CHAPTER 2

Literature Review

Safety Performance Functions in the Highway Safety Manual

SPFs are statistical models that are used to predict annual crash frequency for a given roadway element (e.g., segment or intersection) as a function of site-specific features associated with that roadway element. SPFs in the HSM are generally estimated using negative binomial regression, which accounts for the count nature of crash frequencies (i.e., that crashes take non-negative integer values) and the overdispersion that is commonly present in crash data. (In a negative binomial regression model, overdispersion means that the variance of the response is greater than what’s assumed by the model.) Two types of SPFs exist in the HSM: Part B or Part C SPFs, each referring to the section of the HSM where they are described.

Part B SPFs are high-level SPFs that are typically used for network screening purposes to identify locations with higher-than-expected crash frequencies as sites with potential for safety improvement. These SPFs generally include only traffic volume and segment length (for roadway segments) as input variables. These are also referred to as screening-level or network-screening-level SPFs; the term network-screening-level SPFs is used for consistency throughout this report.

Part C SPFs are more detailed and are typically used for design-level decision-making (e.g., estimating the safety impacts of different facility designs or the implementation of specific changes to a facility). These generally include additional input variables compared to the Part B SPFs, such as roadway curvature and alignment, cross-sectional characteristics, roadside features, and the presence of other safety-influencing features. Often, these Part C SPFs provide safety predictions for sites that meet a set of base conditions, and other features are accommodated via a suite of adjustment factors (AFs) that modify the prediction for changes to these base conditions. These are also referred to as project-level or design-level SPFs; the term design-level SPFs is used for consistency throughout this report.

The general form of an SPF for roadway segments is as follows:

where N_SPF is the predicted annual crash frequency obtained from the SPF, assuming some base conditions; AADT is the annual average daily traffic volume observed over the segment (vehicles/day); L is the segment length (miles); β_AADT and β_L are statistical model coefficients associated with AADT and segment length, respectively; and β₀ is a constant.

A similar equation exists for the general form of intersection SPFs:

where N_SPF is the predicted annual crash frequency obtained from the SPF, assuming some base conditions; Major AADT and Minor AADT refer to the traffic volume on the major and minor intersection legs, respectively; and β_Major and β_Minor are the respective model coefficients.

The HSM further adjusts predictions obtained from SPFs using the following equation:

where N_predicted is the predicted annual crash frequency for a given site, AF_n is an adjustment factor to account for feature x that differs from the base conditions, and CF is the calibration factor.

The first edition of the HSM, published in 2010, includes SPFs for the following facility types and crash type combinations:

• Two-lane, two-way rural roads (Chapter 10)
  • Roadway segments
    • Undivided roadway segments (2U)
  • Intersections
    • Unsignalized three-leg (stop control on minor-road approaches) (3ST)
    • Unsignalized four-leg (stop control on minor-road approaches) (4ST)
    • Signalized four-leg (4SG)
• Multi-lane rural highways (Chapter 11)
  • Roadway segments
    • Rural four-lane undivided segments (4U)
    • Rural four-lane divided segments (4D)
  • Intersections
    • Unsignalized three-leg (stop control on minor-road approaches) (3ST)
    • Unsignalized four-leg (stop control on minor-road approaches) (4ST)
    • Signalized four-leg (4SG)
• Urban and suburban arterials (Chapter 12)
  • Roadway segments
    • Two-lane undivided arterials (2U)
    • Three-lane arterials including a center two-way left-turn lane (TWLTL) (3T)
    • Four-lane undivided arterials (4U)
    • Four-lane divided arterials (i.e., including a raised or depressed median) (4D)
    • Five-lane arterials including a center TWLTL (5T)
  • Intersections
    • Unsignalized three-leg intersections (stop control on minor-road approaches) (3ST)
    • Signalized three-leg intersections (3SG)
    • Unsignalized four-leg intersections (stop control on minor-road approaches (4ST)
    • Signalized four-leg intersections (4SG)

A supplement to the HSM, published in 2014, provided additional SPFs for freeway segments, speed-change lanes, ramps, and ramp terminals.

