites with volumes greater than 10,000 vehicles per 

day. Appendix D of the User’s Guide to Develop Highway Safety Manual Safety Performance 

Function Calibration Factors provides guidance on when to estimate separate calibration factors 

for subsets of data including subsets grouped by AADT.

(2)

MINIMUM SAMPLE SIZES

Sample size refers to the number of sites and number of crashes in the data used for 

calibration. If either few sites or few crashes are used, then the calibration may not be reliable. 

The HSM(1) provides guidance on the required sample size, but this is based on experience 

rather than science. Several research reports show that larger sample sizes are usually required 

for common facility types.(8-11) The User’s Guide to Develop Highway Safety Manual Safety 

Performance Function Calibration Factors Appendix B provides additional guidance on estimating 
THE CALIBRATOR—UPDATED USER GUIDE

8 

required minimum sample sizes for a calibration dataset.(2) The guidance details how to estimate 

the standard error and coefficient of variation of the calibration factor and provides guidance 

on acceptable ranges for the coefficient of variation. 

NCHRP Project 17-62, Improved Prediction Models for Crash Types and Crash Severities, provides

an updated HSM calibration procedure. The procedure estimates the sample size iteratively, 

starting with an available sample that is at least as large as that recommended in the HSM. The 

next step is to estimate and assess a constant calibration factor, which analysts can achieve by 

using The Calibrator tool. If the assessment indicates that the sample is insufficient, then there 

is a need to assemble data for additional sites and re-estimate the calibration factor. This 

continues until the analyst achieves a successful calibration. As a further step, there is an 

opportunity to estimate and assess a calibration function with the final sample. 

In addition, if the analyst is calibrating a dispersion parameter as a function of site characteristics

(i.e., a variable dispersion parameter), then a larger sample may be required than for calibrating 

a constant dispersion parameter. If it is not practically feasible to assemble the suggested 

minimum sample, then it may still be acceptable, with appropriate cautions, to attempt a 

calibration exercise. This was successfully done for calibrations in Oregon, Louisiana, and 

Italy.(12-14)

 For fatal and injury collisions, smaller samples may suffice, given that fatal and injury 

collision data are more reliable than those that include property damage only crashes.(14)

MULTIPLE CALIBRATION FACTORS

It may be appropriate to develop separate calibration factors for large regions with stark 

differences in terrain, climate, driver population, and other factors that can influence crashes. 

This is similar to the issue related to the range of traffic volumes described above in the section 

titled, Comparing the AADT Range of Calibration Data. Appendix D of the User’s Guide to Develop 

Highway Safety Manual Safety Performance Function Calibration Factors provides guidance on when 

to estimate separate calibration factors for subsets of data.(2) Users of The Calibrator are 

encouraged to read both Appendices B and D of that Guide for further guidance on developing 

calibration factors.(2) The following paragraph is merely a summary of the issues raised in that 

Guide. The tool itself does not address these issues; however, it can estimate separate 

calibration factors for subsets of data grouped by levels of a categorical variable or imported as 

separate datasets. 

As the Guide notes, the HSM suggests, “For large jurisdictions, such as entire states, with a 

variety of topographical and climate conditions, it may be desirable (to) develop separate 

calibration factors for each specific terrain type or geographical region.”(1) The underlying 

rationale, according to the Guide, is that calibration factors may differ from terrain to terrain, 

region to region or, more generally, from condition to condition. For example, if there is a 

large difference between the calibration factors for statewide and mountainous conditions, then 

applying the statewide factor to a site located in the mountainous terrain will introduce bias in 

the estimate of the number of crashes expected at that site. 
THE CALIBRATOR—UPDATED USER GUIDE

9 

While the calibration factor can vary across a jurisdiction, there is a practical limit to the 

number of separate calibration factors. As noted in the Guide, how many separate calibration 

factors to estimate depends on two considerations:

1. How close is close enough? Should the difference between the calibration factors be 

within ±10 percent of the calibration factor for the conditions of the site or is ±50 

percent acceptable? 

2. How different are the calibration factors in different conditions? For example, is the 

ratio of the mountainous to statewide calibration factors 1.5 or only 1.05?

INTERPRETATION OF THE CONSTANT CALIBRATION FACTOR

If the sum of the SPF crash predictions in the calibration sample match exactly to the sum of 

the observed crashes, then the process produces a constant calibration factor of 1.0. If the SPF 

under-predicts crashes in the calibration sample, then the calibration factor is greater than 1.0. 

If the SPF over-predicts crashes in the calibration sample, then the calibration factor is less than 

1.0. If the calibration factor is substantially different from 1.0 (i.e., much less or much greater), 

then the agency’s crash experience is much different from the data that were used to estimate 

the original SPF. If the differences are only in the magnitude of crash frequencies, and not the 

form of the distribution, then a calibrated SPF can still perform quite well. The SPF Decision 

Guide: SPF Calibration vs. SPF Development discusses the need to assess the quality of the 

calibration process in addition to the magnitude of the calibration factor.(3)

 

Where the calibration factor is a single multiplier, users need to assess how well the calibrated 

SPF performs in terms of explaining the variability of crash frequency among sites. Various 

goodness-of-fit (GOF) measures are available for this assessment in deciding if the SPF 

calibration is acceptable or in comparing multiple SPFs to determine which is most acceptable 

for calibration. As noted earlier, there is an opportunity to estimate a calibration function once 

the analyst deems an SPF acceptable based on a constant calibration factor. This will 

theoretically improve the SPF performance in terms of explaining the variability of crash 

frequency among sites.

The following section elaborates on GOF measures and their use in assessing the quality of the 

calibration process. Further guidance on assessing the quality of the calibration factor is 

available in the User’s Guide to Develop Highway Safety Manual Safety Performance Function 

Calibration Factors and the SPF Development Guide: Developing Jurisdiction-Specific SPFs.

(2,4) For more 

advanced information, consult The Art of Regression Modeling in Road Safety.

(5) 
THE CALIBRATOR—UPDATED USER GUIDE

10 

3. GOODNESS-OF-FIT MEASURES

This section provides a summary of the GOF measures available in the spreadsheet-based 

calibration tool, including the mean absolute deviation, modified R2

, dispersion parameter, 

coefficient of variation (CV) of the calibration factor, and cumulative residual (CURE) plots. It is 

relatively straightforward to use these GOF measures to compare the relative performance of

competing SPFs considered for application. More challenging is the use in assessing whether a 

single SPF is adequate as there are no guidelines on acceptable thresholds except for the CV of 

the calibration factor and the CURE plot. Thus, some subjective judgment is required to

supplement the assessment based on the CV with a consideration of the other GOF measures. 

MEAN ABSOLUTE DEVIATION

Figure 6 provides the equation for the mean absolute deviation (MAD), which provides a 

measure of the average magnitude of variability of prediction. Smaller values are preferred to 

larger values in comparing two or more competing SPFs. The MAD is the sum of the absolute 

value of predicted minus observed crashes, divided by the number of sites. The values of 

predicted and observed crashes are from the calibration data. 

Figure 6. Equation. Mean absolute deviation.

Where:

yyii = observed counts. 

yy�ıı = predicted values from the SPF. 

n = validation data sample size. 

MODIFIED R2

Figure 7 shows the equation for the modified R2 value.

(15) This GOF measure subtracts the 

normal amount of random variation expected if the SPF were 100 percent accurate. Even with a 

perfect SPF, some variation in observed crash counts would be observed due to the random 

nature of crashes.(15) As a result, the amount of systematic variation explained by the SPF is 

measured. Larger values indicate a better fit to the data in comparing two or more competing 

SPFs. Values greater than 1.0 indicate the SPF is over-fit (i.e., the SPF is incorrectly explaining 

some of the expected random variation as systematic variation). 

Figure 7. Equation. Modified R2 value. 
THE CALIBRATOR—UPDATED USER GUIDE

11 

Where: 

yyii = observed counts. 

yy�ıı = predicted values from the SPF. 

yy�= sample average. 

μμ�ıı = yyii-yy�ıı.

DISPERSION PARAMETER

The dispersion parameter, f(k), in the negative binomial distribution is reported from the 

variance equation. Figure 8 provides the variance equation, rearranged in Figure 9 to provide 

the equation for the dispersion parameter.

Figure 8. Equation. Variance of negative binomial distribution.

Figure 9. Equation. Dispersion parameter.

Where: 

f(k) = estimated dispersion parameter.

Var{m} = estimated variance of mean crash rate. 

E{m} = estimated mean crash rate. 

The estimated variance increases as dispersion increases, and consequently the standard errors 

of estimates are inflated. As a result, all else being equal, an SPF with less dispersion (i.e., 

smaller values of f(k)) is preferred to an SPF with more dispersion. Note that f(k) can be 

specified as a constant or as a function of site characteristics. The tool facilitates the estimation 

of the dispersion parameter, either as a constant or from a function, as one GOF measure.

COEFFICIENT OF VARIATION OF THE CALIBRATION FACTOR

For a constant calibration factor, analysts can use the CV of the calibration factor to assess the 

GOF. Figure 10 provides the equation for the CV of a constant calibration factor, which is the 

standard deviation of the calibration factor divided by the estimate of the calibration factor. 

Figure 10. Equation. Coefficient of variation of a constant calibration factor. 
THE CALIBRATOR—UPDATED USER GUIDE

12 

Where:

CV = coefficient of variation of the calibration factor. 

V(C) = variance of the calibration factor. 

C = estimate of the calibration factor. 

Figure 11 shows the equation for the variance of the calibration factor [V(C)]. The standard 

deviation of the calibration factor is the square root of the variance.

Figure 11. Equation. Variance of calibration factor. 

Where:

yyii = observed counts.

yy�ıı = uncalibrated predicted values from the SPF.

k = dispersion parameter (recalibrated).

Appendix B of the User’s Guide to Develop Highway Safety Manual Safety Performance Function 

Calibration Factors provides guidance on estimating the accuracy of a calibration factor using the 

CV.(2) This guidance is intended for application in assessing the sample size of the calibration 

dataset; however, it seems reasonable to also apply it to assess the accuracy of a calibration 

factor regardless of the sample size.(2)

The Guide suggests that a reasonable upper threshold for the CV is 0.10 to 0.15. Users of the 

calibration tool can apply this threshold to assess whether or not the SPF, and the estimated 

calibration factor based on the calibration dataset, are acceptable. If the CV exceeds this

threshold, then analysts should review the cumulative residual plots, described in the following 

subsection, to determine if the SPF is acceptable. In any case, analysts can use the CV for 

comparative evaluation of two or more SPFs where smaller values are preferred to larger 

values.

CUMULATIVE RESIDUAL PLOTS

Another tool to assess GOF is the CURE plot. A CURE plot is a graph of the cumulative 

residuals (observed minus predicted crashes) against a variable of interest sorted in ascending 

order (e.g., major road traffic volume). CURE plots provide a visual representation of GOF

over the range of a given variable, and help to identify potential concerns such as the following: 
THE CALIBRATOR—UPDATED USER GUIDE

13 

• Long trends: long trends in the CURE plot (increasing or decreasing) indicate regions 

of bias that analysts should rectify through improvement to the SPF either by the 

addition of new variables or by a change of functional form. 

• Percent exceeding the confidence limits: cumulative residuals outside the 

confidence limits indicate a poor fit over that range in the variable of interest. 

Cumulative residuals frequently outside the confidence limits indicate notable bias in the 

SPF. The upper threshold for the percent of cumulative residuals exceeding the 95 

percent confidence limits is five percent. 

• Vertical changes: Large vertical changes in the CURE plot are potential indicators of 

outliers, which require further examination. For further discussion of outliers, see the 

prior section titled, Dealing with Outliers. More advanced users can consult Chapter 7 of 

Hauer’s book, The Art of Regression Modeling in Road Safety, in this regard.

(5)

The tool constructs CURE plots through the following nine steps: 

1. Sort sites in ascending order of the variable of interest, such that N is the number of 

sites, n is an integer between 1 and N, and S(n) is the cumulative sum of residuals from 

1 to n.

2. For each site, calculate the residuals, res, as the observed minus predicted crashes.

3. For each site, calculate the cumulative residuals, S(n), as the sum of residuals from 1 to 

n. 

4. For each site, calculate the squared residuals, res2

. 

5. For each site, calculate the cumulative squared residuals, σ2

(n), as the sum of squared 

residuals from 1 to n.

6. Sum the cumulative squared residuals over all sites to compute the sum of cumulative 

squared residuals, σ2

(N). 

7. For each site, estimate the variance of the random walk, σ2

, using the equation in Figure 

12. 

Figure 12. Equation. Variance of random walk. 

8. For each site, calculate the 95 percent confidence limits using the equations in Figure 13

and Figure 14. 

Figure 13. Equation. Lower 95 percent confidence limit.

Figure 14. Equation. Upper 95 percent confidence limit.

9. Plot the cumulative residuals, S(n), and the 95 percent confidence limits on the y-axis 

against the explanatory variable of interest on the x-axis. 
THE CALIBRATOR—UPDATED USER GUIDE

14 

Figure 15 shows an example CURE plot for the variable indicating major road traffic volume at 

an intersection. In this example, the SPF performs relatively well based on the general pattern 

and the 95 percent confidence interval. The pattern shows the cumulative residuals oscillating 

above and below zero. Note that a sustained increasing or decreasing trend would indicate a 

range of under- or over-prediction, respectively. In this example, the cumulative residuals also 

remain within the 95 percent confidence limits over most of the range, only exceeding the 

confidence limits for a short range of lower AADT. The areas outside the confidence limits 

indicate a poor fit as indicated in the figure. Cumulative residuals frequently outside the 

confidence limits would indicate notable bias in the SPF. Another notable observation is the 

sharp increase in the value of cumulative residuals at an AADT of approximately 175,000

vehicles per day. This may indicate the presence of an outlier in the data.

Figure 15. Chart. Example CURE plot.

The calibration tool automatically provides a CURE plot similar to Figure 15 for fitted values 

(after applying the calibration factor(s)), and allows a user to choose any other available 

continuous variable for the x-axis. The tool calculates the maximum deviation as well as the 

percent of observations outside the 95 percent confidence limits. With this information, users 

can follow the procedure in Hauer’s book to determine whether an SPF is acceptable and in 

comparing multiple SPFs.

(5) 

While the guidance provided by Hauer for making these decisions is useful for users of the tool, 

it is largely subjective. The most objective consideration is a review of the CURE plot and 95 

percent (2σ) confidence limits. As Hauer notes, “inasmuch as the CURE plot is a sum of many 

independent random variables, it is approximately normally distributed. For a normal 

distribution, about 95% of the probability mass is within two standard deviations from the 

mean. Thus, the CURE plot for an ‘everywhere unbiased’ SPF should only rarely go beyond the 

2σ limits.” Hauer’s book (p. 150) also mentions, "the overall fit of the SPF is best judged by the 

CURE plot for fitted values".

(5) Thus, for users of the calibration tool, the following are general 
THE CALIBRATOR—UPDATED USER GUIDE

15 

rules for assessing the percent of the CURE plot exceeding the 95 percent (2σ) confidence 

limit: 

1) An upper threshold of five percent of CURE plot ordinates for fitted values (after 

applying the calibration factor(s)) exceeding 2σ limits is indicative of an SPF that 

calibrates well to the entire range of a jurisdiction’s data. 

2) If the CURE plot exceeds the 95 percent confidence limits by more than five percent, 

then the analyst should consider the CV of the constant calibration factor. If the CV is 

within acceptable limits, then the SPF may be acceptable for application, with due 

recognition for ranges of variables where significant bias is indicated.

Analysts can also use the percent of CURE plot ordinates for fitted values (after applying the 

calibration factor) exceeding the 2σ limits to compare two or more competing SPFs where 

lower values of ‘percent exceeding’ are preferred. 

AKAIKE’S INFORMATION CRITERION (AIC)

Figure 16 shows the equation for the AIC. The AIC penalizes for the addition of parameters, 

and thus helps to select an SPF that fits well, but has a minimum number of parameters. AIC is 

not typically used as a GOF measure, but analysts can use the AIC to compare the relative fit of 

alternate SPFs. Smaller values are preferred to larger values in comparing two or more 

competing SPFs. 

Figure 16. Equation. Akaike’s Information Criterion (AIC). 

Where:

K = number of estimated parameters included in the SPF (i.e., number of variables plus 

the intercept).

Loglikelihood = statistical output reflecting the overall SPF fit (larger values indicate a 

better fit). 

