1

Final Report

Prepared for

Federal Highway Administration

Office of Safety

Prepared by

The University of North Carolina

Highway Safety Research Center

September 2013
2

TECHNICAL DOCUMENTATION PAGE

1. Report No.

FHWA-SA-14-004

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

4. Title and Subtitle

Safety Performance Function Decision Guide: SPF Calibration vs SPF 

Development

5. Report Date

September 2013

6. Performing Organization Code

7.Author(s)

Raghavan Srinivasan, Daniel Carter, and Karin Bauer

8. Performing Organization Report No.

9. Performing Organization Name and Address

Highway Safety Research Center

University of North Carolina

730 Martin Luther King Jr Blvd

Chapel Hill, NC 27599-3430

10. Work Unit No.

11. Contract or Grant No.

TPF-5(255)

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

14. Sponsoring Agency Code

FHWA

15. Supplementary Notes

The contract manager for this report was Ms. Esther Strawder. A special note to all the States participating in the technical 

advisory group and the HSM Implementation Pooled Fund Study: your time and contributions were extremely valuable to 

the project team as we developed the Safety Performance Function Guides.

16. Abstract

This guidebook is intended to provide guidance on whether an agency should calibrate the safety performance functions 

(SPFs) from the Highway Safety Manual (HSM) (AASHTO, 2010) or develop jurisdiction-specific SPFs. The guidebook 

discusses the factors that need to be considered while making the decision. It is intended to be of use to practitioners at 

state and local agencies and to researchers. 

17. Key Words:

Safety Performance Functions, Highway Safety 

Manual, Calibration, calibration function, Pooled 

Fund Study TPF-5(255)

18. Distribution Statement

No restrictions.

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page) 

Unclassified

21. No. of Pages

 31

22. Price

Form DOT F 1700.7 (8-72) Reproduction of completed pages authorized
3

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. 

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

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

document. 

Quality Assurance Statement

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

Government, industry, and the public in a manner that promotes public understanding. Standards 

and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its 

information. FHWA periodically reviews quality issues and adjusts its programs and processes to 

ensure continuous quality improvement.
4

Contents

Acknowledgements................................................................................................................................. 5

Executive Summary ................................................................................................................................. 6

1. Background and Context...................................................................................................................... 7

Organization of this Document............................................................................................................ 7

2. What Are SPFs? ................................................................................................................................... 8

3. How Are SPFs Used?............................................................................................................................ 9

Network Screening Level: Identifying Locations with Promise.............................................................. 9

Project Level: Determining the Expected Safety Impacts of Design Changes......................................... 9

Evaluating the Effect of Engineering Treatments.................................................................................. 9

4. Options for Obtaining SPFs for a Jurisdiction...................................................................................... 11

Calibrating SPFs................................................................................................................................. 11

Developing SPFs ................................................................................................................................ 14

5. Decision Process: How an Agency Obtains SPFs ................................................................................. 17

Step-by-Step Process......................................................................................................................... 17

Staff Time Required for Calibration and Development ....................................................................... 20

References............................................................................................................................................ 22

Appendix A: Roadway and Intersection Types for which SPFs are provided in the HSM (1st Edition) and 

Safety Analyst........................................................................................................................................ 24

Appendix B. Developing an Intersection Inventory................................................................................. 26

Appendix C. Recent SPF Development Efforts from States..................................................................... 28
5

Acknowledgements

This study was funded through the HSM Implementation Pooled Fund Study TPF-5(255). The authors 

thank the pooled fund states for providing the necessary funding that made this effort possible. Esther 

Strawder from FHWA was the COTM. The authors thank Esther Strawder for her support, patience, and 

guidance throughout this effort. Ray Krammes, Stuart Thompson, Clayton Chen, and David Engstrom 

from FHWA reviewed draft versions of this document and provided valuable comments. In addition, the 

following individuals from the States reviewed earlier versions of the document and provided comments 

and suggestions:

Idaho: Brent Jennings

Missouri: John Miller and Ashley Reinkemeyer

Wisconsin: John Corbin and Rebecca Szymkowski

North Carolina: Brian Mayhew

Illinois: Priscilla Tobias

Washington: Tim Carlile and John Milton

Ohio: Derek Troyer and Don Fisher

Kansas: Howard Lubliner

Pennsylvania: Gary Modi and Chris Speese

California: Craig Copelan

Oklahoma: David Glabas and Matt Warren

West Virginia: Donna Hardy

Oregon: Kevin Haas

Mississippi: Daniel Helms

Louisiana: Dan Magri

Nevada: Mike Colety and Ken Mammen
6

Executive Summary

This guidebook is intended to provide guidance on whether an agency should calibrate the safety 

performance functions (SPFs) from the Highway Safety Manual (HSM) or develop jurisdiction-specific 

SPFs. The guidebook discusses the factors that need to be considered while making the decision. It is 

intended to be of use to practitioners at state and local agencies and to researchers.

The guidebook starts with a brief overview of other documents being developed by FHWA and NCHRP to 

facilitate the implementation of the HSM. This is followed by a brief discussion of “What are SPFs”

(Section 2). This is then followed by a brief discussion on how SPFs are used for different applications, 

i.e., network screening, project level analysis, and determining the safety effect of improvements

(Section 3). 

Section 4 is a discussion of the options for obtaining SPFs for a jurisdiction. The two options: (1) 

calibration of existing SPFs, and (2) development of jurisdiction specific SPFs, are discussed along with a 

brief overview of the steps involved in the calibration and development of jurisdiction specific SPFs.

Section 5 discusses the step by step process that an agency could use to obtain SPFs. The following 

steps are discussed:

Step 1. Determine intended use of SPF

Step 2. Determine facility type

Step 3. Identify existing SPF

Step 4. Consider sample size necessary for calibrating SPF

Step 5. Consider roadway data necessary for calibrating SPF

Step 6. Calibrate existing SPF

Step 7. Assess quality of calibration factor

Step 8. Consider statistical expertise necessary for developing SPF

Step 9. Consider sample size necessary for developing SPF

Step 10. Determine crash type to be addressed by SPF

Step 11. Develop SPF

Section 5 also discusses the staff required for calibration and development of jurisdiction-specific SPFs. 

The staff time estimates are based on the judgment of the project team.

This report also includes three appendices. Appendix A provides the list of intersection and roadway 

types for which SPFs are available in the first edition of the HSM and Safety Analyst. Appendix B is a 

discussion of the major considerations in building an intersection inventory. Appendix C is a brief 

description of recent jurisdiction-specific SPF development efforts from different States.
7

1. Background and Context

This guidebook is intended to provide guidance on whether an agency should calibrate the safety 

performance functions (SPFs) from the Highway Safety Manual (HSM) (AASHTO, 2010) or develop 

jurisdiction-specific SPFs. The guidebook discusses the factors that need to be considered while making 

the decision. It is intended to be of use to practitioners at state and local agencies and to researchers.

This document is part of a series of documents currently being developed by the Federal Highway 

Administration (FHWA) and the National Cooperative Highway Research Program (NCHRP) to facilitate 

the implementation of the HSM by the States. Following is the list of the other documents being 

prepared as part of the series:

NCHRP Project 20-7 (Task 332): This effort, led by Dr. Geni Bahar of NAVIGATS will develop a 

User’s Guide to Develop Highway Safety Manual Safety Performance Function Calibration 

Factors (hereafter referred to as the SPF Calibration Guide). This document will provide 

guidelines to assist an agency in developing statistically sound calibration factors. This 

document will also provide guidance for assessing the quality of a calibration factor after it is 

developed.

Safety Performance Function Development Guide: Developing Jurisdiction Specific SPFs

(hereafter referred to as the SPF Development Guide). If a jurisdiction decides that developing 

jurisdiction-specific SPFs will fit their needs, this document will provide knowledge of what data, 

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

effort is currently being funded by FHWA.

SPF Needs Assessment: This project, led by Volpe did a needs and alternatives assessment to 

determine the set of potential resources that would best satisfy the future needs of the states 

using SPFs. Part of this project involved conducting interviews with selected States to better 

understand their needs and requirements regarding SPFs. Further information about this effort 

can be obtained from http://safety.fhwa.dot.gov/rsdp/.

Organization of this Document

The next section of this document gives a brief discussion of “What are SPFs” (Section 2). This is then 

followed by a brief discussion on how SPFs are used for different applications, i.e., network screening, 

project level analysis, and determining the safety effect of improvements (Section 3). Section 4 is a 

discussion of the options for obtaining SPFs for a jurisdiction. Section 5 discusses the step by step 

process that an agency could use to obtain SPFs. This is a followed by a list of references. The 

document concludes with three Appendices.
8

2. What Are SPFs?

SPFs are crash prediction models. They are essentially mathematical equations that relate the number 

of crashes of different types to site characteristics. These models always include traffic volume (AADT) 

but may also include site characteristics such as lane width, shoulder width, radius/degree of horizontal 

curves, presence of turn lanes (at intersections), and traffic control (at intersections). One example is 

the following SPF from Safety Analyst for predicting the total number of crashes on rural multilane 

divided roads:

5 .05 0 .66 P L e ( AADT )

Where:

P is the total number of crashes in 1 year on a segment of length L. 

The primary purpose of this SPF from Safety Analyst1is to assist an agency in their network screening 

process, i.e., to identify sites that may benefit from a safety treatment. This is a relatively simple SPF 

where the predicted number of crashes per mile is a function of just AADT. On the other hand, Bauer 

and Harwood (2012) provide a more complex prediction model for fatal and injury crashes on rural two 

lane roads:

NFI = exp b0 + b1ln AADT + b2G + b3ln 2 ×

5730

R

 × IHC + b4 

1

R

 

1

LC

 × IHC 

Where:

NFI = fatal-and-injury crashes/mi/yr

AADT = veh/day

G = absolute value of percent grade; 0 percent for level tangents; ≥ 1 percent 

otherwise

R = curve radius (ft); missing for tangents

IHC = horizontal curve indicator: 1 for horizontal curves; 0 otherwise

LC = horizontal curve length (mi); not applicable for tangents

ln = natural logarithm function

b0,...,b4 = regression coefficients

This prediction model was estimated using data from Washington. This model was estimated to 

examine the safety aspects of horizontal and vertical curvature.

 

1

Safety Analyst is a set of software tools that can be used by state and local agencies for highway safety 

management. It is available for licensing as an AASHTOWare product (see www.safetyanalyst.org for further 

details).
9

3. How Are SPFs Used?

The HSM outlines at least three different ways in which SPFs can be used by jurisdictions to make better 

safety decisions. One application is to use SPFs as part of network screening to identify sections that 

may have the best potential for improvements (i.e., Part B of the HSM). The second application is to use 

SPFs to determine the safety impacts of design changes at the project level (i.e., Part C of the HSM). The 

third application is the use of SPFs as part of a before-after study to evaluate the safety effects of 

engineering treatments. Following is a brief discussion of these applications.

Network Screening Level: Identifying Locations with Promise

SPFs may be used to identify locations with promise, which are locations that may benefit the most from

a safety treatment. This application is also referred to as network screening. Here, SPFs can be used to 

estimate the predicted number of crashes for a particular facility type with a particular traffic volume. 

This predicted number can then be compared to the observed number of crashes at a particular site to 

predict the expected number of crashes at that site. This result is used to determine if that site should 

be categorized as a “site with promise”. Methods for using SPFs in network screening are discussed in 

Part B of the HSM. SPFs that could be used for network screening are available in Safety Analyst, a set of 

software tools that can be used by state and local agencies for safety management. Appendix A of this 

document provides the default list of roadway, intersection, and ramp types for which SPFs are provided 

in Safety Analyst.

Project Level: Determining the Expected Safety Impacts of Design 

Changes

When SPFs are used in project-level decision making, they are used for estimating the average expected 

crash frequency for existing conditions, alternatives to existing conditions, or proposed new roadways. 

Part C of the HSM provides methods for estimating the average expected crash frequency of a site or 

project. These methods involve the use of SPFs for predicting the crash frequency for a “base” condition 

and crash modification factors (CMFs) to adjust the predictions for situations that differ from that base 

condition. The SPFs for these base conditions along with the CMFs are available in Part C of the HSM. 

The list of roadway and intersection types for which SPFs are available in Part C of the HSM is provided 

in Appendix A of this document.

Evaluating the Effect of Engineering Treatments

Researchers commonly conduct safety evaluation studies to determine the effect on crashes (e.g., CMF) 

from implementing some safety countermeasure. Most safety researchers agree that before-after 

studies provide more reliable estimates of the safety effect of engineering treatments than do crosssectional comparisons of locations with and without a particular treatment. Since many engineering 

treatments are implemented at locations that may have a higher than normal crash count, before-after 

studies need to account for potential bias due to regression to the mean. One way to address this bias is 
10

to make use of the empirical Bayes (EB) procedure developed by Hauer (1997). SPFs are an integral part 

of the EB procedure. This guide does not discuss the application of SPFs as part of before-after 

evaluations. Further discussion of this application can be found in Hauer (1997) and Gross et al. (2010).

For some situations where before-after evaluations are not feasible, the coefficients of the variables 

from SPFs can be used to estimate the CMF associated with a particular treatment. However, there are 

a number of issues associated with this approach for developing CMFs. This guide does not discuss the 

use of SPFs for this application. A detailed discussion of the issues associated with such applications of 

SPFs is provided Hauer (2010, 2013), Elvik (2011), and Carter et al. (2012).
11

4. Options for Obtaining SPFs for a Jurisdiction

An agency has two choices for obtaining SPFs to use in the above applications – calibrating existing SPFs 

or developing jurisdiction-specific SPFs (hereafter referred to as “calibrating SPFs” and “developing 

SPFs”, respectively). These options are described in the following sections.

Calibrating SPFs

One option for obtaining SPFs is to take existing SPFs that were developed in other geographic areas and 

calibrate them for the local jurisdiction. If an agency wants to make use of existing SPFs from sources 

such as the HSM or Safety Analyst, they need to be calibrated for the conditions in the jurisdiction. 

Calibration is necessary because “the general level of crash frequencies may vary substantially from one 

jurisdiction to another for a variety of reasons including crash reporting thresholds and crash reporting 

system procedures” (HSM, page C-18). This section provides an overview of calibration. Further 

discussion of the issues and steps will be available from the SPF Calibration Guide that is being 

developed under NCHRP Project 20-07 (Task 332). 

Sources of Existing SPFs

Existing SPFs may be obtained from sources such as Part C of the Highway Safety Manual (for project 

level analysis) or Safety Analyst (for network screening). Regarding the SPFs in Part C of the HSM, 

Chapter 10 includes SPFs that were estimated for rural two-lane, two-way roads developed using state 

data from Minnesota, Washington, Michigan, and California. Chapter 11 includes SPFs that were 

estimated for rural multilane highways using data from Texas, California, Minnesota, New York, and 

Washington. Chapter 12 includes SPFs for roadway segments in urban and suburban arterials that were 

estimated using data from Minnesota, Michigan, and Washington; the SPFs for intersections in urban 

and suburban arterials were estimated using data from Minnesota, North Carolina, Florida, and Toronto 

(Ontario). It should be noted that before these SPFs were included in the HSM, the roadway segment 

SPFs were calibrated using data from Washington and the intersection SPFs were calibrated using data

from California (Srinivasan et al., 2008).