SCHWARZ BAYESIAN INFORMATION CRITERION (BIC)

Figure 17 shows the equation for the BIC. The BIC is complementary to AIC in that it also 

penalizes for the addition of parameters, and thus selects an SPF that fits well, but has a 

minimum number of parameters. BIC is not typically used as a goodness of fit measure, but 

analysts can use the BIC to compare the relative fit of alternate SPFs. Smaller values are 

preferred to larger values in comparing two or more competing SPFs. 

Figure 17. Equation. Schwarz Bayesian Information Criterion (BIC). 
THE CALIBRATOR—UPDATED USER GUIDE

16 

Where:

K = number of estimated parameters included in the SPF (i.e., number of variables plus 

the intercept).

Loglikelihood = statistical output reflecting the overall SPF fit (larger values indicate a 

better fit). 

ASSESSMENT TABLES

While the CURE plot method works well for continuous variables, it is not applicable to 

variables with few categories (e.g., a database with speed limits of 45, 55, and 65 mph). For such 

variables, it is useful to develop a table of “calibration bias factors” that include factors for each 

category of the variable as in the example below. Calibration bias factors are the sum of the 

observed crashes for the category divided by the sum of the predictions obtained when the 

calibration factor is applied. If this bias factor is less than 1.0, then the calibrated SPF is overpredicting for the category. If this bias factor is greater than 1.0, then the calibrated SPF is 

under-predicting. Analysts can use these bias factors for the comparative assessment of two or 

more SPFs in conjunction with CURE plots for other measures.

In the example in Table 1, there are three categories of speed limit with corresponding

observed crashes and calibration factors. As shown by the calibration factors, the SPF is overpredicting crashes at lower speed limits and under-predicting crashes at higher speed limits.

Table 1. Example of categorical variable assessment. 

Variable 45 mph 55 mph 65 mph

Observed crashes 200 320 275 

Number of sites 30 35 40 

Calibration bias factor 0.85 1.05 1.15 

Analysts can use an assessment table to identify categories or levels of a given variable for 

which there is concern about the quality of the calibration process. Calibration bias factors less 

than 0.8 or greater than 1.2 indicate potential areas of concern, providing these factors are 

based on at least 100 crashes.
THE CALIBRATOR—UPDATED USER GUIDE 

17 

SUMMARY OF SPF ASSESSMENT 

This section provides a quick reference summary of the key considerations in SPF assessment. 

Given a single SPF, analysts can use the CURE plot and the CV of a constant calibration factor 

to determine whether the calibrated SPF is acceptable. Given the choice from multiple SPFs, 

analysts can use several GOF measures to determine the most suitable SPF for the local 

dataset, and subsequently consider the CURE plot and CV of the constant calibration factor to 

determine if the preferred SPF is acceptable. The Calibrator generates these GOF measures, 

but it does not indicate the preferred SPF or acceptability given the need for further research in 

this area. 

Assessing the Acceptability of an SPF 

An analyst may deem an SPF with a constant calibration factor as acceptable if either of the 

following conditions is met: 

1) Five percent or less of CURE plot ordinates for fitted values (after applying the 

calibration factor) exceed the 2σ limits, or 

2) The CV of a constant calibration factor is less than 0.15. 

The analyst should then estimate a calibration function that provides a unique calibration factor 

for each site. The analyst may deem the function preferable if either of the above conditions is 

met (i.e., the calibrated SPF is acceptable based on a constant calibration factor) and the 

percent of CURE plot ordinates for fitted values (after applying the unique calibration factors) 

exceeding the 2limits is lower than that for the constant calibration factor. It is likely that the 

function will then be preferable by other assessment measures (MAD, AIC, BIC). 

As a caution, if the analyst does not deem the constant calibration factor as acceptable, but a 

calibration function shows less than five percent of CURE plot ordinates for fitted values 

exceeding the 2limits, this may be due to a small number of sites or crashes in the calibration 

dataset. Consider the sample size before adopting the calibration function. If there is a large 

sample, then the calibration function may be acceptable. 

If both conditions above are not met, consider increasing the calibration sample. If, with the 

largest feasible calibration sample, both conditions above are still not met for the constant 

calibration factor, and the first condition is not met with the calibration function, then the 

analyst should consider calibrating another existing SPF or developing a jurisdiction-specific SPF.

Comparing Multiple SPFs 

Table 2 presents seven measures for comparing the performance of multiple SPFs. For this 

comparison, the analyst must first estimate a constant calibration factor for each SPF. For each 

measure, the analyst can rank the SPFs numerically from 1 to n, where 1 represents the best 

SPF with respect to the given measure and n represents the number of alternative SPFs. To 

determine the aggregate ranking based on all seven measures, an analyst may sum the numeric 

rankings over the seven measures. The SPF with the lowest sum of ranks is the preferred SPF 

for calibration to a jurisdiction’s data. The analyst may then refine the preferred SPF based on a 
THE CALIBRATOR—UPDATED USER GUIDE

18 

constant calibration factor by estimating a calibration function and assessing the SPF 

performance with this refinement. Note that there is still a need to determine if the preferred 

SPF is acceptable as outlined above based on the CURE plot and CV for the calibration factor

or the CURE plot for the calibration function.

Table 2. Summary of GOF measures for ranking SPFs.

GOF Measure Preferred Values Ranking Method

Mean Absolute Deviation (MAD) Smaller values Smallest value is 

ranked number 1 

Modified R2 Larger values Largest value is 

ranked number 1 

Constant Dispersion Parameter* Smaller values Smallest value is 

ranked number 1 

Coefficient of variation of the constant calibration factor 

(CV) Smaller values Smallest value is ranked number 1 

Percent of CURE plot ordinates for fitted values (after 

calibration) exceeding 2σ limits Smaller values Smallest value is 

ranked number 1 

Akaike’s Information Criterion (AIC) Smaller values Smallest value is 

ranked number 1 

Bayesian Information Criterion (BIC) Smaller values Smallest value is 

ranked number 1 

* Criterion is only considered where all original candidate SPFs have a constant dispersion parameter.
THE CALIBRATOR—UPDATED USER GUIDE

19 

4. ISSUES IN SPF SELECTION

This section discusses general issues in the selection of an appropriate SPF that will be subject 

to the calibration process. These include the following: 

1. Use of HSM or non-HSM SPFs and CMFs. 

2. Meeting the data requirements. 

3. SPFs required for specific subsets of an entity type. 

4. Desired precision of predictions. 

Previous sections partially-address some of these issues.

USE OF HSM OR NON-HSM SPFS AND CMFS

The SPFs presented in Part C of the HSM are mainly for design-level applications. Design-level 

applications involve estimating the predicted number of crashes for alternative designs and 

comparing the change in crashes with changes in specific design features. The CMFs applied to 

the SPFs facilitate this assessment. If an analyst desires to use SPFs for design applications, then 

they should calibrate design-level SPFs such as those in Part C of the HSM. 

SPFs also apply to planning-level safety analyses covered in Part B of the HSM. Planning-level

analyses include the following:

• Network screening to identify sites with promise of safety improvement. For this, two 

types of SPFs are available to predict crashes for average sites of a specific type. One 

type of SPF has traffic volume and possibly segment length as the only predictor

variables. The other type of SPF includes additional variables such as lane width, 

shoulder width, or horizontal curvature. Related to this application is the selection of 

sites for systemic safety mitigations by implicitly ranking sites by predicted benefit-cost

ratio, on the assumption that benefits are proportional to expected crashes (based on 

SPFs) and fixed costs per site or per mile. 

• Estimating the benefit of a proposed treatment to improve the safety of a site. The SPF 

applied should be applicable to sites with the same characteristics as the subject site.

• Evaluating the safety effect of an implemented treatment in the empirical Bayes beforeafter study methodology. Again, the SPF applied should be applicable to sites with the 

same characteristics as the subject site. 

The HSM documents these applications; however, it does not provide specific SPFs to support 

them. For various reasons, the HSM Part C and other design-level SPFs may not be appropriate 

for these applications. Using these SPFs in network screening would necessitate the collection 

of all required data for the HSM Part C Predictive Method for all roads in a jurisdiction, which 

could be cost-prohibitive. For estimating the safety benefits of proposed treatments or 

evaluating the safety effects of implemented treatments, the SPF should reflect the safety 

performance of sites in need of treatment. As such, design-level SPFs such as those in Part C of 

the HSM are not appropriate because they reflect the safety performance of “average” sites. 
THE CALIBRATOR—UPDATED USER GUIDE

20 

For planning-level analyses (Part B of the HSM), the preferred option is to develop SPFs using 

the jurisdiction’s data. Such SPFs will still require calibration when they are applied to a different 

time period or subset of entities (e.g., those in a specific region or those with a different range

in traffic volumes) than were used to develop the original SPFs. If SPFs do not meet desirable 

criteria, then The Calibrator can help assess the suitability of SPFs from other sources. One 

alternative source of existing SPFs for planning-level analyses is the original research reports 

used in developing the HSM (See, e.g., Lord at al. and Vogt and Bared).(16,17) Such SPFs are also 

being developed in NCHRP Project 17-62 (Improved Prediction Models for Crash Types and Crash 

Severities) for various crash types and severities for all facility types for consideration in the 

second edition of the HSM. Other sources include AASHTOWare Safety AnalystTM 

documentation and the reports for evaluations conducted under FHWA’s Development of 

Crash Modification Factors (DCMF) project (See, e.g., Srinivasan et al.).

(18) SPFs developed for 

FHWA’s DCMF project evaluations would be especially applicable for estimating safety effects 

of contemplated or implemented treatments, while SPFs from the other sources would be 

more applicable for network screening. The ‘Resources’ section of the CMF Clearinghouse 

provides a list of States that have developed State-specific SPFs. 

MEETING THE DATA REQUIREMENTS

If a design-related analysis is to be undertaken, then the data needs for applying the HSM Part C 

Predictive Method (i.e., data pertaining to the CMF-related variables) should not be a major 

factor in selecting and calibrating SPFs from the HSM. Detailed data are only required for a 

limited number of sites for calibration, and subsequently only for the corridor that is under 

design during application of SPFs. Agencies should not interpret these data needs as a need to 

collect the required data for all sites in the jurisdiction. [Note: This is a common 

misconception.] 

If the application is not design-related, then the selection of an SPF should consider what 

variables are required for the application and calibration. Ideally, the variables in a contemplated 

SPF should be readily available or easily collected in the jurisdiction of interest. Thus, 

consideration of the data requirements and availability is a vital step in the selection of SPFs for

calibration.

SPFS FOR SPECIFIC CONDITIONS

Analysts need to consider if the SPF is required for a specific condition (e.g., curves) or a 

general facility type (e.g., rural, two-lane roads). As noted earlier, specific SPFs are particularly 

relevant when estimating the safety effects of proposed or implemented treatments. Analysts 

should prioritize SPFs for specific conditions (e.g., an SPF developed for curves on rural, twolane roads) since that should provide more accurate estimates than an SPF developed using 

both curve and tangent segments. Other examples include SPFs for nighttime or motorcycle 

crashes. Evaluation reports for FHWA’s DCMF project are a source for such SPFs. 
THE CALIBRATOR—UPDATED USER GUIDE

21 

DESIRED PRECISION OF PREDICTIONS

In selecting an SPF that will be subject to the calibration process, users should consider the 

desired precision of the predictions from the calibrated SPF. The highest level of precision is 

required for design applications for new facilities; therefore, analysts should select high quality 

SPFs based on quality data and developed using state-of-the-art methods for calibration. For 

estimating the safety benefits of contemplated treatments and evaluating the safety effect of 

implemented treatments of a facility redesign, the precision need not be as high. This is because 

the empirical Bayes procedure adjusts for the precision of the SPF utilizing the crash history of 

a site. Analysts should also perform this adjustment in network screening applications, but since 

the aim is merely to prioritize sites for further investigation, the consequences of using a less 

precise SPF are not as severe as for other applications. 
THE CALIBRATOR—UPDATED USER GUIDE

22 

5. USING THE CALIBRATOR

The Calibrator can help users to calibrate and assess SPF performance. The Calibrator applies

to all SPFs or predictions from the combination of SPFs and CMFs as is consistent with the 

HSM Part C Predictive Method. The tool provides a single calibration factor or calibration 

function for each SPF or SPF and CMF combination, along with various goodness-of-fit 

measures and an assessment of how the predictions are performing over the range of all 

variables. The tool does not address the calibration of standalone CMFs. 

INSTALLATION NOTE: The Calibrator was developed for Microsoft Excel versions 2007 

and later, running on Windows Operating Systems with the SOLVER add-in installed. Since the 

file includes macros, users may need to enable macros or Trust the document. Users may also

encounter issues related to Trust Center settings. Access the Trust Center by navigating to 

(File, Options, and Trust Center). In the Trust Center options, click on Macro Settings and 

adjust according to your organization’s policy. Microsoft also releases updates that can break 

ActiveX/Macros. Refer to your IT department about resolutions for ActiveX controls.

The tool automates the calibration process and provides information to users for assessing the 

suitability of, or comparing between, alternate SPFs. Specifically, the tool can help users to: 

• Assess the performance of the HSM Predictive Method as a whole on local data.

• Assess the performance of the uncalibrated HSM Part C SPFs on local data.

• Assess the performance of SPFs and CMFs from other sources on local data.

• Calibrate existing SPFs to local data using the HSM 1st Edition calibration procedure.

• Calibrate the dispersion parameter of an existing SPF to local data.

• Compare the performance of multiple SPFs.

• Identify the most appropriate SPFs and CMFs to apply from a list of alternatives. 

The previous sections provide a brief background on the theory of SPF calibration, goodnessof-fit measures, and SPF selection. The remainder of this guide provides directions for using the 

tool. The following is an overview of the process, followed by detailed instructions for each 

step. Illustrative screenshots accompany these instructions, representing a variety 

of example applications using real data. Screenshots also accompany the three illustrative 

examples presented later, representing the specific example presented.

1. Importing Data: The first step is to import the calibration dataset for the desired site 

type into the spreadsheet. 

2. Defining SPFs and CMFs: The second step is to define the SPFs and CMFs (if applicable) 

for the desired site types or select predefined HSM or AASHTOWare Safety AnalystTM 

SPFs from a list available in the tool. Note that the Appendix of this guide presents the 

predefined SPFs included in the spreadsheet tool. Section A.1 presents the base 

condition SPFs from the HSM for two-lane rural roads, multilane rural roads, urban and 

suburban arterials, and freeways. Section A.2 presents the SPFs from AASHTOWare 

Safety AnalystTM.

3. Calibrating SPFs: The tool calibrates the desired SPFs to the data, producing the 

calibration factor or function and dispersion parameter or function for each calibrated 

SPF. 
THE CALIBRATOR—UPDATED USER GUIDE

23 

4. Assessing SPFs: The user can request multiple goodness-of-fit statistics. All output is 

contained in the spreadsheet. 

IMPORTING DATA

The first step is to import the data for calibration from an Excel spreadsheet. Analysts can only 

import one dataset at a time. Thus, separate spreadsheets are required for different datasets.

The requirements for importing data are as follows: 

1. The user must create an Excel spreadsheet with calibration data on a tab labeled “Data.” 

2. The data for each site must be in a single row with crash counts and all variables 

required for the selected SPF and CMFs in columns. The variables will depend on the 

SPF selected. Note that Appendix sections A.1 and A.2 present the SPFs and required 

variables for SPFs from the HSM and AASHTOWare Safety AnalystTM, respectively. For 

example, if the analyst selects the SPF from AASHTOWare Safety AnalystTM for rural, 

two-lane segments, then the variables required to apply the SPF are AADT and segment 

length. For HSM SPFs, the variables would be as specified in the HSM for the site type.

3. If multiple years of data are included, then the crash counts in each row of the data file

must represent the sum of crashes across all years and the file should contain a column 

indicating the number of years included. The tool only computes a single calibration 

factor, so if the user desires multiple calibration factors (e.g., one for each year), then 

the user will need to prepare a separate file for each year and run the process 

separately. 

4. The imported file should only include sites applicable to the calibrated SPFs. 

5. If the user selects predefined SPFs, then the column headings must match the variable 

names (case sensitive) for the predefined SPFs. The Appendix documents the predefined 

SPFs and appropriate variable names. 

6. No sites should have missing values for the variables required to apply the SPF or CMFs. 

Figure 18 provides an example of the data structure required for calibration in an Excel file. 
THE CALIBRATOR—UPDATED USER GUIDE

24 

Figure 18. Image. Example road segment database required for calibration.