Safety Analyst includes SPFs for roadway segments, intersections, and ramps. SPFs for roadway 

segments were estimated using data from Ohio, North Carolina, Minnesota, California, and Washington. 

SPFs for intersections were estimated using data from Minnesota, and SPFs for ramps were estimated 

using data from Washington. Calibration of these SPFs is automatically done within the software. 

Although the Safety Analyst program and technical support are only available through purchase from 

AASHTO, the default SPFs used in Safety Analyst are documented in Appendix E of Harwood et al., 

(2010).

The SPFs in Part C of the HSM and in Safety Analyst are negative binomial (NB) regression models 

estimated using a procedure called generalized linear models (GLM). 
12

Calibration Process

As discussed earlier, SPFs are essentially mathematical equations that relate the number of crashes of 

different types to site characteristics. Mathematically speaking, an SPF can be represented in the 

following manner:

N f ( AADT , X 1, X 2 , X 3, X 4 ....)

p

Where Np is the predicted number of crashes during a particular time as a function of traffic volume 

(AADT), and other site characteristics, X1, X2, X3, X4, and so on (f is a mathematical function that relates 

the predicted number of crashes with AADT and other site characteristics). The relevant site 

characteristics (X1, X2, X3, X4 and so on) may also be different depending on the type of road and 

whether it is a roadway segment, intersection, or ramp. For example, in the case of intersections, AADT 

may be replaced by major road AADT and minor road AADT.

In the context of calibration, it is important to understand the distinction between the SPFs in Safety

Analyst that are intended for network screening and the SPFs from Part C of the HSM that are intended 

for project level analysis. 

SPFs for network screening. The SPFs for roadway segments and ramps in Safety Analyst predict 

the number of crashes per mile per year and include AADT as the only independent variable. 

Similarly, the SPFs for intersections in Safety Analyst predict the number of crashes per 

intersection per year and include major and minor road AADT as the only independent variables. 

However, the SPFs in Safety Analyst were not estimated for any particular base condition. These 

SPFs are intended to provide the average number of crashes for a particular traffic volume level 

for a particular type of facility (the list of facility types covered in Safety Analyst is provided in 

Appendix A of this document).

SPFs for project level analysis. As mentioned earlier, the prediction methods in Part C of the 

HSM involve the use of SPFs for predicting the crash frequency for a “base” condition and crash 

modification factors (CMFs) to adjust the predictions for situations that are different from a 

base condition. For roadway segments, the prediction methods provide estimates for the 

number of crashes per mile per year, and for intersections, the prediction methods for base 

conditions provide estimates for the number of crashes per intersection per year. Typically, the 

SPFs for base conditions include AADT (for roadway segments) as the independent variable, and 

major and minor road AADTs as independent variables for intersections. CMFs are then used to 

adjust this prediction for situations other than the base condition.

Below is a brief listing of the steps involved in calibrating network screening SPFs from Safety Analyst

and project level SPFs from Part C of the HSM.

Steps in Calibrating Network Screening SPFs

The steps involved in calibrating network screening SPFs are similar to those when calibrating projectlevel SPFs since the ultimate aim is to determine the ratio of the total number of observed crashes to 
13

the total number of predicted crashes. However, there are differences in the details of these steps since 

both the SPFs and the data requirements are different. Following is an outline of the steps:

Step 1 – Identify facility types and appropriate SPFs. As discussed earlier, the SPFs in Safety 

Analyst are a logical starting point since SPFs are available for a large number of facility types 

and have already been used in the software. However, there is no reason why a jurisdiction 

could not make use of similar SPFs that were developed by other researchers, particularly if they 

had been estimated using data from the same jurisdiction from an earlier time period. In this 

context, it is important to note that Safety Analyst allows users to import custom SPFs and 

calibration is automatically done within the software before further analyses are conducted. 

Hence, the discussion of these steps are intended for those users who may want to use Safety 

Analyst type SPFs for network screening without actually using the software package.

Step 2 – Select sites for calibration. Unlike project level analysis where individual sites or group 

of sites are examined one at a time, network screening makes use of data from the entire 

network (for a particular facility type). Hence, the sample for calibration needs to cover the 

network that needs to be screened. Again, depending on the variation in terrain, climate, 

topography, crash reporting practices, driver population, animal population, and other factors 

across the jurisdiction, multiple calibration factors may be necessary if the jurisdiction feels that 

screening should be done separately for different groups based on these factors. Safety Analyst

allows the user to create regional site sub-types that can be calibrated with regional data.

Step 3 – Obtain data for each facility type. Apart from crash counts, data for calibrating network 

screening SPFs could simply include AADT and segment length (for roadway segments and 

ramps) and major and minor road AADTs for intersections.

Step 4 – Apply the SPFs to predict total crash frequency for each site during the calibration 

period. The SPFs from Safety Analyst could be used to predict the number of crashes at each 

site.

Step 5 – Compute calibration factors for use in Part B predictive model. The calibration factor 

for a facility type is then defined as the ratio of the total number of observed crashes in the 

calibration sample to the total number of predicted crashes from Step 4. By estimating a 

calibration factor, the implicit assumption is that the relationship between observed crashes and 

predicted crashes is a straight line. Hauer (2013) suggests that the analyst should check 

whether this relationship is indeed a straight line by estimating the following model:

Observed crashes = C (predicted crashes)d

Where, the parameters C (calibration factor) and d can be estimated using regression modeling 

(e.g., poisson or negative binomial regression). If the relationship between observed crashes and 

predicted crashes is a straight line, then d will be close to 1.0. Another approach is to estimate C as 

a function of variables such as AADT, terrain, segment length, etc (this results in a calibration 

function rather than a calibration factor). This approach is discussed in the SPF Calibration Guide.

Steps in Calibrating Project Level SPFs

Based on the discussion in the HSM, following are steps that can be used to calibrate the HSM SPFs:

Step 1 – Identify facility types for which the applicable Part C predictive model is to be 

calibrated. As discussed earlier, Part C of the HSM provides predictive methods for three types 

of facility types: rural two-lane, two-way roads, rural multilane roads, and urban and suburban 

arterials. For each facility type, models are provided separately for roadway segments and 

intersections. 
14

Step 2 – Select sites for calibration of the predictive model for each facility type. The HSM 

indicates that sites should be selected without regard to the number of crashes. This can be 

accomplished by selecting sites at random from the pool of available sites. In most states, it 

may not be appropriate to develop a single calibration factor for a particular facility type across 

the entire state. Depending on the variation in terrain, climate, topography, crash reporting 

practices, driver population, animal population, and other factors across the state, multiple 

calibration factors may be necessary based on somewhat homogeneous subsets of sites of that 

particular facility type. In addition to considering these factors, Persaud et al., (2002) has 

argued that different calibration factors may also be necessary for different levels of traffic 

volume within a particular facility type. With regard to sample sizes needed for calibration, the 

HSM indicates that 30-50 sites that experience at least 100 crashes per year should be a 

desirable minimum sample size. This guideline in the HSM was introduced based on engineering 

judgment and has been challenged by a few researchers (e.g., Banihashemi, 2012). Further 

details about the sample sizes needed for calibration is available in the upcoming SPF Calibration 

Guide.

Step 3 – Obtain data for each facility type applicable to a specific calibration period. Data are 

needed on crash frequency and site characteristics. The list of site characteristics is available 

from Appendix C of the HSM. The characteristics which the HSM considered to be high impact 

are called required and other characteristics which the HSM considered as being not that 

sensitive to crash propensity are called desirable for which default values are provided in the 

HSM.