Steps for Importing Data

1. On the ‘Define Variables’ tab click the ‘Import Data’ button.

2. Browse to the desired file, select, and click OK.

This will import the data from the selected file into the ‘ImportedData’ tab. On the ‘Define 

Variables’ tab, all variables will be listed in the ‘Variable List’ box. 

Figure 19 is an example screenshot of data imported to the ‘ImportedData’ tab. There are a 

number of variables, including the following: 

• tot = total observed crashes in 5-year study period. 

• AADT = annual average daily traffic.

• length = segment length in miles. 

• CMFs = product of applicable CMFs for given site conditions.

• years = number of years of crash data. 
THE CALIBRATOR—UPDATED USER GUIDE

25 

Figure 19. Image. Example of imported data.

Figure 20 is an example screenshot showing the imported variables in the ‘Variable List’ box. 

Figure 20. Image. Example of variable list for imported data. 

DEFINING SPFS AND CMFS

The second step is to define the SPFs and CMFs (where the CMFs are not already part of the 

SPF and with values embedded in the imported data). Users may enter SPFs manually (userdefined), or select from available HSM and AASHTOWare Safety AnalystTM SPFs hard coded in 

the tool (predefined). Figure 21 is a screenshot showing a user-defined SPF. The SPF name is 

‘Model1’ and the SPF predicts total crashes as a function of years, length, and AADT. The 

example shows one CMF already defined for lane width in the area titled ‘CMFs for this SPF.’ It 

shows another CMF for lighting in the ‘CMF Formulae’ area, which is in development. The 

example specifies the dispersion parameter as an inversely-proportional function of length. The 

steps required for producing the inputs for this screenshot follow the figure.
THE CALIBRATOR—UPDATED USER GUIDE

26 

Figure 21. Image. Example of user-defined SPF and CMFs. 

Steps for Defining SPFs 

1. Enter a name for the SPF in the ‘SPF Name’ box. In the Figure 21 example, this is 

“Model1”.

2. Enter the dependent variable (i.e., the crash type the SPF is predicting) from the 

‘Variable List’. In the original dataset file (Figure 19) and the associated variable list 

(Figure 20), the label for the dependent variable is ‘tot’, representing the total observed 

crashes in the five-year study period. Users can enter the variable name manually or by 

selecting the variable from the ‘Variable List’ (as shown in Figure 20) and then doubleclicking in the left box under the ‘SPF Formula’ section (as shown in Figure 21).

Important: If entering variables manually, then remember to enclose the variable name in

square brackets (e.g., [tot]). 
THE CALIBRATOR—UPDATED USER GUIDE

27 

3. Enter the independent variables (i.e., the variables used in the SPF to predict crashes)

from the ‘Variable List’. Click in the right box under the ‘SPF Formula’ section and enter 

the SPF formula as one would in a cell of an Excel spreadsheet. Users can enter the 

variable name manually or by selecting the variable from the ‘Variable List’ (as shown in 

Figure 20) and then double-clicking in the right box under the ‘SPF Formula’ section (as 

shown in Figure 21). SPFs may require the use of CMFs, which users can define as 

individual formulas within the tool or pre-calculate with associated values embedded in 

the imported data. The following section describes the steps for defining CMFs.

Important: If entering variables manually, then remember to enclose the variable name in

square brackets (e.g., [AADT]). 
THE CALIBRATOR—UPDATED USER GUIDE

28 

Steps for Selecting a Predefined SPF

To add a predefined SPF into the ‘Available SPFs’ list, select the Classification, Facility Type, 

Crash Severity and/or Source of interest and click ‘Choose Default SPFs’. All eligible SPFs will 

be added to the ‘Available SPFs’ list as illustrated in the Figure 22 screenshot. 

Figure 22. Image. Example of selection of predefined SPFs.
THE CALIBRATOR—UPDATED USER GUIDE

29 

Steps for Defining CMFs

If CMFs are part of the crash prediction and not already embedded in the data, then the user 

must define these CMFs in the ‘CMF Formulae’ box using standard Excel syntax. This is the case 

when using SPFs from Part C of the HSM. The Figure 21 screenshot shows example CMFs. The 

following describes how to enter the CMF for lighting in the ‘CMF Formulae’ box. 

1. In the ‘CMF Formulae’ box, enter the CMF as one would in Excel using an IF statement. 

[Note: Excel defines an IF statement as follows: IF(logical test, value if true, value if false)

where ‘logical test’ is the condition to test, ‘value if true’ is the value returned if the 

logical test is true, and ‘value if false’ is the value returned if the logical test is false.]

Users can enter variable names manually or by selecting the variable from the ‘Variable 

List’ and then double-clicking in the ‘CMF Formulae’ box. Figure 21 provides an example 

screenshot that illustrates this step with a CMF for lighting presence.

Important: If entering variables manually, then remember to enclose the variable name in

square brackets (e.g., [lighting]). 

2. Click the down arrow to add the CMF to the list of CMFs associated with the given SPF. 

The Figure 21 example shows a CMF already added for lane width.

Important: Note the user needs to define all potential values of a CMF. For example, if a 

CMF for lighting presence is 0.90, then user should also define the alternative condition (i.e., 

not present): 

• If lighting = ‘not present’ then CMF=1.00.

• If lighting = ‘present’ then CMF=0.90.

Important: If NOT all conditions are defined, then the SPF will assume a value of zero for 

the undefined conditions, resulting in zero predicted crashes for sites with those conditions.

It may be simplest to use numerical values for categorical variables. For example, if the 

presence of lighting is defined as lighting=1, and absence of lighting is defined as lighting=0, then 

the CMF formula could be written as follows using the Excel syntax for ‘if-then’ statements: 

IF([lighting]=1,0.9,1) 

The IF statement assigns a CMF value of 0.9 if the lighting variable is equal to 1.0. The IF 

statement assigns a value of 1.0 if the lighting variable is not equal to 1.0. As noted, this is the 

example shown in the Figure 21 screenshot. 

Users can delete CMFs by selecting the CMF and then clicking ‘Delete Selected CMF’.
THE CALIBRATOR—UPDATED USER GUIDE

30 

Steps for Defining Dispersion Parameter

The tool calibrates the dispersion parameter of the SPF for one of three assumptions: 1) 

constant dispersion, 2) variable dispersion (constant/length), or 3) variable dispersion as a 

power function of length. 

1. Click the applicable box to select the desired dispersion option. 

2. If the user selects a variable dispersion parameter, then the user must also specify the 

name of the length variable in the imported data. Users can enter the variable name 

manually or by selecting the variable from the ‘Variable List’ (as shown in Figure 20) and 

then double-clicking in the ‘Length Variable’ box (as shown in Figure 21). 

Important: If entering variables manually, then remember to enclose the variable name in

square brackets (e.g., [length]). 

Saving and Editing SPFs and CMFs

Save the SPF and associated CMFs, along with the dispersion parameter specification, before 

applying the tool. To do this, click the ‘Save as new SPF’ box shown in Figure 21. 

Select an existing SPF for application or editing by double clicking the SPF name in the ‘Available 

SPFs’ box. Delete SPFs by selecting the SPF name in the ‘Available SPFs’ box and then clicking 

the ‘Delete Selected SPF’ button. 

When editing an existing SPF, replace the existing SPF by clicking the ‘Replace SPF’ button or 

save as a new SPF by clicking the ‘Save as new SPF’ button.

CALIBRATION AND GOODNESS-OF-FIT MEASURES

The third step is to calibrate the selected SPFs. The tool automatically computes the GOF 

measures in this step. 

Steps for Calibrating SPFs and Dispersion Parameters

1. Select the SPF(s) for calibration from the ‘Available SPFs’ list as shown in Figure 23. If 

the SPF is selected by double-clicking, the ‘SPF Formula,’ ‘SPF Name,’ and ‘Dispersion 

Formula’ boxes are populated as shown in Figure 23. If the user specifies CMFs for the 

SPF, then the tool will populate ‘CMFs for this SPF’ as well. 

2. If a calibration factor is desired, click the ‘Estimate Calibration Factors’ button. If a 

calibration function is desired, click the ‘Estimate Calibration Functions’ button. These 

are shown in the lower right of Figure 23. 

3. As illustrated in Figure 24, the Excel Solver box will appear once the tool finds a 

solution for calibrating the SPF and dispersion parameter. Click on ‘Keep Solver 

Solution’ and then click ‘OK’. 
THE CALIBRATOR—UPDATED USER GUIDE

31 

Figure 23. Image. Example of selecting an SPF to calibrate from predefined SPFs. 

Figure 24. Image. Example of the solver results screen.
THE CALIBRATOR—UPDATED USER GUIDE

32 

The ‘Results’ tab then appears. As illustrated in Figure 25, this contains the SPF name, total 

observed crashes, total predicted crashes using the uncalibrated SPF. When applicable, it also 

shows the calibration factor(s), variance of the calibration factor(s), covariance of the 

calibration factor(s), parameter estimates of the calibration function(s), calibrated dispersion 

parameter(s), and parameter estimates of the dispersion parameter function(s) for each SPF

selected for calibration.

The GOF measures, MAD, and modified R2 are determined during the SPF calibration and 

displayed on the ‘Results’ tab. Also displayed are the AIC, BIC, and sum of loglikelihood values. 

A CURE plot for the SPF against the calibrated predictions is also prepared and shown on the 

Cure Plots tab. The Results tab shows the maximum absolute deviation from zero and percent 

of observations exceeding the two standard error limits.

Figure 25. Image. Example results from ‘Results’ tab. 

CURE PLOTS AND ASSESSMENT TABLES

Users can create CURE plots and assessment tables for any variable from the ‘Assessments’ tab

as illustrated in Figure 26. 

Steps for Creating CURE Plots and Assessment Tables

1. Select the variable(s) of interest.

2. Select the SPF(s) of interest.

3. If a CURE plot is desired, click the ‘Generate Graphs’ button. The CURE plot(s) will be 

displayed on the ‘CUREPlots’ tab. On the ‘Results’ tab, for each SPF and variable that a 

CURE plot is developed, the maximum absolute deviation from zero of the cumulative 

residuals is provided as well as the percentage of observations that are outside of the 

two standard deviation limits.

4. If an assessment table is desired for variables with a limited number of discrete values, 

click the ‘Generate Tables’ button. The ‘TableResults’ tab displays the results.
THE CALIBRATOR—UPDATED USER GUIDE

33 

Figure 26. Image. Example assessment creating CURE plots for two variables.

The tool presents the results in separate tabs as illustrated in Figure 27 (CURE plots) and 

Figure 28 (assessment tables). Note the examples shown in Figure 27 and Figure 28 are from 

another dataset, as the sample data shown in the previous screenshots did not include any 

categorical variables.

Important: If the user generates CURE plots or assessment tables and subsequently selects an 

additional variable to create a new CURE plot or assessment table, then the original plots or 

tables will be lost. For this reason, the user should select all variables of interest at the same 

time for creating CURE plots or assessment tables. The exception is the CURE plot for the 

calibrated predictions constructed when the user calibrates the SPF. These results remain on 

the ‘Results’ tab. 
THE CALIBRATOR—UPDATED USER GUIDE

34 

Figure 27. Image. Example CURE plots from "Generate Graphs." 
THE CALIBRATOR—UPDATED USER GUIDE

35 

Figure 28. Image. Example assessment tables from "Generate Tables." 
THE CALIBRATOR—UPDATED USER GUIDE

36 

6. EXAMPLES

This section illustrates the use of the tool through the following three examples. 

• Example 1: SPF for Motorcycle Crashes on Urban Freeways—this example 

demonstrates how to calibrate and assess the calibration of a single SPF.

• Example 2: SPF and CMFs for 3-Leg STOP Controlled Intersections on Rural 2-Lane 

Roads—this example demonstrates how to calibrate and assess the calibration of a 

single SPF.

• Example 3: HSM SPF and CMFs, AASHTOWare Safety AnalystTM SPF, and Custom SPF 

Applied to Rural 2-Lane Roads—this example demonstrates how to calibrate, assess, 

and compare multiple SPFs to determine which is most appropriate for application

Users can import the data for these examples from the upper-middle of the ‘Define Variables’ 

tab. Users may use these data to replicate the findings.

EXAMPLE 1: SPF FOR MOTORCYCLE CRASHES ON URBAN FREEWAYS

This example demonstrates how to calibrate and assess the calibration of a single SPF. The SPF 

in question is for motorcycle crashes on freeways. Figure 29 shows the equation for the SPF in 

question. The tool provides this SPF as “test1” in the ‘Available SPFs’ box once the user clicks 

‘Import Sample Data 1’ from the upper-middle of the ‘Define Variables’ tab. This represents the 

existing SPF for calibration as shown in the Figure 30 screenshot. 

Figure 29. Equation. SPF for example 1. 

Where:

motocrash = count of motorcycle crashes.

years = years of data for each site.

length = length of segment in miles.

AADT = average annual daily motorcycle volume.

Dispersion = constant. 

This example uses data for 483 road segments on urban freeways. Import the data by selecting 

‘Import Sample Data 1’ on the ‘Define Variables’ tab. The crash type of interest is motorcycle 

crashes of which there are 174, or 0.36 per segment on average, during a five-year period. 

Figure 30 shows the variables in the “Variable List” box. Note the data should also appear in 

the ‘ImportedData’ tab.
THE CALIBRATOR—UPDATED USER GUIDE

37 

Figure 30. Image. Information in ‘Define Variables’ tab for example 1.

Where:

id = identification number for segment.

nolanes = number of lanes.

spdlimt = posted speed limit in miles per hour.

surfwidth = surface width in feet.

outshldwid = outside shoulder width in feet.

medwidth = median width in feet.

inshldwid = inside shoulder width in feet.

length = length of segment in miles.

motocrash = count of motorcycle crashes.

AADT = average annual daily motorcycle volume.

years = years of data for each site.
THE CALIBRATOR—UPDATED USER GUIDE

38 

Calibrate the SPF by selecting the SPF name (i.e., test1) from the list of ‘Available SPFs’ in the 

‘Define Variables’ tab as shown in Figure 30, and then clicking ‘Estimate Calibration Factors’ or 

‘Estimate Calibration Functions’ in the lower right of the same tab. Figure 31 shows a 

screenshot of the ‘Results’ tab, which presents the results of the calibration after clicking 

‘Estimate Calibration Factors’, including the following variables.

• Calibration factor = 1.49 

• Modified R2

 = 0.65 

• MAD = 0.43 

• Dispersion parameter = 0.44 

• V(C) = 0.02

• CV(C) = 0.10

• Max Absolute Cure Deviation (for the calibrated fitted values) = 9.08

• % Cure Deviation (for the calibrated fitted values) = 1.24% 

Figure 31. Image. Calibration results from example 1.

The calibration factor indicates the uncalibrated SPF under-predicts crashes. The calibration 

factor increases the predictions by approximately 50 percent. The modified R2 of 0.65, MAD of 

0.43, and dispersion parameter of 0.44 all indicate a reasonable goodness-of-fit to the data. The 

CV(C) is less than 0.15 indicating the calibration factor is reasonably accurate. By itself, this CV 

value is indicative of a successful calibration. The percent curve deviation for the fitted values is 

less than five percent, which also indicates a successful calibration.

To further test the goodness-of-fit, Figure 32 through Figure 36 present additional CURE plots 

for the continuous variables, including outside shoulder width, inside shoulder width, median 

width, and AADT. Users can create CURE plots from the ‘Assessments’ tab by selecting the 

variables of interest from the variable list, selecting the SPF of interest from the list of available 

SPFs, and clicking ‘Generate Graphs.’ 

The CURE plot for outside shoulder width indicates there is some bias in the SPF predictions at 

widths of 10 feet. The SPF tends to over-predict motorcycle crashes for this value of shoulder 

width. The user might consider separate calibration factors for different shoulder widths in this 

case.
THE CALIBRATOR—UPDATED USER GUIDE

39 

Figure 32. Chart. CURE plot for outside shoulder width for example 1. 

The CURE plot for inside shoulder width indicates the SPF performs well over most of the 

range of values. The cumulative residuals plot only briefly exceeds the two standard deviation 

confidence limits for narrow shoulders, indicating an under-prediction in crashes in this range. 

The fit is acceptable in this case.

Figure 33. Chart. CURE plot for inside shoulder width for example 1.

The CURE plot for median width indicates the SPF performs reasonably well although there 

may be some bias or a potential outlier at low values of median width. Specifically, there is a 

large vertical drop at 25 feet, and a constant decreasing trend from approximately 50 feet to 

150 feet, indicating a small, yet consistent, bias. The analyst should check the data for potential 
THE CALIBRATOR—UPDATED USER GUIDE

40 

outliers contributing to the drop at 25 feet. If the data appear unreliable, then the analyst 

should remove outliers and run the calibration again.