Step 4 – Apply the applicable Part C predictive model to predict total crash frequency for each 

site during the calibration period as a whole. The predictive method and the SPFs from Chapters 

10, 11, and 12, are used to compute the predicted number of crashes for each site in the 

calibration sample.

Step 5 – Compute calibration factors for use in Part C predictive model. The calibration factor

for a facility type is then defined as the ratio of the total number of observed crashes in the 

calibration sample to the total number of predicted crashes from Step 4 (as discussed earlier, a 

calibration function could be estimated instead of a calibration factor). If the calibrated models 

are used to estimate the expected number of crashes based on the EB procedure, then the 

overdispersion parameter of the negative binomial SPF needs to be included in this calculation. 

For this calculation, both the HSM procedures and Safety Analyst make use of the 

overdispersion parameter that was estimated from the data used to estimate the original SPFs 

in Safety Analyst and the HSM. Some researchers have suggested that the overdispersion 

parameters should be recalibrated based on the data from the calibration sample (e.g., CDOT, 

2009).

It is important to note that in applying these steps, the implicit assumption is that the CMFs in Part C of 

the HSM (for adjusting the predictions to situations other than the base conditions) are universal, i.e., 

they are applicable for all the States and are not functions of specific site characteristics. Persaud et al., 

(2012) and Sacci et al., (2012) have challenged this assumption based on their work when calibrating the 

HSM prediction models using data from Ontario and Italy, respectively.

Developing SPFs

As discussed earlier, instead of calibrating existing SPFs, an agency may choose to develop their own 

SPFs in order to improve the accuracy of the predictions. The HSM indicates that jurisdiction-specific 
15

SPFs “are likely to enhance the reliability of the Part C predictive method” (HSM, page A-9). The 

advantages of jurisdiction-specific SPFs are also discussed in previous studies (e.g., Lu et al., 2012; Sacci 

et al., 2012). Jurisdiction-specific SPFs also provide the opportunity to examine alternative functional 

forms (depending on the data) rather than using the default forms in the HSM and Safety Analyst.

Further discussion is provided in the SPF Development Guide that is being developed through funding 

from FHWA.

In order to develop SPFs, it is necessary, at the minimum, to have an analyst with statistical expertise for 

estimating simple negative binomial regression models using generalized linear modeling techniques. 

The analyst also needs experience with the statistical tools discussed earlier. Such experience is 

available in many Universities and research institutes across the country. Hence, at least a few states 

have estimated jurisdiction-specific SPFs for network screening, especially for roadway segments (e.g., 

Srinivasan and Carter, 2011; Tegge et al., 2010).

With respect to project level SPFs, Appendix A to Part C of the HSM outlines two possible approaches for 

developing SPFs. Following is a quote from page A-10 of the HSM:

“Two types of data sets may be used for SPF development. First, SPFs may be developed using 

only data that represent the base conditions, which are defined for each SPF in Chapter 10, 11, 

and 12. Second, it also acceptable to develop models using data for a broader set of conditions 

than the base condition. In this approach, all variables that are part of the applicable basecondition definition, but have non-base-condition values, should be included in the initial model. 

Then, the initial model should be made applicable to the base conditions by substituting values 

that correspond to those base conditions into the model”.

With either approach, detailed information is necessary about the site characteristics in addition to 

traffic volume so that it can be determined whether the characteristics of the site correspond to the 

base condition or not. As discussed earlier, at a minimum, data are needed for the site characteristics 

that are considered required by the HSM for calibrating the Part C prediction (project level) models. 

Unlike calibration, developing SPFs requires such data to be available or compiled for a relatively large 

sample of sites (see Table 1

2

for sample size estimates). Very few states have such a database. States 

that do not have a sufficiently detailed database may begin with calibrating SPFs from existing sources 

but might find it cost prohibitive to develop SPFs. 

Steps in Developing SPFs

Below is an overview of steps that are needed in developing SPFs. 

Step 1 - Identify Facility Type. The first step is to identify the type of facility for which SPFs will

be developed. Depending on whether the SPF is being estimated for project-level analysis or 

network screening, the jurisdiction can decide which facility types they are most interested in.

Step 2 - Compile Necessary Data. Depending on whether the SPFs will be used for project level 

analysis or network screening, the data needs are quite different. 

 

2

Table 1 is available in Section 5 of this document.
16

o For network screening SPFs, for each facility type, the number of crashes for each unit 

(intersection, segment, or ramp), and the traffic volume (AADT) associated with that 

unit are required. For intersections, it is recommended that AADT for both major and 

minor roads be available3. If SPFs are to be estimated for a particular crash type or 

severity, the number of crashes by severity and type will be necessary for each unit.

o For SPFs that will be used for project-level analysis, data on other site characteristics 

(apart from AADT) will be necessary. A good starting point is the list of variables that 

are considered required by the HSM for calibrating the Part C prediction models. This 

list for the different facility types is available in the Appendix to Part C of the HSM.

o At this stage, the sample size that is required for developing jurisdiction specific SPFs

needs to be determined. This sample needs to be substantially higher than the 

minimum sample size suggested by the HSM for calibration (see Table 1).

o A decision needs to be made on how routes will be divided into segments for the 

analysis. A common approach is to use homogenous segments with respect to site 

characteristics and traffic volume. This often results in short segments. However, others 

have suggested using longer, though non-homogenous, sections to account for spatial 

correlation (Martinelli et al., 2009).

Step 3 - Determine Functional Form. The SPFs in Part C of the HSM and in Safety Analyst are 

negative binomial regression models with a log-linear relationship between crash frequency and 

site characteristics. However, that may not be most appropriate form (Hauer, 2004; Kononov et 

al., 2011). Different types of exploratory analysis need to be conducted to determine the 

appropriate functional form of the relationship between crash counts and independent 

variables, and the possible need for including interaction terms between independent variables. 

Examples include using plots to illustrate the functional form of the relationship between crash 

counts and different independent variables and a discussion of methods such as classification 

and regression trees (CART) to identify which independent variables and interactions are 

relevant in the model. This step is easier to accomplish for network screening SPFs where fewer 

variables (usually just AADT) are involved.

Step 4 - Develop the SPF. A number of statistical tools (statistical software) are available to 

develop SPFs. Common ones include SAS, STATA, and GENSTAT (all commercially available 

software packages). However, other software tools including R, an open source programming 

language, and Microsoft Excel, can be used as well. It is, however, important to consider in the 

modeling effort that crashes typically follow a negative binomial distribution, not a normal 

distribution.

Step 5 - Conduct Model Diagnostics. There are different steps involved in conducting effective 

diagnostics to determine if the estimated SPF is reasonable. These include checking the sign of 

the parameters’ coefficients, examining residuals via residual plots and cumulative residual plots 

(i.e., CURE plots), and identifying potential outliers using Cook’s D or other tools, and examining 

goodness-of-fit measures.

Step 6 - Re-estimate the SPF. Based on the results of Step 5, the SPF may have to be reestimated using a different statistical model or functional form. The SPF may also need to be reestimated after removing outliers that were identified in the diagnostics step.

 

3

There has been some discussion in the highway safety research community on whether SPFs for network 

screening will be significantly improved by including other explanatory variables in addition to traffic volume and 

segment length – Srinivasan et al., (2011) provides some discussion on this topic.
17

5. Decision Process: How an Agency Obtains SPFs

An agency will have to undergo a process for determining the appropriate course to take when deciding 

on the final SPFs to use. This may involve only calibrating existing SPFs or going further to develop their 

own SPFs. Several factors can affect this process, including intended use of the SPF, intended facility 

type, available sample size, quality of existing roadway data, and available analytical expertise. The 

process is outlined below.