Figure 34. Chart. CURE plot for median width for example 1. 

The CURE plot for motorcycle AADT indicates the SPF is performing well overall and the plot 

of cumulative residuals rarely exceeds the two standard deviation confidence limits. Between 

AADT values of approximately 75 and 120 vehicles per day, the SPF over-predicts crashes, 

while it tends to under-predict crashes between AADT values of 120 and 200 vehicles per day. 

The analyst could consider dividing the data into two datasets and develop separate calibration 

factors for each range, assuming sample sizes are sufficient, or develop a calibration function. 

Figure 35. Chart. CURE plot for motorcycle AADT for example 1. 
THE CALIBRATOR—UPDATED USER GUIDE

41 

The CURE plot for fitted (calibrated) values indicates the SPF performs well overall and the plot 

of cumulative residuals rarely exceeds the two standard deviation confidence limits. According 

to the suggested assessment criteria, this result by itself would deem the SPF acceptable.

Figure 36. Chart. CURE plot for fitted (calibrated) values for example 1. 

Figure 37 shows a screenshot of the summary results from the ‘Results’ tab based on the CURE 

plots selected from the ‘Assessments’ tab. For each CURE plot, the ‘Results’ tab provides the 

maximum absolute deviation from zero as well as the percentage of observations exceeding the 

two standard deviation confidence limits. The percent of ordinates exceeding the two standard 

deviation limits is greater than five percent for the variables related to inside shoulder width

and AADT, indicating some bias in the predictions for these two variables.

Figure 37. Image. CURE plot assessment results for example 1.

It is also of interest to determine how the SPF is performing for the categorical variables: 

number of lanes and posted speed limit. Since these are not continuous variables, assessment 

tables are more appropriate than CURE plots. The user can create assessment tables from the 

‘Assessments’ tab by selecting the variables of interest from the variable list, selecting the SPF of 

interest from the list of available SPFs, and clicking ‘Generate Tables.’ Figure 38 shows the 

assessment tables for motorcycle crashes. 
THE CALIBRATOR—UPDATED USER GUIDE

42 

Figure 38. Image. Assessment table results for example 1.

For number of lanes, the SPF slightly over-predicts crashes for four-lane segments and underpredicts crashes for six-lane segments. There is only one crash for the eight-lane segment 

group; therefore, the calibration bias factor for this group is not meaningful. 

For posted speed limit, the SPF does not over- or under-predict crashes for 70 mph segments. 

The SPF over-predicts crashes for segments with a posted speed limit of 65 mph; however, this 

result is based on only five crashes, which is uninformative. 
THE CALIBRATOR—UPDATED USER GUIDE

43 

EXAMPLE 2: SPF AND CMFS FOR 3-LEG STOP-CONTROLLED 

INTERSECTIONS ON RURAL 2-LANE ROADS 

This example demonstrates how to calibrate and assess the calibration of a single SPF. The SPF 

in question is for three-legged,stop-controlled intersections on rural, two-lane roads. Figure 39

shows the equation for the SPF in question. The tool provides this SPF as “test2” in the 

‘Available SPFs’ box once the user clicks ‘Import Sample Data 2’ from the upper-middle of the 

‘Define Variables’ tab. This represents the existing SPF for calibration as shown in the Figure 40

screenshot: 

Figure 39. Equation. SPF for example 2.

Where:

intcrash = count of intersection-related crashes.

years = years of data for each site.

AADTMAJ = annual average daily traffic for major road.

AADTMIN = annual average daily traffic for minor road.

Dispersion = constant. 

This example uses data for 3,534 three-legged, stop-controlled intersections on rural, two-lane 

roads. Import the data by selecting ‘Import Sample Data 2’ on the ‘Define Variables’ tab. The 

crash type of interest is total intersection-related crashes. There are 7,208 total intersectionrelated crashes, or 2.04 crashes on average per site, or 0.24 crashes on average per site-year. 

Figure 40 shows the variables in the “Variable List” box. Note the data should also appear in 

the ‘ImportedData’ tab.
THE CALIBRATOR—UPDATED USER GUIDE

44 

Figure 40. Image. Information in ‘Define Variables’ tab for example 2.

Where:

location = jurisdiction of the intersection.

RTlanes = number of right-turn lanes on major road.

LTlanes = number of left-turn lanes on major road.

AADTMAJ = annual average daily traffic for major road.

AADTMIN = annual average daily traffic for minor road.

intcrash = count of intersection-related crashes.

years = years of data for each site.
THE CALIBRATOR—UPDATED USER GUIDE

45 

Relevant CMFs, some of which are visible in the Figure 40 screenshot, include the following: 

• 1 left-turn lane on major road: CMF = 0.56. 

• 2 left-turn lanes on major road: CMF = 0.31. 

• 1 right-turn lane on major road: CMF = 0.86. 

• 2 right-turn lanes on major road: CMF = 0.74. 

Calibrate the SPF by selecting the SPF name (i.e., test2) from the list of ‘Available SPFs’ in the 

‘Define Variables’ tab as shown in Figure 40, and then clicking ‘Estimate Calibration Factors’ or 

‘Estimate Calibration Functions’ in the lower right of the same tab. Figure 41 shows a 

screenshot of the ‘Results’ tab, which presents the results of the calibration after clicking 

‘Estimate Calibration Factors’, including the following variables.

• Calibration factor = 0.51

• Modified R2

 = 0.46 

• MAD = 1.57 

• Dispersion parameter = 0.66 

• V(C) = 0.00 

• CV(C) = 0.03 

• Max Absolute Cure Deviation (for the calibrated fitted values) = 267.12 

• % Cure Deviation (for the calibrated fitted values) = 79% 

Figure 41. Image. Calibration results from example 2.

The calibration factor indicates the uncalibrated SPF over-predicts crashes and the calibration 

factor reduces the predictions by approximately 50 percent. The modified R2 of 0.46 relatively

low, but the MAD of 1.57 and dispersion parameter of 0.66 indicate a reasonable goodness-offit to the data. The CV(C) is less than 0.15 indicating the calibration factor is reasonably 

accurate despite its size, and the analyst may consider the calibrated SPF for application based 

on this value. The percent of ordinates exceeding the two standard deviation limits is greater 

than five percent for the fitted values, indicating some bias in the predictions.
THE CALIBRATOR—UPDATED USER GUIDE

46 

To further test the goodness-of-fit, Figure 42 through Figure 44 present additional CURE plots 

for the continuous variables, including major road AADT and minor road AADT. Users can 

create CURE plots from the ‘Assessments’ tab by selecting the variables of interest from the 

variable list, selecting the SPF of interest from the list of available SPFs, and clicking ‘Generate 

Graphs.’ 

The CURE plot for major road AADT shows the SPF generally over-predicts crashes for major 

road AADT less than 5,000 vehicles per day and under-predicts crashes for major road AADT 

from 12,500 to 17,500 vehicles per day. The plot of cumulative residuals strays outside the two 

standard deviation confidence limits for a substantial portion of the plot, indicating significant 

bias in SPF predictions. 

Figure 42. Image. CURE plot for major road AADT for example 2. 

The CURE plot for minor road AADT shows the SPF performs well except for very low values 

of minor road AADT where the plot of cumulative residuals strays far outside the two standard 

deviation confidence limits.
THE CALIBRATOR—UPDATED USER GUIDE

47 

Figure 43. Image. CURE plot for minor road AADT for example 2. 

The CURE plot for fitted (calibrated) values shows the cumulative residuals straying outside the 

two standard deviation confidence limits for a portion of the plot, indicating some bias in SPF 

predictions for lower fitted values. 

Figure 44. Image. CURE plot for fitted (calibrated) values for example 2. 

Figure 45 shows a screenshot of the summary results from the ‘Results’ tab based on the CURE 

plots selected from the ‘Assessments’ tab. For each CURE plot, the ‘Results’ tab provides the 

maximum absolute deviation from zero as well as the percentage of observations exceeding the 

two standard deviation confidence limits. The percent of ordinates exceeding the two standard 

deviation limits is greater than five percent for both variables: major road AADT and minor 

road AADT, indicating substantial bias within the SPF. At first glance, the percent cure deviation 
THE CALIBRATOR—UPDATED USER GUIDE

48 

for minor road AADT seems at odds with Figure 43. Evidently, a substantial number of minor 

road AADTs are in the range where the CURE values exceed the 2σ boundary. Even so, with a 

maximum deviation of the cumulative residuals in the low 300s for both major and minor

AADT, and less than 300 for fitted values, this calibration may be considered acceptable given

there are 7,208 crashes in the dataset and the CV was in the acceptable range. 

Figure 45. Image. CURE plot assessment results for example 2. 

It is also of interest to observe how the SPF is performing for the categorical variables: rightturn lanes and left-turn lanes. Since these are not continuous variables, assessment tables are 

more appropriate than CURE plots. This user can create assessment tables from the 

‘Assessments’ tab by selecting the variables of interest from the variable list, selecting the SPF of 

interest from the list of available SPFs, and clicking ‘Generate Tables.’ Figure 46 shows the 

assessment tables for intersection crashes. 

For right turn lanes, the SPF performs well for both zero and one right turn lane on the major 

road as evidenced by the calibration bias factors close to 1.0. For left turn lanes, the bias factors 

indicate the SPF over-predicts crashes for sites without a major road left-turn lane and underpredicts crashes for sites with one major road left-turn lane. For this dataset, there were no

sites with two right- or left-turn lanes on the major road.

Figure 46. Image. Assessment table results for example 2. 
THE CALIBRATOR—UPDATED USER GUIDE

49 

EXAMPLE 3: HSM SPF AND CMFS, AASHTOWARE SAFETY ANALYSTTM SPF, 

AND CUSTOM SPF APPLIED TO RURAL 2-LANE ROADS 

This example assesses and compares multiple SPFs to determine which is most appropriate for 

application in the given jurisdiction. The SPFs in question are for rural, two-lane roads from the 

HSM, AASHTOWare Safety AnalystTM, and a neighboring State (State X). Figure 47 shows the 

equation for a custom SPF from State X. The tool provides this SPF as “test3” in the ‘Available 

SPFs’ box once the user clicks ‘Import Sample Data 3’ from the upper-middle of the ‘Define 

Variables’ tab. The tool also provides the HSM and AASHTOWare Safety AnalystTM SPFs as 

predefined SPFs. 

Figure 47. Equation. SPF for example 3. 

Where:

tot = count of crashes on a segment.

years = years of data for each site. 

AADT = annual average daily traffic volume.

length = length of segment in miles.

Dispersion = variable (constant/length). 

The example uses data for 509 rural, two-lane road segments for a five-year period. Import the 

data by selecting ‘Import Sample Data 3’ on the ‘Define Variables’ tab. The crash type of 

interest is total crashes. There are 753 total crashes, or 1.48 crashes on average per site, or 

0.30 crashes on average per site-year. Figure 48 shows the variables in the “Variable List” box. 

Note the data should also appear in the ‘ImportedData’ tab. The column headings in the 

‘ImportedData’ tab match the variable names in the predefined HSM and AASHTOWare Safety 

AnalystTM SPFs. Figure 47 specifies the variable names to match the column headings.

Figure 48. Image. Variable list on ‘Define Variables’ tab for example 3.
THE CALIBRATOR—UPDATED USER GUIDE

50 

Where:

tot = count of crashes on a segment.

AADT = annual average daily traffic volume.

length = length of segment in miles.

CMFs = product of individual HSM CMFs for the segment.

years = years of data for each site. 

Note the data in this example contain a variable “CMFs” that is the product of all relevant Part 

C CMFs from the HSM for each road segment. As such, it is not necessary to specify CMFs 

using the ‘CMF Formulae’ feature of the tool. In this case, it would have been cumbersome to 

use the tool to specify CMFs for lane and shoulder width since these are functions. Look-up 

tables are more appropriate to handle functions, a feature not currently in the tool.

To select the predefined HSM and AASHTOWare Safety AnalystTM SPFs for this example, use 

the filters on the right side of the ‘Define Variables’ tab. Select the applicable Classification, 

Facility Type, Crash Severity, and/or Source of interest along the right side of the ‘Define 

Variables’ tab, and then click ‘Choose Default SPFs’. In this case, the ‘Classification’ is defined as 

‘Rural,’ the ‘Facility Type’ is defined as ‘Non-Freeway Segment,’ the ‘Crash Severity’ is defined 

as ‘KABCO1

,’ and the ‘Source’ is defined as ‘Highway Safety Manual’ and ‘AASHTOWare Safety 

Analyst.’ Figure 49 shows the options and illustrates the use of the filters to select the 

predefined HSM and AASHTOWare Safety AnalystTM SPFs for total crashes for rural, nonfreeway segments for this example. 

 

1 KABCO refers to a scale that is used to represent injury severity in crash reporting: K is fatal injury, A is serious 

injury, B is minor injury, C is possible injury, and O is property damage only.
THE CALIBRATOR—UPDATED USER GUIDE

51 

Figure 49. Image. Selecting predefined SPFs for example 3.

Figure 50 shows the names of available SPFs in the ‘Available SPFs’ box with the baseline SPF 

from the HSM selected. The figure also shows the other two SPFs of interest in this example: 

“1,test3” and “5,SA-RUR2U-KABCO.” Users can edit the SPFs by double clicking on the SPF 

name, editing the SPF formula, and clicking ‘Replace SPF.’ This may be necessary where a 

variable name in the SPF formula requires editing to match the variable name in the data. In 

other cases, it may be necessary to add variables such as CMFs to the baseline SPF.
THE CALIBRATOR—UPDATED USER GUIDE

52 

Figure 50. Image. Selecting predefined HSM SPF for example 3.

For this example, the user needs to edit the baseline SPF from the HSM to include the variable 

for CMFs. The underlying dataset includes a variable ‘CMFs,’ which is the product of applicable 

CMFs from the HSM. Note the user would need to specify the CMFs using the ‘SPF Formula’ 

feature of the tool if the underlying data did not include the variable ‘CMFs.’ Figure 51 shows

the SPF from the HSM edited in the ‘SPF Formula’ box. The figure shows the variable ‘CMFs’ 

added to the SPF by typing “*” and then “[CMFs].” 

Recall the user could also enter the variable “[CMFs]” by selecting the variable from the 

‘Variable List’ and then double-clicking in the ‘SPF Formula’ box. 

The HSM dispersion formula varies with segment length as indicated in the SPF specification in 

Appendix section A1. The user must save any revisions to the SPF or dispersion formula before 

applying the SPF. This is done by clicking ‘Replace SPF’ on the ‘Define Variables’ tab.
THE CALIBRATOR—UPDATED USER GUIDE

53 

Figure 51. Image. Editing predefined HSM SPF for example 3. 

The next step is to calibrate the SPFs. Users can calibrate the three SPFs simultaneously by 

holding ‘CTRL’ and selecting the SPFs of interest in the ‘Available SPFs’ box, and then clicking

‘Estimate Calibration Factors’ or ‘Estimate Calibration Functions’ in the lower right of the 

‘Define Variables’ tab. In this example, the analyst first selects ‘Estimate Calibration Factors.’

Figure 52 presents the results of the calibration for a constant calibration factor. The calibration

factor indicates the uncalibrated State X (test3) and HSM SPFs slightly under-predict crashes 

while the uncalibrated AASHTOWare Safety AnalystTM SPF over-predicts crashes. The State X 

(test3) and HSM calibration factors increase predictions by 12 percent and 8 percent, 

respectively, and the AASHTOWare Safety AnalystTM calibration factor reduces predictions by 

approximately 50 percent. The modified R2 values are relatively low, but the MAD and 

dispersion parameters indicate a reasonable fit to the data. The CV(C) values are less than 0.15, 

indicating the calibration factors are reasonably accurate, and the user may consider the 

calibrated SPFs for application. The percent of ordinates exceeding the two standard deviation 

limits is less than five percent for the State X (test3) SPF, indicating a good fit. The percent of 
THE CALIBRATOR—UPDATED USER GUIDE

54 

ordinates exceeding the two standard deviation limits is much greater than five percent for the 

HSM and AASHTOWare Safety AnalystTM SPFs, indicating some bias in the predictions.

Comparing the AIC, BIC, and sum of log likelihood, the values suggest the State X SPF is slightly 

preferred.

Figure 52. Image. Calibration results for example 3 (based on calibration factor). 

The Calibrator automatically generates the CURE plots for fitted values and displays the plots 

on the Cure Plots tab. Figure 53 through Figure 55 show the CURE plots for fitted values for 

Example 3. The CURE plot for fitted values for the State X (test3) SPF indicates a reasonable 

goodness-of-fit to the data with few cumulative residuals straying outside the two standard 

deviation confidence limits. The sharp increase near fitted values of 4.0 indicate a potential 

outlier in the data. By contrast, the CURE plots for fitted values for the AASHTOWare Safety 

AnalystTM and HSM SPFs stray outside the two standard deviation confidence limits for a 

substantial portion of the plot, indicating bias in the SPF predictions. 
THE CALIBRATOR—UPDATED USER GUIDE

55 

Figure 53. Image. State X CURE plot for fitted (calibrated) values for example 3

(based on constant calibration factor). 

Figure 54. Image. AASHTOWare Safety AnalystTM CURE plot for fitted 

(calibrated) values for example 3 (based on constant calibration factor). 
THE CALIBRATOR—UPDATED USER GUIDE

56 

Figure 55. Image. HSM CURE plot for fitted (calibrated) values for example 3

(based on constant calibration factor). 

Figure 56 through Figure 59 show equivalent results to Figure 52 through Figure 55, but this is 

based on a calibration function instead of a calibration factor. To estimate a calibration function, 

start on the ‘Define Variables’ tab, select the SPFs of interest, and click on ‘Estimate Calibration 

Function’ in the lower right. All assessment measures for the AASHTOWare Safety AnalystTM 

and HSM calibrated SPFs indicate a marked improvement after calibrating a function rather than 

a factor. This is particularly true for the HSM SPF, which now slightly outperforms the 

AASHTOWare Safety AnalystTM SPF for modified R2, mean absolute deviation, and maximum 

absolute cure deviation. The assessment measures remain similar for the calibrated State X SPF

after calibrating a function rather than a factor.

Figure 56. Image. Calibration results for example 3 (based on calibration function). 
THE CALIBRATOR—UPDATED USER GUIDE

57 

Figure 57. Image. State X CURE plot for fitted (calibrated) values for example 3 

(based on calibration function).

Figure 58. Image. AASHTOWare Safety AnalystTM CURE plot for fitted 

(calibrated) values for example 3 (based on calibration function).
THE CALIBRATOR—UPDATED USER GUIDE

58 

Figure 59. Image. HSM CURE plot for fitted (calibrated) values for example 3 

(based on calibration function).

If the analyst desires additional CURE plots to further test the goodness-of-fit, they can go to 

the ‘Assessments Tab,’ select the variable(s) of interest from the variable list, select the SPF(s) 

of interest from the list of available SPFs, and click ‘Generate Graphs.’

The final step is to compare and select an appropriate SPF by 1) determining which of the SPFs, 

if any, are suitable, and 2) selecting which of the suitable SPFs is most appropriate for the given 

dataset. Recall from the section, Summary of SPF Assessment, an SPF with a constant calibration 

factor is acceptable if either of the following conditions is met:

1) Five percent or less of CURE plot ordinates for fitted values (after applying the 

calibration factor) exceed the 2σ limits, or

2) The CV of the constant calibration factor is less than 0.15.

Table 3 presents a summary of the calibration results for the three SPFs in question based on a 

constant calibration factor. Considering the percent CURE deviation, only the calibrated State 

X SPF is within the acceptable range of CURE plot ordinates for fitted values exceeding the 2σ

limits. Considering the CV(C) parameter, the values for all three SPFs are less than the 0.15 

threshold, indicating a reasonable goodness-of-fit. Based on the CV(C) parameter, the analyst 

may retain all three SPFs for further comparison. 
THE CALIBRATOR—UPDATED USER GUIDE 

59 

Table 3. Comparison of multiple SPFs (based on calibration factor). 

Parameter State X S.A. HSM Assessment 

Observed crashes 753 753 753 -- 

Predicted crashes 673.4 1427.8 697.7 -- 

Calibration factor 1.12 0.53 1.08 Close to 1.0 

V(C) 0.01 0.00 0.01 Smaller values preferred

CV(C) 0.07 0.09 0.08 Less than 0.15 preferred 

Modified R2 0.34 0.29 0.21 Larger values preferred

MAD 1.23 1.28 1.29 Smaller values preferred

Dispersion k 0.24 0.78 0.31 Smaller values preferred

Max Cure Deviation 41.49 88.20 111.96 Smaller values preferred

% Cure Deviation 4.52% 43.81% 73.48% Less than 5% preferred 

AIC 210.48 215.47 260.50 Smaller values preferred

BIC 214.72 219.71 264.73 Smaller values preferred

Note: Bold values indicate the preferred SPF for a given parameter. 

Given that all three SPFs are suitable, it is appropriate to estimate a calibration function for 

each SPF. The analyst may deem the function preferable to the factor if the percent of CURE 

plot ordinates for fitted values (after applying the unique calibration factors) exceeding the 

2limits is lower than that for the constant calibration factor. 

Table 4 presents a summary of the calibration results for the three SPFs in question based on a 

calibration function. Considering the percent CURE deviation, the values improve for all three 

SPFs, indicating the function is preferable to the factor. The final step is to compare the relative 

performance of all suitable SPFs. The final column of the table indicates the preferred values for 

each parameter if applicable. The State X (test3) SPF performs best with respect to five of the 

seven measures (i.e., modified R2

, MAD, dispersion (k), max CURE deviation, and percent 

CURE deviation). Based on these results, the State X (test3) SPF is the preferred SPF for 

application. 
THE CALIBRATOR—UPDATED USER GUIDE

60 

Table 4. Comparison of multiple SPFs (based on calibration function).

Parameter State X S.A. HSM Assessment

Observed crashes 753 753 753 --

Predicted crashes 673.4 1427.8 697.7 --

Modeled A value 1.15 0.67 1.37 --

Modeled B value 0.96 0.85 0.69 --

Modified R2 0.35 0.32 0.34 Larger values preferred

MAD 1.22 1.28 1.25 Smaller values preferred

Dispersion k 0.24 0.74 0.26 Smaller values preferred

Max Cure Deviation 36.85 42.29 41.33 Smaller values preferred

% Cure Deviation 3.73% 12.57% 12.57% Less than 5% preferred 

AIC 212.03 209.02 221.52 Smaller values preferred

BIC 220.49 217.49 229.99 Smaller values preferred

Note: Bold values indicate the preferred SPF for a given parameter. 
THE CALIBRATOR—UPDATED USER GUIDE

61 

APPENDIX: PREDEFINED SPFS

This appendix presents the predefined SPFs included in the related spreadsheet tool. Section

A.1 presents the base condition SPFs from the HSM for two-lane rural roads, multilane rural 

roads, urban and suburban arterials, and freeways. Section A.2 presents the SPFs from 

AASHTOWare Safety AnalystTM.

A.1. HSM BASE CONDITION SPFS

This section documents the base SPFs in the first edition of the HSM. These SPFs are already 

available in the spreadsheet tool (see predefined SPFs). The tool does not include the 

associated CMFs, and users of the tool can add CMFs as desired. Each subsection below

presents the name of the predefined SPF in parentheses. 

Note: In order to apply the SPFs in the spreadsheet tool, the variable names for the imported 

data will need to match those used in the predefined SPFs and documented here. 

A.1.1 Two-Lane Rural Road Chapter

Error! Reference source not found. through Error! Reference source not found.

provide SPFs for rural two-lane segments and intersections. The dispersion parameter is equal 

to k divided by segment length for the segment SPF and is equal to k for intersection SPFs. The 

following variable definitions apply to all SPFs in this subsection:

• length = segment length in miles.

• AADT = average annual daily traffic on road segment.

• AADTMAJ = average annual daily traffic on major road.

• AADTMIN = average annual daily traffic on minor road.

Figure 60. Equation. SPF for segments (HSM-RUR2U-KABCO).

Figure 61. Equation. SPF for three-leg STOP controlled intersections (HSM-RUR2-

3ST-KABCO).

Figure 62. Equation. SPF for four-leg STOP controlled intersections (HSM-RUR2-

4ST-KABCO).

Figure 63. Equation. SPF for four-leg signalized intersections (HSM-RUR2-4SGKABCO).
THE CALIBRATOR—UPDATED USER GUIDE

62 

A.1.2 Multi-Lane Rural Road Chapter

Error! Reference source not found. through Error! Reference source not found.

provide SPFs for rural multilane undivided segments. Error! Reference source not found.

through Error! Reference source not found. provide SPFs for rural multilane divided 

segments. Error! Reference source not found. through Error! Reference source not 

found. provide SPFs for three-leg STOP controlled intersections. Error! Reference source 

not found. through Error! Reference source not found. provide SPFs for four-leg STOP 

controlled intersections. Error! Reference source not found. through Error! Reference 

source not found. provide SPFs for four-leg signalized intersections. The dispersion 

parameter is equal to k divided by segment length for all segment SPFs. The dispersion 

parameter is equal to k for all intersection SPFs. The following variable definitions apply to all 

SPFs in this subsection:

• length = segment length in miles

• AADT = average annual daily traffic on road segment

• AADTMAJ = average annual daily traffic on major road

• AADTMIN = average annual daily traffic on minor road

4 Lane Undivided Segments 

TT CC h = yy ∗ ee −9.653 ∗ h ∗ 1.176

Figure 64. Equation. SPF for total crashes (HSM-RUR4U-KABCO).

KK CC h = yy ∗ ee −9.410 ∗ h ∗ 1.094

Figure 65. Equation. SPF for KABC crashes (HSM-RUR4U-KABC).

KK CC h = yy ∗ ee −8.577 ∗ h ∗ 0.938

Figure 66. Equation. SPF for KAB crashes (HSM-RUR4U-KAB).

4 Lane Divided Segments 

TT CC h = yy ∗ ee −9.025 ∗ h ∗ 1.049

Figure 67. Equation. SPF for total crashes (HSM-RUR4D-KABCO).

KK CC h = yy ∗ ee −8.837 ∗ h ∗ 0.958

Figure 68. Equation. SPF for KABC crashes (HSM-RUR4D-KABC).
THE CALIBRATOR—UPDATED USER GUIDE

63 

KK CC h = yy ∗ ee −8.505 ∗ h ∗ 0.874

Figure 69. Equation. SPF for KAB crashes (HSM-RUR4D-KAB).
THE CALIBRATOR—UPDATED USER GUIDE

64 

Three-leg STOP Controlled Intersections 

TT CC h = yy ∗ ee −12.526 AA1.204 AA 0.236

Figure 70. Equation. SPF for total crashes (HSM-RUR4-3ST-KABCO).

KK CC h = yy ∗ ee −12.664 AA1.107 AA 0.272

Figure 71. Equation. SPF for KABC crashes (HSM-RUR4-3ST-KABC).

KK CC h = yy ∗ ee −11.989 AA1.013 AA 0.228

Figure 72. Equation. SPF for KAB crashes (HSM-RUR4-3ST-KAB).

Four-leg STOP Controlled Intersections 

TT CC h = yy ∗ pp−10.008 AA0.848 AA 0.448

Figure 73. Equation. SPF for total crashes (HSM-RUR4-4ST-KABCO).

KK CC h = yy ∗ ee −11.554 AA0.888 AA 0.525

Figure 74. Equation. SPF for KABC crashes (HSM-RUR4-4ST-KABC).

KK CC h = yy ∗ ee −10.734 AA0.828 AA 0.412

Figure 75. Equation. SPF for KAB crashes (HSM-RUR4-4ST-KAB).
THE CALIBRATOR—UPDATED USER GUIDE

65 

Four-leg Signalized Intersections 

TT CC h = yy ∗ ee −7.182 AA0.722 AA 0.337

Figure 76. Equation. SPF for total crashes (HSM-RUR4-4SG-KABCO).

KK CC h = yy ∗ ee −6.393 AA0.638 AA 0.232

Figure 77. Equation. SPF for KABC crashes (HSM-RUR4-4SG-KABC).

KK CC h = yy ∗ ee −12.011( AA + AA )1.279

Figure 78. Equation. SPF for KAB crashes (HSM-RUR4-4SG-KAB).
THE CALIBRATOR—UPDATED USER GUIDE

66 

A.1.3 Urban and Suburban Arterials Chapter

Error! Reference source not found. through Error! Reference source not found.

provide SPFs for urban and suburban arterial segment crashes. Error! Reference source not 

found. through Error! Reference source not found. provide SPFs for urban and suburban 

arterial intersection crashes. The dispersion parameter is equal to k for all SPFs. The following 

are relevant site types for urban and suburban arterials: 

• 2U – two-lane undivided

• 3T – 3-lane with two-way left-turn lane

• 4U – 4-lane undivided

• 4D – 4-lane divided

• 5T – 5-lane with two-way left-turn lane

• 3ST – 3-leg STOP-controlled

• 3SG – 3-leg Signalized

• 4ST – 4-leg STOP-controlled

• 4SG – 4-leg Signalized

The following variable definitions apply to all SPFs in this subsection:

• length = segment length in miles

• AADT = average annual daily traffic on road segment

• AADTMAJ = average annual daily traffic on major road

• AADTMIN = average annual daily traffic on minor road

• MAJCOMM = count of major commercial driveways

• MINCOMM = count of minor commercial driveways

• MAJIND = count of major industrial driveways

• MININD = count of minor industrial driveways

• MAJRES = count of major residential driveways

• MINRES = count of minor residential driveways

• OTHER = count of other driveways

Multiple-Vehicle Non-Driveway Segment Crashes

MM NNOO OOOO CC h = yy ∗ ee ∗ h ∗

Figure 79. Equation. SPF for MVNONDWY crashes.

KK MM MM CC h = yy ∗ ee ∗ h ∗

Figure 80. Equation. SPF for KABC MVNONDWY crashes.

MM MM CC h = yy ∗ ee ∗ h ∗

Figure 81. Equation. SPF for PDO MVNONDWY crashes.
THE CALIBRATOR—UPDATED USER GUIDE

67 

Error! Reference source not found. presents the coefficients for multiple-vehicle nondriveway segment SPFs.

Table 5. Coefficients for multiple-vehicle non-driveway segment SPFs.

SPF ID Road Type Crash Severity Level a b

HSM-URB2U-MVNONDWY-KABCO 2U Total -15.22 1.68 

HSM-URB2U-MVNONDWY-KABC 2U KABC -16.22 1.66 

HSM-URB2U- MVNONDWY-PDO 2U PDO -15.62 1.69 

HSM-URB3T- MVNONDWY-KABCO 3T Total -12.4 1.41 

HSM-URB3T- MVNONDWY-KABC 3T KABC -16.45 1.69 

HSM-URB3T- MVNONDWY-PDO 3T PDO -11.95 1.33 

HSM-URB4U MVNONDWY—KABCO 4U Total -11.63 1.33 

HSM-URB4U- MVNONDWY-KABC 4U KABC -12.08 1.25 

HSM-URB4U- MVNONDWY-PDO 4U PDO -12.53 1.38 

HSM-URB4D- MVNONDWY-KABCO 4D Total -12.34 1.36 

HSM-URB4D- MVNONDWY-KABC 4D KABC -12.76 1.28 

HSM-URB4D- MVNONDWY-PDO 4D PDO -12.81 1.38 

HSM-URB5T- MVNONDWY-KABCO 5T Total -9.7 1.17 

HSM-URB5T- MVNONDWY-KABC 5T KABC -10.47 1.12 

HSM-URB5T- MVNONDWY-PDO 5T PDO -9.97 1.17 
THE CALIBRATOR—UPDATED USER GUIDE

68 

Single-Vehicle Segment Crashes

Figure 82. Equation. SPF for SV crashes.

Figure 83. Equation. SPF for KABC SV crashes.

Figure 84. Equation. SPF for PDO SV crashes.

Error! Reference source not found. provides the coefficients for single-vehicle segment 

SPFs.

Table 6. Coefficients for single-vehicle segment SPFs.