Step-by-Step Process

This process outlines the steps that an agency needs to take in order to obtain the final SPF to be used in 

its jurisdiction. This process begins with SPF calibration and then moves to SPF development if the 

calibration is deemed too low quality.

Step 1. Determine intended use of SPF. 

As discussed in Section 3 of this guidebook, the two main uses of SPFs in this context are network 

screening level and project level. Network screening level SPFs are used to identify sites that may have 

the best potential for improvements. Project level SPFs are used to determine the safety impacts of 

design changes at the project level. The agency must determine the intended use of the SPF. For more 

description of these uses, see Section 3.

Step 2. Determine facility type.

The agency must determine which facility type will be addressed by the SPF. Facility types include 

roadway segments, intersections, and ramps. The type of facility to be addressed by the SPF will affect 

the type of data to be collected and will direct the identification of existing SPFs. Additionally, it is 

conceivable that an agency may decide to develop jurisdiction-specific SPFs for certain facility types, but 

calibrate existing SPFs (i.e., from the HSM, Safety Analyst, or other sources) for other facility types. 

Developing SPFs for project-level analysis will require assembling a database with sufficient number of 

sites with detailed information on site characteristics. Depending on the variables available in the 

State’s roadway inventory files, the process of assembling a database may be easier for some facility 

types than for others.

Step 3. Identify existing SPF.

The agency must identify an existing SPF according to the intended use and facility type. As described in 

Section 4, existing SPFs for network screening may be obtained from Safety Analyst. Existing SPFs for

project level analysis may be obtained from Part C of the Highway Safety Manual. Appendix A lists the 

types of facilities for which SPFs are available in these resources (e.g., rural two-lane roads, etc.).

Step 4. Consider sample size necessary for calibrating SPF.

The agency must consider what sample size is required to calibrate the SPF. For project level SPFs (as 

determined in Step 1), the HSM specifies that 30 to 50 sites with at least 100 crashes per year would be 

a reasonable sample for calibrating the HSM SPFs (the upcoming SPF Calibration Guide provides

guidance on the number of sites and crashes needed to estimate the calibration factor to a given 
18

accuracy). For facility types that are fairly common (e.g., rural two-lane roads), identifying the site 

needed for calibration would be a fairly easy task. For facility types that may be less common (e.g., rural 

four-lane undivided), this could be more challenging and time consuming. In some cases, the number of 

sites or miles of a particular facility type may be so small that developing a calibration factor for that 

facility type would be of low priority, and the agency should consider whether it is worth the cost of

undergoing the calibration process for that facility type.

For urban facilities, this target crash number of 100 crashes (based on the HSM) would likely be met 

with a small number of sites (given the higher traffic and crash frequencies at urban sites). For rural 

facilities, it is likely that the agency would need to identify a larger group of sites in order to meet the 

required minimum number of crashes per year to establish a good statistical base for calibration. 

It should be noted that this group of sites for calibration should NOT be selected on the basis of crash 

counts. That is, the agency should not hand pick a group of high crash sites simply to meet the minimum 

crash frequency requirement. Doing so would strongly bias the calibration process. Rather, the selection 

should be random from the population of the appropriate facility type (i.e., random selection of X 

number of sites from the entire list of rural four-leg signalized intersections throughout the agency). A 

procedure for randomly selecting sites for calibration is discussed in the upcoming SPF Calibration 

Guide.

With respect to network screening SPFs, these SPFs will be used on a broad scale basis across the whole 

network. Thus, all sites of the particular facility type (as determined in Step 2) over the entire network 

should be used for the calibration effort.

Step 5. Consider roadway data necessary for calibrating SPF.

The requirements for roadway data depends on the intended use of the SPF (product of Step 1) and the 

intended facility type (product of Step 2). In general, calibrating project level SPFs requires more 

detailed data than calibrating network screening level SPFs. For project level SPFs, an agency could 

calibrate an SPF from the HSM. Calibrating the HSM SPFs requires detailed roadway data for calculating 

the various crash modification factors (CMFs) that are part of the HSM predictive process. The list of site 

characteristics is available from the Appendix to Part C of the HSM. The characteristics which the HSM 

considered to be high impact are called required and other characteristics which the HSM considered as 

being not as sensitive to crash propensity are called desirable (default values for desirable characteristics

are provided in the HSM).

For calibrating network screening level SPFs, the data requirements would be less stringent, including 

only AADT and segment length (for roadway segments and ramps) and major and minor road AADT for 

intersections. The data requirements are less detailed, since the intended use of network screening level 

SPFs is on the broad scale across the whole network in order to select sites with promise for safety 

improvements. Traffic volume data for roadway segments is available in most states. On the other 

hand, many states do not have an inventory of intersections and ramps. Some have an inventory of 

intersections on their state maintained roads but may not have minor road AADT, especially if the minor 

roads are not state maintained. If this is the case, then the time required for site identification and data 
19

collection will increase. Appendix B discusses the major considerations in building an intersection 

inventory and some discussion of the cost involved.

The agency must evaluate the roadway data requirements and compare to its own roadway inventory. If 

the level of detail available in the agency’s existing roadway inventory is high, then the work required to 

assemble the data necessary for calibration will be minimal. However, if the existing roadway inventory 

has only very basic data, then a more significant effort will be required to assemble the necessary data. 

Table 1 provides an estimate of the hours required for data collection.

Step 6. Calibrate existing SPF.

Once the previous steps have been executed, and the agency has determined the intended use of the 

SPF, identified the facility type to be addressed, identified an SPF from the HSM or Safety Analyst, and 

considered the requirements for sample size and roadway data, the agency can undertake the 

calibration process. Calibration can be done by staff with limited to no statistical experience and can be 

implemented using spreadsheet software such as Microsoft Excel. See section 4 for step-by-step 

description of the calibration process. The result of this process is a calibration factor that is used to 

adjust the crash predictions of the SPF to be accurate to the agency’s jurisdiction. As discussed earlier, 

separate calibration factors may be needed for each specific terrain type, region, climate, or AADT 

category. Further guidance for estimating the calibration factor along with its standard deviation is 

available in the upcoming SPF Calibration Guide.

Step 7. Assess quality of calibration factor/function.

Once the calibration factor has been developed, the agency must assess the quality of the calibration 

process. There are many ways to do this. One is the value of the calibration factor itself. If the total SPF 

crash predictions match exactly to the agency’s total number of observed crashes, then the process 

would produce a calibration factor of 1.0. If the SPF under predicts an agency’s crashes, the calibration 

factor would be greater than 1.0. If the SPF over predicts, the calibration factor would be less than 1.0. If 

the calibration factor is very different from 1.0 (i.e., much less or much greater), this would indicate that 

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

SPFs. 

Another way to assess the quality of calibration process is to use goodness of fit (GOF) tests such as 

cumulative residual (CURE) plots. CURE plots and other GOF tests are discussed in Hauer (2013) and the 

SPF Development guide. Further guidance on assessing the quality of the calibration is provided in the 

upcoming SPF Calibration Guide.

For project level SPFs, if the calibration factor is of good quality, then it can be used along with the HSM 

predictive methodology to conduct project level analysis. For network screening SPFs, if the quality of 

the calibration factor is considered good, then it can be used for network screening. If the calibration 

factor is not of good quality, then the agency should follow Steps 8-10 below to develop SPFs using the 

procedure discussed in the upcoming SPF Development Guide.
20

Step 8. Consider statistical expertise necessary for developing SPF.

Calibrating existing SPFs and developing new SPFs require different skill levels. As mentioned in Step 6, 

calibration requires little to no statistical experience. However, developing SPFs requires personnel with 

a background in statistical modeling. Agencies without such in-house expertise might consider hiring a 

consultant (e.g., university consultants).