SPF ID Road Type Crash Severity Level a b

HSM-URB2U-SV-KABCO 2U Total -5.47 0.56 

HSM-URB2U-SV-KABC 2U KABC -3.96 0.23 

HSM-URB2U- SV-PDO 2U PDO -6.51 0.64 

HSM-URB3T- SV-KABCO 3T Total -5.74 0.54 

HSM-URB3T- SV-KABC 3T KABC -6.37 0.47 

HSM-URB3T- SV-PDO 3T PDO -6.29 0.56 

HSM-URB4U SV--KABCO 4U Total -7.99 0.81 

HSM-URB4U- SV-KABC 4U KABC -7.37 0.61 

HSM-URB4U- SV-PDO 4U PDO -8.5 0.84 

HSM-URB4D- SV-KABCO 4D Total -5.05 0.47 

HSM-URB4D- SV-KABC 4D KABC -8.71 0.66 

HSM-URB4D- SV-PDO 4D PDO -5.04 0.45 

HSM-URB5T- SV-KABCO 5T Total -4.82 0.54 

HSM-URB5T- SV-KABC 5T KABC -4.43 0.35 

HSM-URB5T- SV-PDO 5T PDO -5.83 0.61 
THE CALIBRATOR—UPDATED USER GUIDE

69 

Multiple-Vehicle Driveway-Related Segment Crashes

MM MM CC h = yy

∗ ff ∗ �

15,000� ( ∗ MMMM MMMM + cc ∗ MM MMMM + ∗ MMMM MM + ∗ MM MM + ff ∗ MMMM + ∗ MM + h

∗ OO OO )

Figure 85. Equation. SPF for MVDWY crashes.

KK MM MM CC h

= yy

∗ ff ∗ �

15,000� ( ∗ MM AA + cc ∗ MM MMMM + ∗ MMMM MM + ∗ MM MM + ff ∗ MMMM + ∗ MM + h

∗ OO OO )

Figure 86. Equation. SPF for KABC MVDWY crashes.

MM MM CC h = yy

∗ ff ∗ �

15,000� ( ∗ MMMM MMMM + cc ∗ MM MMMM + ∗ MMMM MM + ∗ MM MM + ff ∗ MMMM RR + ∗ MM + h

∗ OO OO )

Figure 87. Equation. SPF for PDO MVDWY crashes.

Error! Reference source not found. provides the coefficients for multiple-vehicle drivewayrelated segment SPFs.
THE CALIBRATOR—UPDATED USER GUIDE

70 

Table 7. Coefficients for multiple-vehicle driveway-related segment SPFs.

SPF ID

Road

Type

Crash 

Severity

Level f a b c d e f g h

HSMURB2UMVDWYKABCO 2U Total 1.000 1.000 0.158 0.050 0.172 0.023 0.083 0.016 0.025

HSMURB2UMVDWYKABC 2U KABC 0.323 1.000 0.158 0.050 0.172 0.023 0.083 0.016 0.025

HSMURB2UMVDWYPDO 2U PDO 0.677 1.000 0.158 0.050 0.172 0.023 0.083 0.016 0.025

HSMURB3TMVDWYKABCO 3T Total 1.000 1.000 0.102 0.032 0.110 0.015 0.053 0.010 0.016

HSMURB3TMVDWYKABC 3T KABC 0.243 1.000 0.102 0.032 0.110 0.015 0.053 0.010 0.016

HSMURB3TMVDWYPDO 3T PDO 0.757 1.000 0.102 0.032 0.110 0.015 0.053 0.010 0.016

HSMURB4UMVDWYKABCO 4U Total 1.000 1.172 0.182 0.058 0.198 0.026 0.096 0.018 0.029

HSMURB4UMVDWYKABC 4U KABC 0.342 1.172 0.182 0.058 0.198 0.026 0.096 0.018 0.029

HSMURB4UMVDWYPDO 4U PDO 0.658 1.172 0.182 0.058 0.198 0.026 0.096 0.018 0.029

HSMURB4DMVDWYKABCO 4D Total 1.000 1.106 0.033 0.011 0.036 0.005 0.018 0.003 0.005
THE CALIBRATOR—UPDATED USER GUIDE

71 

SPF ID

Road

Type

Crash 

Severity

Level f a b c d e f g h

HSMURB4DMVDWYKABC 4D KABC 0.284 1.106 0.033 0.011 0.036 0.005 0.018 0.003 0.005

HSMURB4DMVDWYPDO 4D PDO 0.716 1.106 0.033 0.011 0.036 0.005 0.018 0.003 0.005

HSMURB5TMVDWYKABCO 5T Total 1.000 1.172 0.165 0.053 0.181 0.024 0.087 0.016 0.027

HSMURB5TMVDWYKABC 5T KABC 0.269 1.172 0.165 0.053 0.181 0.024 0.087 0.016 0.027

HSMURB5TMVDWYPDO 5T PDO 0.731 1.172 0.165 0.053 0.181 0.024 0.087 0.016 0.027
THE CALIBRATOR—UPDATED USER GUIDE

72 

Multiple-Vehicle Intersection Crashes

Figure 88. Equation. SPF for MVINT crashes.

Figure 89. Equation. SPF for KABC MVINT crashes.

Figure 90. Equation. SPF for PDO MVINT crashes.

Error! Reference source not found. provides the coefficients for multiple-vehicle 

intersection SPFs.

Table 8. Coefficients for multiple-vehicle intersection SPFs.

SPF ID Road Type Crash Severity Level a b c

HSM-URB3ST-MV-KABCO 3ST Total -13.36 1.11 0.41 

HSM- URB 3ST-MV-KABC 3ST KABC -14.01 1.16 0.30 

HSM- URB 3ST-MV-PDO 3ST PDO -15.38 1.2 0.51 

HSM- URB 3SG-MV-KABCO 3SG Total -12.13 1.11 0.26 

HSM- URB 3SG-MV-KABC 3SG KABC -11.58 1.02 0.17 

HSM- URB 3SGMV-PDO 3SG PDO -13.24 1.14 0.30 

HSM- URB 4ST-MV-KABCO 4ST Total -8.9 0.82 0.25 

HSM- URB 4ST-MV-KABC 4ST KABC -11.13 0.93 0.28 

HSM- URB 4ST-MV-PDO 4ST PDO -8.74 0.77 0.23 

HSM- URB 4SG-MV-KABCO 4SG Total -10.99 1.07 0.23 

HSM- URB 4SG-MV-KABC 4SG KABC -13.14 1.18 0.22 

HSM- URB 4SG-MV-PDO 4SG PDO -11.02 1.02 0.24 
THE CALIBRATOR—UPDATED USER GUIDE

73 

Single-Vehicle Intersection Crashes

Figure 91. Equation. SPF for SVINT crashes.

Figure 92. Equation. SPF for KABC SVINT crashes.

Figure 93. Equation. SPF for PDO SVINT crashes.

Error! Reference source not found. provides the coefficients for single-vehicle intersection 

SPFs.

Table 9. Coefficients for single-vehicle intersection SPFs.

SPF ID Road Type Crash Severity Level a b c

HSM- URB 3ST-SV-KABCO 3ST Total -6.81 0.16 0.51 

HSM- URB 3ST-SV-PDO 3ST PDO -8.36 0.25 0.55 

HSM- URB 3SG-SV-KABCO 3SG Total -9.02 0.42 0.40 

HSM- URB 3SG-SV-KABC 3SG KABC -9.75 0.27 0.51 

HSM- URB 3SG-SV-PDO 3SG PDO -9.08 0.45 0.33 

HSM- URB 4ST-SV-KABCO 4ST Total -5.33 0.33 0.12 

HSM- URB 4ST-SV-PDO 4ST PDO -7.04 0.36 0.25 

HSM- URB 4SG-SV-KABCO 4SG Total -10.21 0.68 0.27 

HSM- URB 4SG-SV-KABC 4SG KABC -9.25 0.43 0.29 

HSM- URB 4SG-SV-PDO 4SG PDO -11.34 0.78 0.25 
THE CALIBRATOR—UPDATED USER GUIDE

74 

A.1.3 Freeway Chapter

The freeway SPFs are not in the first edition of the HSM, but are planned for inclusion in the 

second edition. The final report for NCHRP Project 17-45 documents these SPFs in detail. 

Error! Reference source not found. through Error! Reference source not found.

provide SPFs freeway segment and speed change lane crashes. The dispersion parameter is 

equal to k divided by segment length for Error! Reference source not found. through 

Error! Reference source not found.. The dispersion parameter is equal to k for Error! 

Reference source not found. and Error! Reference source not found.. Error! 

Reference source not found. through Error! Reference source not found. provide SPFs 

for ramp segments. The dispersion parameter is equal to k divided by ramp length for all SPFs. 

Error! Reference source not found. and Error! Reference source not found. provide 

SPFs for ramp terminals. The dispersion parameter is equal to k for both SPFs. The following 

variables definitions apply to all SPFs in this subsection:

• L* = effective length of freeway segment miles (see NCHRP report for details on how 

to calculate)

• Len =length of ramp entrance

• Lex =length of ramp exit

• LR =length of ramp

• AADT = Average Annual Daily Traffic on road segment

• AADTr = Average Annual Daily Traffic on ramp segment

• AADTxrd = Average Annual Daily Traffic on crossroad, equal to (AADTin + AADTout)/2

• AADTin = Average Annual Daily Traffic for crossroad leg between ramps

• AADTout = Average Annual Daily Traffic for crossroad leg outside interchange

• AADTex = Average Annual Daily Traffic for exit ramp

• AADTen = Average Annual Daily Traffic for entrance ramp
THE CALIBRATOR—UPDATED USER GUIDE

75 

Multiple-Vehicle Freeway Segment Crashes

Figure 94. Equation. SPF for freeway KABC MV crashes.

Figure 95. Equation. SPF for freeway PDO MV crashes.

Error! Reference source not found. provides the coefficients for multiple-vehicle freeway 

segment SPFs.

Table 10. Coefficients for multiple-vehicle freeway segment SPFs.

SPF ID

Area

Type

Number of

Through

Lanes

Crash

Severity

Level a b

HSM-RURFWY4-MV-KABC Rural 4 KABC -5.975 1.492

HSM-RURFWY6-MV-KABC Rural 6 KABC -6.092 1.492

HSM-RURFW8-MV-KABC Rural 8 KABC -6.140 1.492

HSM-URBFWY4-MV-KABC Urban 4 KABC -5.470 1.492

HSM-URBFWY6-MV-KABC Urban 6 KABC -5.587 1.492

HSM-URBFWY8-MV-KABC Urban 8 KABC -5.635 1.492

HSM-URBFWY10-MV-KABC Urban 10 KABC -5.842 1.492

HSM-RURFWY4-MV-O Rural 4 PDO -6.880 1.936

HSM-RURFWY6-MV-O Rural 6 PDO -7.141 1.936

HSM-RURFW8-MV-O Rural 8 PDO -7.329 1.936

HSM-URBFWY4-MV-O Urban 4 PDO -6.548 1.936

HSM-URBFWY6-MV-O Urban 6 PDO -6.809 1.936

HSM-URBFWY8-MV-O Urban 8 PDO -6.997 1.936

HSM-URBFWY10-MV-O Urban 10 PDO -7.260 1.936
THE CALIBRATOR—UPDATED USER GUIDE

76 

Single-Vehicle Freeway Segment Crashes

Figure 96. Equation. SPF for freeway KABC SV crashes.

Figure 97. Equation. SPF for freeway PDO SV crashes.

Error! Reference source not found. provides the coefficients for single-vehicle freeway 

segment SPFs.

Table 11. Coefficients for single-vehicle freeway segment SPFs.

SPF ID

Area

Type

Number of

Through

Lanes

Crash

Severity

Level a b

HSM-RURFWY4-SV-KABC Rural 4 KABC -2.126 0.646

HSM-RURFWY6-SV-KABC Rural 6 KABC -2.055 0.646

HSM-RURFW8-SV-KABC Rural 8 KABC -1.985 0.646

HSM-URBFWY4-SV-KABC Urban 4 KABC -2.126 0.646

HSM-URBFWY6-SV-KABC Urban 6 KABC -2.055 0.646

HSM-URBFWY8-SV-KABC Urban 8 KABC -1.985 0.646

HSM-URBFWY10-SV-KABC Urban 10 KABC -1.915 0.646

HSM-RURFWY4-SV-O Rural 4 PDO -2.235 0.876

HSM-RURFWY6-SV-O Rural 6 PDO -2.274 0.876

HSM-RURFW8-SV-O Rural 8 PDO -2.312 0.876

HSM-URBFWY4-SV-O Urban 4 PDO -2.235 0.876

HSM-URBFWY6-SV-O Urban 6 PDO -2.274 0.876

HSM-URBFWY8-SV-O Urban 8 PDO -2.312 0.876

HSM-URBFWY10-SV-O Urban 10 PDO -2.351 0.876
THE CALIBRATOR—UPDATED USER GUIDE

77 

Ramp Entrance Related Speed-Change Lanes Crashes

Figure 98. Equation. SPF for ramp entrance KABC crashes.

Figure 99. Equation. SPF for ramp entrance PDO crashes.

Error! Reference source not found. provides the coefficients for ramp entrance speedchange lane SPFs.

Table 12. Coefficients for ramp entrance speed-change lane SPFs.

SPF ID

Area

Type

Number of

Through

Lanes

Crash

Severity

Level a b

HSM-RURFWY4-ENT-KABC Rural 4 KABC -3.894 1.173

HSM-RURFWY6-ENT-KABC Rural 6 KABC -4.154 1.173

HSM-RURFWY8-ENT-KABC Rural 8 KABC -4.414 1.173

HSM-URBFWY4-ENT-KABC Urban 4 KABC -3.714 1.173

HSM-URBFWY6-ENT-KABC Urban 6 KABC -3.974 1.173

HSM-URBFWY8- ENT-KABC Urban 8 KABC -4.234 1.173

HSM-URBFWY10- ENT-KABC Urban 10 KABC -4.494 1.173

HSM-RURFWY4- ENT-O Rural 4 PDO -2.895 1.215

HSM-RURFWY6- ENT-O Rural 6 PDO -3.097 1.215

HSM-RURFW8- ENT-O Rural 8 PDO -3.299 1.215

HSM-URBFWY4- ENT-O Urban 4 PDO -2.796 1.215

HSM-URBFWY6- ENT-O Urban 6 PDO -2.998 1.215

HSM-URBFWY8- ENT-O Urban 8 PDO -3.200 1.215

HSM-URBFWY10- ENT-O Urban 10 PDO -3.402 1.215
THE CALIBRATOR—UPDATED USER GUIDE

78 

Ramp Exit Related Speed-Change Lanes Crashes

Figure 100. Equation. SPF for ramp exit KABC crashes.

Figure 101. Equation. SPF for ramp exit PDO crashes.

Error! Reference source not found. provides the coefficients for ramp exit speed-change 

lane SPFs.

Table 13. Coefficients for ramp exit speed-change lane SPFs.

SPF ID

Area

Type

Number of

Through

Lanes

Crash

Severity

Level a b

HSM-RURFWY4-EXT-KABC Rural 4 KABC -2.679 0.903

HSM-RURFWY6-EXT-KABC Rural 6 KABC -2.679 0.903

HSM-RURFWY8-EXT-KABC Rural 8 KABC -2.679 0.903

HSM-URBFWY4-EXT-KABC Urban 4 KABC -2.679 0.903

HSM-URBFWY6-EXT-KABC Urban 6 KABC -2.679 0.903

HSM-URBFWY8- EXT-KABC Urban 8 KABC -2.679 0.903

HSM-URBFWY10- EXT-KABC Urban 10 KABC -2.679 0.903

HSM-RURFWY4- EXT-O Rural 4 PDO -1.798 0.932

HSM-RURFWY6- EXT-O Rural 6 PDO -1.798 0.932

HSM-RURFW8- EXT-O Rural 8 PDO -1.798 0.932

HSM-URBFWY4- EXT-O Urban 4 PDO -1.798 0.932

HSM-URBFWY6- EXT-O Urban 6 PDO -1.798 0.932

HSM-URBFWY8- EXT-O Urban 8 PDO -1.798 0.932

HSM-URBFWY10- EXT-O Urban 10 PDO -1.798 0.932
THE CALIBRATOR—UPDATED USER GUIDE

79 

Multiple-Vehicle Crashes on Ramp Segments

Figure 102. Equation. SPF for ramp segment KABC MV crashes.

Figure 103. Equation. SPF for ramp segment PDO MV crashes.

Error! Reference source not found. provides the coefficients for multiple-vehicle ramp 

segment SPFs.

Table 14. Coefficients for multiple-vehicle ramp segment SPFs.

SPF ID

Area

Type

Number

of Ramp

Lanes

Ramp

Type

Crash

Severity

Level a b c

HSM-RURRMP-ENT1-MVKABC Rural 1 Entrance KABC -5.226 0.524 0.0699

HSM-RURRMP-EXT1-MVKABC Rural 1 Exit KABC -6.692 0.524 0.0699

HSM-URBRMP-ENT1-MVKABC Urban 1 Entrance KABC -3.505 0.524 0.0699

HSM-URBRMP-EXT1-MVKABC Urban 1 Exit KABC -4.971 0.524 0.0699

HSM-URBRMP-ENT2-MVKABC Urban 2 Entrance KABC -3.023 0.524 0.0699

HSM-URBRMP-EXT2-MVKABC Urban 2 Exit KABC -4.489 0.524 0.0699

HSM-RURRMP-ENT1-MV-O Rural 1 Entrance PDO -3.819 1.256 N/A

HSM-RURRMP-EXT1-MV-O Rural 1 Exit PDO -4.851 1.256 N/A

HSM-URBRMP-ENT1-MV-O Urban 1 Entrance PDO -3.819 1.256 N/A

HSM-URBRMP-EXT1-MV-O Urban 1 Exit PDO -4.851 1.256 N/A

HSM-URBRMP-ENT2-MV-O Urban 2 Entrance PDO -2.983 1.256 N/A

HSM-URBRMP-EXT2-MV-O Urban 2 Exit PDO -4.015 1.256 N/A
THE CALIBRATOR—UPDATED USER GUIDE

80 
THE CALIBRATOR—UPDATED USER GUIDE

81 

Single-Vehicle Crashes on Ramp Segments

Figure 104. Equation. SPF for ramp segment KABC SV crashes.

Figure 105. Equation. SPF for ramp segment PDO SV crashes.

Error! Reference source not found. provides the coefficients for single-vehicle ramp 

segment SPFs.

Table 15. Coefficients for single-vehicle ramp segment SPFs.

SPF ID

Area

Type

Number

of Ramp

Lanes

Ramp

Type

Crash

Severity

Level a b

HSM-RURRMP-ENT1-SVKABC Rural 1 Entrance KABC -2.120 0.718

HSM-RURRMP-EXT1-SVKABC Rural 1 Exit KABC -1.799 0.718

HSM-URBRMP-ENT1-SVKABC Urban 1 Entrance KABC -1.966 0.718

HSM-URBRMP-EXT1-SVKABC Urban 1 Exit KABC -1.645 0.718

HSM-URBRMP-ENT2-SVKABC Urban 2 Entrance KABC -1.999 0.718

HSM-URBRMP-EXT2-SVKABC Urban 2 Exit KABC -1.678 0.718

HSM-RURRMP-ENT1-SV-O Rural 1 Entrance PDO -1.946 0.689

HSM-RURRMP-EXT1-SV-O Rural 1 Exit PDO -1.739 0.689

HSM-URBRMP-ENT1-SV-O Urban 1 Entrance PDO -1.715 0.689

HSM-URBRMP-EXT1-SV-O Urban 1 Exit PDO -1.508 0.689

HSM-URBRMP-ENT2-SV-O Urban 2 Entrance PDO -1.400 0.689

HSM-URBRMP-EXT2-SV-O Urban 2 Exit PDO -1.193 0.689
THE CALIBRATOR—UPDATED USER GUIDE

82 
THE CALIBRATOR—UPDATED USER GUIDE

83 

Crashes at Ramp Terminals

Figure 106. Equation. SPF for ramp terminal KABC MV crashes.

Figure 107. Equation. SPF for ramp terminal PDO MV crashes.

Error! Reference source not found. provides the coefficients for ramp terminal SPFs.

Table 16. Coefficients for ramp terminal SPFs.

SPF ID

Number of

Crossroad

Lanes Ramp Type

Crash

Severity

Level a b c 

HSMSIGTERM1-

2LN-KABC 2 

Signalized 3 leg at TwoQuadrant Parclo A or B KABC -0.458 0.325 0.212 

HSMSIGTERM1-

3LN-KABC 3 

Signalized 3 leg at TwoQuadrant Parclo A or B KABC -0.298 0.325 0.212 

HSMSIGTERM1-

4LN-KABC 4 

Signalized 3 leg at TwoQuadrant Parclo A or B KABC -0.138 0.325 0.212 

HSMSIGTERM1-

5LN-KABC 5

Signalized 3 leg at TwoQuadrant Parclo A or B KABC 0.022 0.325 0.212 

HSMSIGTERM1-

6LN-KABC 6

Signalized 3 leg at TwoQuadrant Parclo A or B KABC 0.182 0.325 0.212 

HSMSIGTERM1-

2LN-O 2

Signalized 3 leg at TwoQuadrant Parclo A or B PDO -1.537 0.592 0.516 

HSMSIGTERM1-

3LN-O 3 

Signalized 3 leg at TwoQuadrant Parclo A or B PDO -1.449 0.592 0.516 

HSMSIGTERM1-

4LN-O 4

Signalized 3 leg at TwoQuadrant Parclo A or B PDO -1.361 0.592 0.516 
THE CALIBRATOR—UPDATED USER GUIDE

84 

SPF ID

Number of

Crossroad

Lanes Ramp Type

Crash

Severity

Level a b c 

HSMSIGTERM1-

5LN-O 5

Signalized 3 leg at TwoQuadrant Parclo A or B PDO -1.274 0.592 0.516 

HSMSIGTERM1-

6LN-O 6

Signalized 3 leg at TwoQuadrant Parclo A or B PDO -1.186 0.592 0.516 

HSMSIGTERM2-

2LN-KABC 2

Signalized 3 leg at Diagonal 

exit or 4 leg at Fourquadrant Parclo A KABC -1.352 0.379 0.394 

HSMSIGTERM2-

3LN-KABC 3

Signalized 3 leg at Diagonal 

exit or 4 leg at Fourquadrant Parclo A KABC -1.192 0.379 0.394 

HSMSIGTERM2-

4LN-KABC 4

Signalized 3 leg at Diagonal 

exit or 4 leg at Fourquadrant Parclo A KABC -1.032 0.379 0.394 

HSMSIGTERM2-

5LN-KABC 5

Signalized 3 leg at Diagonal 

exit or 4 leg at Fourquadrant Parclo A KABC -0.872 0.379 0.394 

HSMSIGTERM2-

6LN-KABC 6 

Signalized 3 leg at Diagonal 

exit or 4 leg at Fourquadrant Parclo A KABC -0.712 0.379 0.394 

HSMSIGTERM2-

2LN-O 2

Signalized 3 leg at Diagonal 

exit or 4 leg at Fourquadrant Parclo A PDO -2.247 0.797 0.384 

HSMSIGTERM2-

3LN-O 3

Signalized 3 leg at Diagonal 

exit or 4 leg at Fourquadrant Parclo A PDO -2.159 0.797 0.384 

HSMSIGTERM2-

4LN-O 4

Signalized 3 leg at Diagonal 

exit or 4 leg at Fourquadrant Parclo A PDO -2.071 0.797 0.384 

HSMSIGTERM2-

5LN-O 5 

Signalized 3 leg at Diagonal 

exit or 4 leg at Fourquadrant Parclo A PDO -1.984 0.797 0.384 

HSMSIGTERM2-

6LN-O 6

Signalized 3 leg at Diagonal 

exit or 4 leg at Fourquadrant Parclo A PDO -1.896 0.797 0.384 
THE CALIBRATOR—UPDATED USER GUIDE

85 

SPF ID

Number of

Crossroad

Lanes Ramp Type

Crash

Severity

Level a b c 

HSMSIGTERM3-

2LN-KABC 2

Signalized 3 leg at Diagonal 

entrance or 4 leg at Fourquadrant Parclo A KABC -2.068 0.265 0.905 

HSMSIGTERM3-

3LN-KABC 3

Signalized 3 leg at Diagonal 

entrance or 4 leg at Fourquadrant Parclo A KABC -1.908 0.265 0.905 

HSMSIGTERM3-

4LN-KABC 4

Signalized 3 leg at Diagonal 

entrance or 4 leg at Fourquadrant Parclo A KABC -1.748 0.265 0.905 

HSMSIGTERM3-

5LN-KABC 5

Signalized 3 leg at Diagonal 

entrance or 4 leg at Fourquadrant Parclo A KABC -1.588 0.265 0.905 

HSMSIGTERM3-

6LN-KABC 6

Signalized 3 leg at Diagonal 

entrance or 4 leg at Fourquadrant Parclo A KABC -1.428 0.265 0.905 

HSMSIGTERM3-

2LN-O 2

Signalized 3 leg at Diagonal 

entrance or 4 leg at Fourquadrant Parclo A PDO -2.931 0.741 0.845 

HSMSIGTERM3-

3LN-O 3 

Signalized 3 leg at Diagonal 

entrance or 4 leg at Fourquadrant Parclo A PDO -2.843 0.741 0.845 

HSMSIGTERM3-

4LN-O 4

Signalized 3 leg at Diagonal 

entrance or 4 leg at Fourquadrant Parclo A PDO -2.755 0.741 0.845 

HSMSIGTERM3-

5LN-O 5

Signalized 3 leg at Diagonal 

entrance or 4 leg at Fourquadrant Parclo A PDO -2.668 0.741 0.845 

HSMSIGTERM3-

6LN-O 6

Signalized 3 leg at Diagonal 

entrance or 4 leg at Fourquadrant Parclo A PDO -2.580 0.741 0.845 

HSMSIGTERM4-

2LN-KABC 2

Signalized 4 leg terminal 

with diagonal ramps KABC -2.655 1.191 0.131 

HSMSIGTERM4-

3LN-KABC 3

Signalized 4 leg terminal 

with diagonal ramps KABC -2.495 1.191 0.131 
THE CALIBRATOR—UPDATED USER GUIDE

86 

SPF ID

Number of

Crossroad

Lanes Ramp Type

Crash

Severity

Level a b c 

HSMSIGTERM4-

4LN-KABC 4

Signalized 4 leg terminal 

with diagonal ramps KABC -2.335 1.191 0.131 

HSMSIGTERM4-

5LN-KABC 5

Signalized 4 leg terminal 

with diagonal ramps KABC -2.175 1.191 0.131 

HSMSIGTERM4-

6LN-KABC 6

Signalized 4 leg terminal 

with diagonal ramps KABC -2.015 1.191 0.131 

HSMSIGTERM4-

2LN-O 2

Signalized 4 leg terminal 

with diagonal ramps PDO -2.248 0.879 0.545 

HSMSIGTERM4-

3LN-O 3

Signalized 4 leg terminal 

with diagonal ramps PDO -2.160 0.879 0.545 

HSMSIGTERM4-

4LN-O 4

Signalized 4 leg terminal 

with diagonal ramps PDO -2.072 0.879 0.545 

HSMSIGTERM4-

5LN-O 5

Signalized 4 leg terminal 

with diagonal ramps PDO -1.985 0.879 0.545 

HSMSIGTERM4-

6LN-O 6

Signalized 4 leg terminal 

with diagonal ramps PDO -1.897 0.879 0.545 

HSMSTOPTERM5-

2LN-KABC All 

One-way stop-controlled 

at 3 leg terminal at twoquadrant parclo A or B KABC -2.363 0.260 0.947 

HSMSTOPTERM5-

3LN-KABC All

One-way stop-controlled 

at 3 leg terminal at twoquadrant parclo A or B KABC -2.687 0.260 0.947 

HSMSTOPTERM5-

2LN-O All

One-way stop-controlled 

at 3 leg terminal at twoquadrant parclo A or B PDO -3.055 0.773 0.878 

HSMSTOPTERM5-

3LN-O All 

One-way stop-controlled 

at 3 leg terminal at twoquadrant parclo A or B PDO -3.055 0.773 0.878 
THE CALIBRATOR—UPDATED USER GUIDE

87 

SPF ID

Number of

Crossroad

Lanes Ramp Type

Crash

Severity

Level a b c 

HSMSTOPTERM6-

2LN-KABC All

One-way stop-controlled 

at 3 leg terminal with 

diagonal exit ramp or 4 leg 

terminal at four-quadrant 

parclo A KABC -2.899 0.582 0.899 

HSMSTOPTERM6-

3LN-KABC All

One-way stop-controlled 

at 3 leg terminal with 

diagonal exit ramp or 4 leg 

terminal at four-quadrant 

parclo A KABC -3.223 0.582 0.899 

HSMSTOPTERM6-

2LN-O All

One-way stop-controlled 

at 3 leg terminal with 

diagonal exit ramp or 4 leg 

terminal at four-quadrant 

parclo A PDO -2.670 0.595 0.937 

HSMSTOPTERM6-

3LN-O All

One-way stop-controlled 

at 3 leg terminal with 

diagonal exit ramp or 4 leg 

terminal at four-quadrant 

parclo A PDO -2.670 0.595 0.937 

HSMSTOPTERM7-

2LN-KABC All

One-way stop-controlled 

at 3 leg terminal with 

diagonal entrance ramp or 

4 leg terminal at fourquadrant parclo B KABC -2.817 0.709 0.730 

HSMSTOPTERM7-

3LN-KABC All

One-way stop-controlled 

at 3 leg terminal with 

diagonal entrance ramp or 

4 leg terminal at fourquadrant parclo B KABC -3.141 0.709 0.730 

HSMSTOPTERM7-

2LN-O All

One-way stop-controlled 

at 3 leg terminal with 

diagonal entrance ramp or 

4 leg terminal at fourquadrant parclo B PDO -2.358 0.885 0.350 

HSMSTOPTERM7-

3LN-O All

One-way stop-controlled 

at 3 leg terminal with 

diagonal entrance ramp or 

4 leg terminal at fourquadrant parclo B PDO -2.358 0.885 0.350 
THE CALIBRATOR—UPDATED USER GUIDE

88 

SPF ID

Number of

Crossroad

Lanes Ramp Type

Crash

Severity

Level a b c 

HSMSTOPTERM8-

2LN-KABC All

One-way stop-controlled 

at 4 leg terminal with 

diagonal ramps KABC -2.740 1.008 0.177 

HSMSTOPTERM8-

3LN-KABC All

One-way stop-controlled 

at 4 leg terminal with 

diagonal ramps KABC -3.064 1.008 0.177 

HSMSTOPTERM8-

2LN-O All

One-way stop-controlled 

at 4 leg terminal with 

diagonal ramps PDO -2.432 0.845 0.476 

HSMSTOPTERM8-

3LN-O All

One-way stop-controlled 

at 4 leg terminal with 

diagonal ramps PDO -2.432 0.845 0.476 
THE CALIBRATOR—UPDATED USER GUIDE

89 

A.2. AASHTOWARE SAFETY ANALYSTTM SPFS

This section documents the SPFs included in the AASHTOWare Safety AnalystTM software. 

These SPFs are already available in the spreadsheet tool. In order to apply these SPFs directly,

the variable names for the imported data will need to match those used in the predefined SPFs 

and documented here. Error! Reference source not found. and Error! Reference source 

not found. provide the AASHTOWare Safety AnalystTM SPFs for segments. Error! 

Reference source not found. and Error! Reference source not found. provide the 

AASHTOWare Safety AnalystTM SPFs for intersections. The dispersion parameter equals k for 

all SPFs. Error! Reference source not found. presents the coefficients for AASHTOWare 

Safety AnalystTM SPFs, including the name of the predefined SPF in the SPF ID column.

The following variable definitions apply to all SPFs in this subsection:

• length = segment length in miles

• AADT = average annual daily traffic on road segment

• AADTMAJ = average annual daily traffic on major road

• AADTMIN = average annual daily traffic on minor road

The SPF forms are:

Segments

TT CC h = yy ∗ h ∗ ee

Figure 108. Equation. Safety AnalystTM SPF for segment total crashes.

KK CC h = yy ∗ h ∗ ee

Figure 109. Equation. Safety AnalystTM SPF for segment KABC crashes.

Intersections

TT CC h = yy ∗ ee AA AA cc

Figure 110. Equation. Safety AnalystTM SPF for intersection total crashes.

KK CC h = yy ∗ ee AA AA cc

Figure 111. Equation. Safety AnalystTM SPF for intersection KABC crashes.
THE CALIBRATOR—UPDATED USER GUIDE

90 

Table 17. Coefficients for AASHTOWare Safety AnalystTM SPFs.