Step 9. Consider sample size necessary for developing SPF.

As compared to calibrating SPFs, developing SPFs would typically require a larger sample. The amount 

of sample required depends on the intended use (product of Step 1). For project level SPFs, the agency 

should identify 100-200 intersections (for intersections models) or 100-200 miles (for segment models)

with at least 300 crashes per year for the whole group.

With respect to network screening SPFs, these SPFs will be used on a broad scale basis across the whole 

network. Thus, all sites of the particular facility type (as determined in Step 2) over the entire network 

should be used for the calibration effort. However, if the agency cannot assemble a group of at least 

100-200 intersections or 100-200 miles with at least 300 crashes per year for the total group, then the 

reliability of SPF development may be questionable.

Step 10. Determine crash type to be addressed by SPF.

When conducting SPF calibration, only total crash counts are typically used to calculate the calibration 

factor. However, when developing SPFs, there may be separate models to address each crash type. That 

is, one SPF could be developed to predict total crashes and a separate SPF could be developed to predict 

run-off-road crashes. The agency must determine which crash type will be addressed by the SPF. 

Multiple crash types may require multiple SPFs to be developed. Further discussion of this topic will be 

available in the SPF Development Guide.

Step 11. Develop SPF.

Once Steps 8-10 have been executed, the agency can undertake the development of the SPF. Section 4 

provides a description of the basic steps involved in developing the SPF. Further detailed guidance on 

developing an SPF will be provided in the SPF Development Guide.

Staff Time Required for Calibration and Development

Many agencies will want to have an idea of the cost of the effort to calibrate and/or develop SPFs. Table 

1 provides the estimated ranges of staff time required for each endeavor. The staff time required to 

collect and prepare the data can range greatly depending on the following factors:

Whether one or many SPFs are being addressed. If many SPFs are being calibrated or developed

in the same project, then the data collection is more efficient per SPF, since the data collector 

can obtain data on many types of sites during the same effort. For instance, a data collector who 

is collecting data on rural two-lane road segments can also gather information on rural two-lane 

road intersections with minimal additional effort.

Available data in existing roadway inventory. If most of the required data elements are 

contained in the agency’s existing inventory, the data collection time will be minimal. However, 
21

the fewer the data elements available in the inventory, the greater is the time needed to 

assemble the required data. Methods for collecting the data may involving aerial photos, online 

imagery, construction plans, and/or field visits.

Table 1. Level of Effort Estimates for SPF Calibration and Development

Intended Use Process Sample needed

Staff hours

needed - data 

collection and 

preparation 

(per SPF)

Staff hrs 

needed -

statistical 

analyst 

(per SPF)

Project level Calibrate SPF

30-50 sites; at least 100 

crashes per year for total 

groupa. At least 3 years of 

data are recommended.

150 to 350 n/ad

Project level Develop SPF

100-200 intersections or 

100-200 miles; at least 300

crashes per year for total 

groupc. At least 3 years of 

data are recommended.

450 to 1050 16 to 40

Network 

screening Calibrate SPF

Must use entire network to 

be screened. No minimum 

sample specified. At least 3 

years of data are 

recommended.

24 to 40bn/ad

Network 

screening Develop SPF

Must use entire network to 

be screened. Minimum 

sample would be 100-200 

intersections or 100-200 

miles; at least 300 crashes 

per year for total groupc. 

At least 3 years of data are 

recommended.

24 to 40b8 to 24

Notes:

a

This is based on the guidance from the HSM. The SPF Calibration Guide will provide further guidance on this issue.

b

In estimating the staff hours for data collection and preparation for network screening, it was assumed that all the 

necessary data are available in the jurisdiction’s inventory file. All state DOTs have some form of basic roadway 

segment inventory due to the requirements of the Highway Performance Monitoring System (HPMS). However, 

the situation is different for intersections. Very few states have an inventory of intersections along their public 

roads. Appendix B discusses the major considerations in building an intersection inventory and some discussion of 

the cost involved.

c

The sample size estimates are based on the judgment of the project team. Methods for estimating the sample 

size for poisson type regression models are available (e.g., Shieh, 2001), but the project team did not feel that such 

methods were directly applicable for this situation.

d

No statistical analytical experience is required for calibration.
22

References

AASHTO (2010), Highway Safety Manual, AASHTO, Washington, D.C.

Banihashemi, M. (2012), Highway Safety Manual Calibration Dataset Sensitivity Analysis, Presented at 

the 91st Annual Meeting of the Transportation Research Board, Washington, D.C.

Bauer, K. and Harwood, D. (2012), Safety Effects of Horizontal Curve and Grade Combinations, Submitted 

to Federal Highway Administration.

Carter, D., R. Srinivasan, F. Gross, and F. Council (2012), Recommended Protocols for Developing Crash 

Modification Factors, Prepared as part of NCHRP Project 20-07 (Task 314), Washington, D.C. Available at 

http://www.cmfclearinghouse.org/resources_develop.cfm. Accessed January 2013.

CDOT (2009), Safety Performance Functions for Intersections, Report CDOT-2009-10, Developed for

Colorado Department of Transportation, Developed by Persaud and Lyon, Inc. and Felsburg Holt & 

Ullevig, December 2009.

Dixon, K., C. Monsere, F. Xie, and K. Gladhill (2012), Calibrating the Future Highway Safety Manual 

Predictive Methods for Oregon State Highways, Final Report SPR 684, OTREC-RR-12-02, Oregon State 

University and Portland State University, Oregon.

Elvik, R. (2011), Assessing Causality in Multivariate Accident Models, Accident Analysis and Prevention, 

Vol. 43, pp. 253-264.

Gross, F., B. Persaud, and C. Lyon (2010), A Guide for Developing Quality Crash Modification Factors, 

Report FHWA-SA-10-032, Federal Highway Administration, Washington, D.C. Available at 

http://www.cmfclearinghouse.org/resources_develop.cfm. Accessed January 2013.

Harwood, D.W., D. J. Torbic, K. R. Richard, and M. M. Meyer (2010), SafetyAnalyst: Software Tools for 

Safety Management of Specific Highway Sites, Federal Highway Administration, Report Number FHWAHRT-10-063, Available at http://www.safetyanalyst.org/docs.htm. Accessed January 2013.

Hauer, E. (1997), Observational Before After Studies in Road Safety, Elsevier Science, New York.

Hauer, E. (2004), Statistical Road Safety Modeling, Transportation Research Record 1897, pp. 81-87.

Hauer, E. (2010), Cause, Effect, and Regression in Road Safety: A Case Study, Accident Analysis and 

Prevention, Vol. 42, pp. 1128-1135.

Hauer, E. (2013), Safety Performance Functions: A Workshop, Baton Rouge, Louisiana, July 16-18, 2013.

Kononov, J., C. Lyon, B.K. Allery (2011), Relationship of Flow, Speed, and Density of Urban Freeways to 

Functional Form of a Safety Performance Function, Transportation Research Record 2236, pp. 11-19.

Lu, J., A. Gan, K. Haleem, P. Alluri, and K. Liu (2012), Comparing Locally-Calibrated and Safety-Analyst 

Default Safety Performance Functions for Florida’s Urban Freeways, Presented at the 91st Annual 

Meeting of the Transportation Research Board, Washington, D.C.

Martinelli, F., F. la Torre, and P. Vadi (2009), Calibration of the Highway Safety Manual’s Accident 

Prediction Model for Italian Secondary Road Network, Transportation Research Record 2103, pp. 1-9.
23

Persaud, B., D. Lord, and J. Palmisano (2002), Calibration and Transferability of Accident Prediction 

Models for Urban Intersections, Transportation Research Record 1784, pp. 57-64.