SPF ID Site Subtype

Crash

Severity

Level a b c 

SA-RUR2U-KABCO Seg/Rur; 2-lane Total -3.63 0.53 N/A

SA-RUR2U-KABC Seg/Rur; 2-lane KABC -4.86 0.53 N/A

SA-RURMU-KABCO Seg/Rur; Multilane undivided Total -3.17 0.49 N/A

SA-RURMU-KABC Seg/Rur; Multilane undivided KABC -4.20 0.50 N/A

SA-RURMD-KABCO Seg/Rur; Multilane divided Total -5.05 0.66 N/A

SA-RURMD-KABC Seg/Rur; Multilane divided KABC -7.46 0.72 N/A

SA-RUR4FWY-KABCO Seg/Rur; Fwy (4 ln) Total -6.82 0.81 N/A

SA-RUR4FWY-KABC Seg/Rur; Fwy (4 ln) KABC -8.82 0.89 N/A

SA-RUR6+FWY-KABCO Seg/Rur; Fwy (6+ ln) Total -8.28 0.94 N/A

SA-RUR6+FWY-KABC Seg/Rur; Fwy (6+ ln) KABC -10.25 1.03 N/A

SA-RUR4INTCHG-KABCO Seg/Rur; Fwy in intchng area (4 ln) Total -7.76 0.97 N/A

SA-RUR4INTCHG-KABC Seg/Rur; Fwy in intchng area (4 ln) KABC -8.86 0.96 N/A

SA-RUR6+INTCHG-KABCO Seg/Rur; Fwy in intchng area (6+ ln) Total -9.63 1.06 N/A

SA-RUR6+INTCHG-KABC Seg/Rur; Fwy in intchng area (6+ ln) KABC -10.48 1.04 N/A

SA-URB2U-KABCO Seg/Urb; 2-lane arterial Total -7.16 0.84 N/A

SA-URB2U-KABC Seg/Urb; 2-lane arterial KABC -8.84 0.89 N/A

SA-URBMU-KABCO Seg/Urb; Multilane undivided Total -10.24 1.29 N/A

SA-URBMU-KABC Seg/Urb; Multilane undivided KABC -12.07 1.39 N/A

SA-URBMD-KABCO Seg/Urb; Multilane divided Total -11.85 1.34 N/A

SA-URBMD-KABC Seg/Urb; Multilane divided KABC -14.87 1.52 N/A

SA-URBONEWAY-KABCO Seg/Urb; One-way arterial Total -3.53 0.6 N/A

SA-URBONEWAY-KABC Seg/Urb; One-way arterial KABC -5.15 0.65 N/A

SA-URB4FWY-KABCO Seg/Urb; Fwy (4 ln) Total -7.85 1 N/A

SA-URB4FWY-KABC Seg/Urb; Fwy (4 ln) KABC -8.82 1.02 N/A

SA-URB6FWY-KABCO Seg/Urb; Fwy (6 ln) Total -5.96 0.78 N/A

SA-URB6FWY-KABC Seg/Urb; Fwy (6 ln) KABC -7.6 0.85 N/A

SA-URB8+FWY-KABCO Seg/Urb; Fwy (8+ ln) Total -16.24 1.67 N/A

SA-URB8+FWY-KABC Seg/Urb; Fwy (8+ ln) KABC -19.16 1.85 N/A

SA-URB4INTCHG-KABCO Seg/Urb; Fwy in intchng area (4 ln) Total -11.23 1.3 N/A

SA-URB4INTCHG-KABC Seg/Urb; Fwy in intchng area (4 ln) KABC -12.89 1.38 N/A

SA-URB6INTCHG-KABCO Seg/Urb; Fwy in intchng area (6 ln) Total -11.25 1.28 N/A
THE CALIBRATOR—UPDATED USER GUIDE

91 

SPF ID Site Subtype

Crash

Severity

Level a b c 

SA-URB6INTCHG-KABC Seg/Urb; Fwy in intchng area (6 ln) KABC -13.62 1.42 N/A

SA-URB8+INTCHG-KABCO Seg/Urb; Fwy in intchng area (8+ ln) Total -26.76 2.58 N/A

SA-URB8+INTCHG-KABC Seg/Urb; Fwy in intchng area (8+ ln) KABC -25.63 2.42 N/A

SA-RUR-3ST-KABCO Int/Rur; 3-leg minor-rd STOP Total -8.78 0.71 0.24

SA-RUR-3ST-KABC Int/Rur; 3-leg minor-rd STOP KABC -9.35 0.71 0.21

SA-RUR-3STAW-KABCO Int/Rur; 3-leg all-way STOP Total -12.37 1.22 0.27

SA-RUR-3STAW-KABC Int/Rur; 3-leg all-way STOP KABC -10.02 1.27 -0.22

SA-RUR-3SG-KABCO Int/Rur; 3-leg signalized Total -6.57 0.66 0.2

SA-RUR-3SG-KABC Int/Rur; 3-leg signalized KABC -7.83 0.75 0.14

SA-RUR-4ST-KABCO Int/Rur; 4-leg minor-rd STOP Total -8.96 0.65 0.47

SA-RUR-4ST-KABC Int/Rur; 4-leg minor-rd STOP KABC -9.36 0.66 0.4

SA-RUR-4STAW-KABCO Int/Rur; 4-leg all-way STOP Total -12.37 1.22 0.27

SA-RUR-4STAW-KABC Int/Rur; 4-leg all-way STOP KABC -10.02 1.27 -0.22

SA-RUR-4SG-KABCO Int/Rur; 4-leg signalized Total -6.57 0.66 0.2

SA-RUR-4SG-KABC Int/Rur; 4-leg signalized KABC -7.83 0.75 0.14

SA-URB-3ST-KABCO Int/Urb; 3-leg minor-rd STOP Total -5.35 0.34 0.28

SA-URB-3ST-KABC Int/Urb; 3-leg minor-rd STOP KABC -8.45 0.49 0.39

SA-URB-3STAW-KABCO Int/Urb; 3-leg all-way STOP Total -12.37 1.22 0.27

SA-URB-3STAW-KABC Int/Urb; 3-leg all-way STOP KABC -10.02 1.27 -0.22

SA-URB-3SG-KABCO Int/Urb; 3-leg signalized Total -9.85 0.97 0.18

SA-URB-3SG-KABC Int/Urb; 3-leg signalized KABC -10.22 0.91 0.21

SA-URB-4ST-KABCO Int/Urb; 4-leg minor-rd STOP Total -3.12 0.27 0.16

SA-URB-4ST-KABC Int/Urb; 4-leg minor-rd STOP KABC -4.35 0.29 0.19

SA-URB-4STAW-KABCO Int/Urb; 4-leg all-way STOP Total -12.37 1.22 0.27

SA-URB-4STAW-KABC Int/Urb; 4-leg all-way STOP KABC -10.02 1.27 -0.22

SA-URB-4SG-KABCO Int/Urb; 4-leg signalized Total -3.47 0.42 0.14

SA-URB-4SG-KABC Int/Urb; 4-leg signalized KABC -5.11 0.49 0.16

SA-RUR-DIAMOFF-KABCO Ramp/Rur; Diamond (off) Total -3.07 0.46 N/A

SA-RUR-DIAMOFF-KABC Ramp/Rur; Diamond (off) KABC -4.54 0.47 N/A

SA-RUR-DIAMON-KABCO Ramp/Rur; Diamond (on) Total -2.16 0.19 N/A

SA-RUR-DIAMON-KABC Ramp/Rur; Diamond (on) KABC -8.12 0.86 N/A

SA-RUR-PARCLOOFF-KABCO Ramp/Rur; Parclo loop (off) Total -1.15 0.26 N/A
THE CALIBRATOR—UPDATED USER GUIDE

92 

SPF ID Site Subtype

Crash

Severity

Level a b c 

SA-RUR-PARCLOOFF-KABC Ramp/Rur; Parclo loop (off) KABC -4.29 0.59 N/A

SA-RUR-PARCLOON-KABCO Ramp/Rur; Parclo loop (on) Total -5.59 0.82 N/A

SA-RUR-PARCLOON-KABC Ramp/Rur; Parclo loop (on) KABC -1.3 0.24 N/A

SA-RUR-FFLOWOFF-KABCO Ramp/Rur; Free-flow loop (off) Total -5.1 0.78 N/A

SA-RUR-FFLOWOFF-KABC Ramp/Rur; Free-flow loop (off) KABC -4.29 0.59 N/A

SA-RUR-FFLOWON-KABCO Ramp/Rur; Free-flow loop (on) Total -1.17 0.35 N/A

SA-RUR-FFLOWON-KABC Ramp/Rur; Free-flow loop (on) KABC -1.3 0.24 N/A

SA-RUR-FFLOWOUT-KABCO Ramp/Rur; Free-flow outer connection Total -2.83 0.49 N/A

SA-RUR-FFLOWOUT-KABC Ramp/Rur; Free-flow outer connection KABC -4.89 0.61 N/A

SA-RUR-DIR-KABCO

Ramp/Rur; Direct/semi-direct 

connection Total -3.21 0.56 N/A

SA-RUR-DIR-KABC

Ramp/Rur; Direct/semi-direct 

connection KABC -4.22 0.55 N/A

SA-URB-DIAMOFF-KABCO Ramp/Urb; Diamond (off) Total -3.52 0.54 N/A

SA-URB-DIAMOFF-KABC Ramp/Urb; Diamond (off) KABC -3.86 0.47 N/A

SA-URB-DIAMON-KABCO Ramp/Urb; Diamond (on) Total -8.2 1.03 N/A

SA-URB-DIAMON-KABC Ramp/Urb; Diamond (on) KABC -8 0.86 N/A

SA-URB-PARCLOOFF-KABCO Ramp/Urb; Parclo loop (off) Total -1.15 0.26 N/A

SA-URB-PARCLOOFF-KABC Ramp/Urb; Parclo loop (off) KABC -3.68 0.53 N/A

SA-URB-PARCLOON-KABCO Ramp/Urb; Parclo loop (on) Total -5.59 0.82 N/A

SA-URB-PARCLOON-KABC Ramp/Urb; Parclo loop (on) KABC -1.34 0.24 N/A

SA-URB-FFLOWOFF-KABCO Ramp/Urb; Free-flow loop (off) Total -4.6 0.73 N/A

SA-URB-FFLOWOFF-KABC Ramp/Urb; Free-flow loop (off) KABC -3.68 0.53 N/A

SA-URB-FFLOWON-KABCO Ramp/Urb; Free-flow loop (on) Total -0.55 0.29 N/A

SA-URB-FFLOWON-KABC Ramp/Urb; Free-flow loop (on) KABC -1.34 0.24 N/A

SA-URB-FFLOWOUT-KABCO Ramp/Urb; Free-flow outer connection Total -3.5 0.57 N/A

SA-URB-FFLOWOUT-KABC Ramp/Urb; Free-flow outer connection KABC -6.12 0.75 N/A

SA-URB-DIR-KABCO

Ramp/Urb; Direct/semi-direct 

connection Total -1.28 0.35 N/A

SA-URB-DIR-KABC

Ramp/Urb; Direct/semi-direct 

connection KABC -2.5 0.37 N/A
THE CALIBRATOR—UPDATED USER GUIDE

93 

ACKNOWLEDGMENTS

The project team would like to thank the following individuals who served as members on the 

Technical Working Group and provided reviews for this effort.

TECHNICAL WORKING GROUP

Stuart Thompson, FHWA Office of Safety

Ray Krammes, FHWA Office of Safety

Yanira Rivera, FHWA Office of Safety

Jerry Roche, FHWA Office of Safety

Dave Engstrom, FHWA Resource Center and Design Team

Dave Petrucci, FHWA Resource Center and Design Team

Matt Warren, Oklahoma Department of Transportation

Eric Green, Kentucky Transportation Center
THE CALIBRATOR—UPDATED USER GUIDE

94 

REFERENCES

1. American Association of State Highway and Transportation Officials (AASHTO). 

Highway Safety Manual. Washington, DC, 2010.

2. User’s Guide to Develop Highway Safety Manual Safety Performance Function 

Calibration Factors. NCHRP Report HR 20-7(332), 2014.

http://safety.fhwa.dot.gov/rsdp/toolbox-content.aspx?toolid=116. 

3. Safety Performance Function Decision Guide: SPF Calibration vs. SPF Development. 

FHWA-SA-14-004, Federal Highway Administration, 2013.

http://safety.fhwa.dot.gov/rsdp/toolbox-content.aspx?toolid=99. 

4. Safety Performance Function Development Guide: Developing Jurisdiction-Specific SPFs. 

FHWA-SA-14-005, Federal Highway Administration, 2013. 

http://safety.fhwa.dot.gov/rsdp/toolbox-content.aspx?toolid=100. 

5. Hauer, E. The Art of Regression Modeling in Road Safety. Springer International 

Publishing Switzerland, 2015.

6. Srinivasan, R., M. Colety, G. Bahar, B. Crowther and M. Farmen. Estimation of 

Calibration Functions for Predicting Crashes on Rural Two-Lane Roads in Arizona. 

Transportation Research Record: Journal of the Transportation Research Board, No. 

2583, Transportation Research Board of the National Academies, Washington, D.C., 

2016, pp. 17-24. 

7. Hauer, E. Statistical Road Safety Modeling. Transportation Research Record: Journal of 

the Transportation Research Board, No. 1897, Transportation Research Board of the 

National Academies, Washington, D.C., 2004, pp. 81-87. 

8. Shirazi, M, D. Lord, and S.R. Geedipally. Sample-Size Guidelines for Recalibrating Crash 

Prediction Models: Recommendations for the Highway Safety Manual. Presented at the 

95th Annual Meeting of the Transportation Research Board, Washington, D.C., 2016.

9. Banihashemi, M. Sensitivity Analysis of Data Set Sizes for Highway Safety Manual 

Calibration Factors. Transportation Research Record: Journal of the Transportation 

Research Board, No. 2279, Transportation Research Board of the National Academies, 

Washington, D.C., 2012, pp. 75-81. 

10. Alluri, P., D. Saha, and A. Gan. Minimum Sample Sizes for Estimating Reliable Highway 

Safety Manual (HSM) Calibration Factors. Journal of Transportation Safety & Security, 

2014. 

11. Trieu, V., S. Park, and J. McFadden. Use of Monte Carlo Simulation for a Sensitivity 

Analysis of Highway Safety Manual Calibration Factors. Transportation Research Record: 

Journal of the Transportation Research Board, No. 2435, Transportation Research 

Board of the National Academies, Washington, D.C., 2014, pp. 1-10. 

12. Xie, F., K. Gladhill, K. K. Dixon, and C. M. Monsere. Calibration of Highway Safety 

Manual Predictive Models for Oregon State Highways. Transportation Research Record: 

Journal of the Transportation Research Board, No. 2241, Transportation Research 

Board of the National Academies, Washington, D.C., 2011, pp. 19–28. 

13. Sun, X., D. Magri, H. H. Shirazi, S. Gillella, and L. Li. Application of the Highway Safety 

Manual: Louisiana Experience with Rural Multilane Highways. Presented at 90th Annual 

Meeting of the Transportation Research Board, Washington, D.C., 2011.
THE CALIBRATOR—UPDATED USER GUIDE

95 

14. Sacchi, E., Persaud B., and M. Bassani. Assessing International Transferability of Highway 

Safety Manual Crash Prediction Algorithm and Its Components. Transportation 

Research Record: Journal of the Transportation Research Board, No. 2279, 

Transportation Research Board of the National Academies, Washington, D.C., 2012, pp. 

90–98. 

15. Fridstrom, L., Ifver, J., Ingebrigtsen, S., Kulmala, R., and Thomsen, L. K. Measuring the 

contribution of randomness, exposure, weather, and daylight to the variation in road 

accident counts. Accident Analysis and Prevention, Vol. 27, pp. 1-20. 1995.

16. Lord, D., S. R. Geedipally, B. N. Persaud, S. P. Washington, I. van Schalkwyk, J. N. Ivan, 

C. Lyon, and T. Jonsson. NCHRP Web-Only Document 126: Methodology to Predict 

the Safety Performance of Rural Multilane Highways. Transportation Research Board of 

the National Academies, Washington, D.C., 2008. 

http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_w126.pdf. 

17. Vogt, A., and J. Bared. Accident Models for Two-Lane Rural Segments and Intersections. 

Transportation Research Record: Journal of the Transportation Research Board, No. 

1635, Transportation Research Board of the National Academies, Washington, D.C., 

1998, pp. 18–29. 

18. Srinivasan, R., Baek, J., Carter, D., Persaud, B., Lyon, C., Eccles, K., Gross, F., Lefler, N., 

"Safety Evaluation of Improved Curve Delineation." Report No. FHWA-HRT-09-045, 

Federal Highway Administration, Washington, D.C., 2009.
For More Information: 

Stuart Thompson 

Stuart.Thompson@dot.gov 

202-366-8090 

Federal Highway Administration 

Office of Safety 

1200 New Jersey Avenue SE 

Washington, DC 20590 

http://safety.fhwa.dot.gov/ 

Publication # FHWA-SA-17-016