Persaud, B., Y. Chen, J. Sabbaghi, and C. Lyon (2012), Adoption of the Highway Safety Manual 

Methodologies for Safety Performance Assessment of Ontario Highway Segments, Proceedings of the 

22nd Canadian Multidisciplinary Road Safety Conference, Alberta, June 2012.

Sacci, E., B. Persaud, and M. Bassani (2012), Assessing International Transferability of the Highway Safety 

Manual Crash Prediction Algorithm and its Components, Presented at the 91st Annual Meeting of the 

Transportation Research Board, Washington, D.C.

Shieh, G. (2001), Sample Size Calculations for Logistic and Poisson Regression Models, Biometrika, Vol. 

88(2), pp. 1193-1199.

Srinivasan, R., Council, F., and Harkey, D. (2008), Calibration Factors for HSM Part C Predictive Models, 

Submitted to FHWA and HSM Task Force, October 2008.

Srinivasan, R. and D. Carter (2011), Development of Safety Performance Functions for North Carolina, 

Report FHWA/NC/2010-09, Submitted to NCDOT, December 2011.

Srinivasan, R., Lyon, C., Persaud, B., Martell, C., and Baek, J. (2011), Methods for Identifying High 

Collision Concentration Locations (HCCL) for Potential Safety Improvements – Phase II: Evaluation of 

Alternative Methods for Identifying HCCL, Submitted to California Department of Transportation (CFS 

Number 2078A DRI), January 2011.

Tegge, R.A., J. Jang-Hyeon, Y. Ouyang (2010), Development and Application of Safety Performance 

Functions for Illinois, Research Report ICT-10-066, Illinois Center for Transportation, Civil Engineering 

Studies, March 2010.

Vogt, A. and Bared, J.G. (1998), Accident Models for Two-lane Rural Roads: Segments and Intersections, 

Federal Highway Administration, Report # FHWA-RD-98-133.
24

Appendix A: Roadway and Intersection Types for which SPFs 

are provided in the HSM (1st Edition) and Safety Analyst

Facility Types Included in Part C of the HSM (1st Edition)

For roadway sections, Part C of the HSM provides SPFs for the following 8 types:

Rural two lane roads

Rural four-lane divided 

Rural four-lane undivided roads

Two lane urban and suburban arterials, 

Three lane (with center TWLTL) urban and suburban arterials, 

Four lane divided urban and suburban arterials, 

Four lane undivided urban and suburban arterials, 

Five lane (with center TWLTL) urban and suburban arterials.

For intersections, SPFs are available for the following 9 types:

Three-leg minor road stop controlled intersections on rural two lane roads 

Four-leg minor road stop controlled intersections on rural two lane roads

Four-leg signalized intersections on rural two lane roads

Three-leg intersections on rural four lane roads

Four-leg minor road stop controlled intersections on rural four lane roads

Three-leg minor road stop controlled intersections on urban and suburban arterials

Four-leg minor road stop controlled intersections on urban and suburban arterials

Three-leg signalized intersections on urban and suburban arterials

Four-leg signalized intersections on urban and suburban arterials

Facility Types in Safety Analyst

For roadway segments, SPFs are available for the following 17 types:

Rural two-lane roads

Rural multilane undivided roads

Rural multilane divided roads

Rural freeways – 4 lanes

Rural freeways – 6+ lanes

Rural freeway segments within an interchange area – 4 lanes

Rural freeway segments within an interchange area – 6+ lanes

Urban two-lane arterial segments

Urban multilane undivided arterial segments

Urban multilane divided arterial segments
25

Urban one-way arterial segments

Urban freeway segments – 4 lanes

Urban freeway segments – 6 lanes

Urban freeway segments – 8+ lanes

Urban freeway segments within an interchange area – 4 lanes

Urban freeway segments within an interchange area – 6 lanes

Urban freeway segments within an interchange area – 8+ lanes

For intersections, SPFs are available for the following 12 types:

Rural three-leg intersections with minor-road stop control

Rural three-leg intersections with all-way stop control

Rural three-leg signalized intersections

Rural four-leg intersections with minor-road stop control

Rural four-leg intersections with all-way stop control

Rural four-leg signalized intersections

Urban three-leg intersections with minor-road stop control

Urban three-leg intersections with all-way stop control

Urban three-leg signalized intersections

Urban four-leg intersections with minor-road stop control

Urban four-leg intersections with all-way stop control

Urban four-leg signalized intersections

For ramps, SPFs are available for the following 16 types:

Rural diamond off-ramps

Rural diamond on-ramps

Rural parco loop off-ramps

Rural parco loop on-ramps

Rural free-flow loop off-ramps

Rural free-flow loop on-ramps

Rural free-flow outer connection ramps

Rural direct and semidirect connection ramps

Rural diamond off-ramps

Rural diamond on-ramps

Rural parclo loop off-ramps

Rural parclo loop on-ramps

Rural free-flow loop off-ramps

Rural free-flow loop on-ramps

Rural free-flow outer connection ramps

Rural direct and semidirect connection ramps
26

Appendix B. Developing an Intersection Inventory

Developing network screening SPFs requires an existing inventory for the facility of interest. For 

roadway segments, this is not typically an issue. All state DOTs have some form of basic roadway 

segment inventory, due to the requirements of the Highway Performance Monitoring System (HPMS). 

However, the situation is different for intersections. Very few states have an inventory of intersections 

along their public roads. States who are considering the use of network screening SPFs may be 

interested in exploring the creation of an intersection inventory, particularly the staff time and cost that 

would be necessary to develop such an inventory. Below are listed several of the major considerations in 

building an intersection inventory and some discussion of the cost involved.

Location of Intersections

Determining the location of each intersection is the most critical element for any intersection inventory. 

Two of the most common ways of referencing an intersection location are a Linear Referencing System 

(LRS) or Geographic Information System (GIS). Typically, an agency would use the same location system

that is used for their roadway segment inventory. Locating and assigning a unique ID to each 

intersection is a substantial task. Ohio DOT developed a semi-automatic in-house process to create the 

initial intersection inventory file (i.e., locations and unique identifiers). They report that it took 

approximately 3 person months to develop the semi-automated process, but that the process was 

designed to be used on an annual basis and takes 2-3 hours to run each time. Other agencies who keep 

their roadway inventory in GIS have used built-in GIS tools to automatically create points where 

roadway lines intersect. They then manually identified which points were intersections and assigned an 

appropriate ID number. The amount of time required for this manual identification is unknown to the 

authors.

Traffic Volume

Another crucial piece of an intersection inventory is traffic volumes on both the major and minor roads 

of the intersection. This information can often be gleaned from the roadway segments adjacent to the 

intersection. This is usually not an issue for the major road (especially, if the major road is state 

maintained), but it can be a problem for obtaining volumes on the minor roads. The state roadway 

inventory may not contain volume data on the minor road of the intersection, especially if it is not a 

state-owned road. 

Ohio DOT reports that they use a hierarchical approach in assigning traffic volume to the intersection 

file. First, they use the volume information from the adjacent roadway sections. If that is not available 

for one or more intersection legs, they obtain any volume information that can be supplied from 

Metropolitan Planning Organization (MPO) data. If that is not available, they assign a traffic volume 

value using default values for functional class by county. 

Geometry and Traffic Control

The other major piece of information is the geometry and traffic control of the intersection. This is 

necessary for categorizing intersections (SPFs are developed according to intersection type). Ohio DOT 
27

obtained this information by manual effort, using interns to collect the data. They estimate 

approximately 3000 hours were necessary to collect this information (along with other intersection-level 

characteristics that were of interest). This was performed for a total of 47,000 intersections that lay on 

Ohio state-maintained roads, for an average cost of $1.30 per intersection (assuming intern pay is 

$20/hr).

The FHWA Office of Safety recently released a report containing estimated costs for collecting basic 

inventory variables, known as the Model Inventory Roadway Elements (MIRE) Fundamental Data 

Elements (Fiedler et al., 2013). They estimate that the cost of collecting basic geometry and traffic 

control would be approximately $1.00 per intersection. 

References

Fiedler, Rebecca, Kim Eccles, Nancy Lefler, Ana Fill, and Elsa Chan. MIRE Fundamental Data Elements 

Cost-Benefit Estimation. Final Report, Contract DTFH61-11-C-00050, March 2013.
28

Appendix C. Recent SPF Development Efforts from States

Following is a brief description of recent jurisdiction specific SPF development efforts (rather than the 

calibration of existing SPFs) from States. These were compiled based on a review of the published 

literature. The focus was on SPF development for the purpose of network screening or project level 

analysis. In addition to the states listed here, there are states that are in the process of developing SPFs 

(examples include Alabama, Louisiana, and Washington).

Colorado

Persaud and Lyon, Inc. and Felsburg Holt and Ullevig, Safety Performance Functions for Intersections, 

Report CDOT-2009-10, Developed for Colorado Department of Transportation, Denver, Colorado, 

December 2009.

This study developed SPFs for 10 intersection categories:

Urban 4-Lane Divided Signalized 4-Leg

Urban 6-Lane Divided Signalized 4-Leg

Urban 4-Lane Divided Signalized 3-Leg

Urban 2-Lane Undivided Unsignalized 4-Leg

Urban 4-Lane Divided Unsignalized 4-Leg

Urban 2-Lane Undivided Unsignalized 3-Leg

Urban 4-Lane Divided Unsignalized 3-Leg

Urban 4-Lane Undivided Unsignalized 4-Leg

Urban 2-Lane Divided Unsignalized 3-Leg

Urban 4-Lane Undivided Unsignalized 3-Leg

At least 5 years of data were available for each intersection that was used in the analysis. SPFs were 

estimated for total and injury and fatal crashes. CURE plots and other goodness of fit measures were 

used to assess the validity of the SPFs. Since the SPFs just used major and minor road AADT data, they 

could be used for network screening.

Florida

Lu, J., A. Gan, K. Haleem, P. Alluri, and K. Liu, Comparing Locally-Calibrated and Safety Analyst Default 

Safety Performance Functions for Florida’s Urban Freeways, Presented at the 91st Annual Meeting of the 

Transportation Research Board, January 2012.

SPFs were estimated for network screening consistent with the format in Safety Analyst. SPFs were 

estimated for total and fatal and injury crashes for the following road types:

4 lane urban freeways outside influence of interchanges

4 lane urban freeways within the influence of interchanges

6 lane urban freeways outside influence of interchanges

6 lane urban freeways within the influence of interchanges
29

8+ lane urban freeways outside influence of interchanges

8+ lane urban freeways within the influence of interchanges

Illinois

Tegge, R.A., J. Jang-Hyeon, and Y. Ouyang (2010), Development and Application of Safety Performance 

Functions for Illinois, Research Report ICT-10-066, Illinois Center for Transportation, Civil Engineering 

Studies, March 2010.

SPFs were estimated for roadway segments and intersections on state-maintained roads. SPFs were 

estimated for fatal, type A injury, type B injury, and fatal and injury combined. The main focus was to 

estimate the SPFs for network screening that could be used within Safety Analyst. For roadway 

segments, SPFs were estimated for the following roadway types:

Rural Two-Lane Highway

Rural Multilane Undivided Highway

Rural Multilane Divided Highway

Rural Freeway, 4 Lanes

Rural Freeway, 6+ Lanes

Urban Two-Lane Highway

Urban One-Way Arterial

Urban Multilane Undivided Highway

Urban Multilane Divided Highway

Urban Freeway, 4 Lanes

Urban Freeway, 6 Lanes

Urban Freeway, 8+ Lanes

For intersections, SPFs were estimated for the following types:

Rural Minor Leg Stop Control

Rural All-Way Stop Control

Rural Signalized Intersection

Rural Undetermined

Urban Minor Leg Stop Control

Urban All-Way Stop Control

Urban Signalized Intersection

Urban Undetermined

In addition to the SPFs for network screening, an SPF was estimate for KAB injury crashes for roadway 

segments. This SPF included information about access control, shoulder width and type, lane width, 

median type and other segment characteristics. This SPF is a possible starting point for project level 

analysis.

North Carolina

Srinivasan, R. and D. Carter, Development of Safety Performance functions for North Carolina, Report 

FHWA/NC/2010-09, Submitted to North Carolina Department of Transportation, December 2011.
30

All SPFs predicted the number of crashes per mile as a function of AADT consistent with the functional 

form in Safety Analyst. North Carolina specific SPFs were estimated for the following crash types:

Total crashes

Injury and fatal crashes (K, A, B, C)

Injury and fatal crashes (K, A, B)

Property damage only (PDO) crashes

Lane departure crashes 

Single vehicle crashes (including animal crashes)

Multi vehicle crashes

Wet crashes

Night crashes – This included crashes with Ambient Light = (4) Dark – lighted roadway, or (5) 

Dark – roadway not lighted, or (6) Dark – unknown lighting

SPFs were estimated for the following roadway types:

Rural Two Lane Roads

Rural Freeways - 4 lanes - outside the influence of interchanges

Rural Freeways – 6+ lanes - outside the influence of interchanges

Rural Freeways - 4 lanes - within the influence of interchanges

Rural Freeways – 6+ lanes - within the influence of interchanges

Rural Multilane Divided Roads

Rural Multilane Undivided Roads

Urban Two Lane Roads

Urban Freeway - 4 lanes - outside the influence of interchanges

Urban Freeway - 6 lanes - outside the influence of interchanges

Urban Freeway - 8+ lanes - outside the influence of interchanges

Urban Freeway - 4 lanes - within the influence of interchanges

Urban Freeway - 6 lanes - within the influence of interchanges

Urban Freeway - 8+ lanes - within the influence of interchanges

Urban Multilane Divided Roads

Urban Multilane Undivided Roads

In addition to these SPFs for network screening, SPFs were estimated for rural two lane roads that 

included terrain, shoulder width, shoulder type, in addition to AADT. These SPFs are possible starting 

points for project level analysis.

Utah

Brimley, B.K., M. Saito, and G.G. Schultz, Calibration of Highway Safety Manual Safety Performance 

Function: Development of Models for Rural Two-Lane Two-Way Highways, Transportation Research 

Record 2279, pp. 82-89.

SPFs for total crashes were estimated for rural two lane roads. The independent variables considered 

included AADT, information about whether passing was permitted, whether shoulder rumble strips were 

present, percent multiple-unit trucks, and speed limit. Different models were examined and a model 
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was selected based on the Bayesian Information Criterion (BIC). The recommended model could be 

used for network screening and could be a starting point for project level analysis.

Virginia

Garber, N.J. and G. Rivera, Safety Performance Functions for Intersections on Highways Maintained by 

the Virginia Department of Transportation, FHWA/VTRC 11-CR1, Virginia Department of Transportation, 

October 2010.

SPFs were estimated primarily for use in Safety Analyst for network screening. SPFs were estimated for 

the following intersection types:

Urban 4 leg signalized

Urban 4 leg minor road stop controlled

Urban 3 leg signalized

Urban 3 leg minor road stop controlled

Rural 4 leg signalized

Rural 4 leg minor road stop controlled

Rural 3 leg signalized

Rural 3 leg minor road stop controlled

SPFs were estimated total and fatal and injury crashes. Separate SPFs were also estimated for different 

regions in Virginia.