A full summary of the SPFs included in the HSM is provided in Table 2. Note that injury severity levels for some SPFs are described using the KABCO scale, in which K represents fatal crashes, A represents crashes resulting in incapacitating injuries, B represents crashes resulting in non-incapacitating injuries, C represents crashes resulting in possible/non-evident injuries, and O represents crashes resulting in no indication of injury or property damage-only crashes. Also,

Table 2. Summary of SPFs included in the HSM.

note that these include both network-screening-level SPFs and design-level SPFs; the former are baseline SPFs with just exposure (i.e., traffic volume and segment length) as input variables, while the latter incorporate adjustment factors for a range of design features that may differ from some presumed baseline conditions.

Table 3 provides a list of design features that can be accommodated via adjustment factors (AFs) for each of the SPFs included in the HSM.

Calibration

HSM Calibration Procedure

The calibration factor (CF) in Equation (3) is intended to adapt the SPF to local conditions since the data used to estimate the crash frequency models were developed using information from only a few states and would likely not reflect local conditions in others.

The HSM suggests the following procedure to estimate the calibration factor in Equation (3).

1. Identify a set of sites for which the SPF is applicable.
2. Obtain site-specific features from each site needed to apply the SPF and annual crash frequencies for each site.
3. Apply the SPF to obtain predicted crash frequencies according to the SPF.
4. Compute the calibration factor according to Equation (4).

where N_o,i is the observed number of crashes on site i, N_u,i is the unadjusted predicted number of crashes for site i, and n is the total number of sites used for calibration. As shown, this calculation is simply the ratio of total number of observed crashes for a sample of sites in a jurisdiction to the total number of predicted crashes for these same sites.

The overdispersion parameter for the SPF can also be calibrated. This is typically done via a numerical maximum likelihood procedure using software such as the SPF Calibrator Tool (Lyon et al., 2016).

Alternative Calibration Options/Forms

The calibration factor definition in the HSM simply scales the predicted crash values to ensure that the total number of crashes observed at all sites is the same as the total number predicted. However, many studies have found that calibration in this way does not accurately predict crashes since it assumes the same relationship between crash frequency and other factors that are inherent in the SPF that is applied. Thus, several research studies have proposed alternative definitions of the calibration factor. A brief review of these is provided as follows:

• Mehta and Lou (2013) propose to model the relationship between predicted and observed crash frequency using a negative binomial regression model with the following functional form: N_o,i = e^ln(CF1)+ln(^Nu,i). Using this relationship, the calibration factor (CF₁) simplifies to the following definition:

  $C{F}_1=\frac{{\displaystyle {\sum }_i^n{N}_{a,i}/N_{u.i}}}{n}$

  (5)

Table 3. Summary of design features for which adjustment factors exist in the HSM.

Thus, this study defines the calibration factor as the average of the individual “calibration factors” computed for each site.

• Rajabi et al. (2018) propose two additional calibration factors based on maximum likelihood estimation (CF₂) and least squares estimation (CF₃).
  • MLE-based: this calibration factor definition does not have a closed-form solution. Instead, the calibration factor can be obtained by numerically solving the following relationship for CF₂:

    $n={\displaystyle {\sum }_i^n\frac{N_{o,i}+\text{φ}}{C{F}_2{N}_{u,i}+{\text{φ}}^{\prime }}}$

    (6)

    where φ is the inverse of the overdispersion parameter of the distribution of observed crashes. Use of this calibration factor is expected to maximize the likelihood that the predicted crashes obtained from the SPF fit the observed crash data when a constant calibration factor is applied.

  • LSE-based: this calibration factor definition minimizes the sum of squared errors between observed and predicted crashes across the set of sites. It is defined as

    $C{F}_3=\frac{{\displaystyle {\sum }_i^n{N}_{o,i}\times N_{u,i}}}{{\displaystyle {\sum }_i^n{\left(N_{u,i}\right)}^2}}$

    (7)

• Martinelli et al. (2009) propose two additional calibration factors: one that considers crash densities (CF₄) and another that uses a weighted ratio (CF₅).
  • Crash densities: this calibration factor is defined as the ratio of the densities of observed and predicted crashes. This essentially weights each observation by the inverse of the segment length, as follows:

where L_i is the length of segment i.

• Weighted ratio: this calibration factor weights each predicted and observed value by the length of the segment in which each crash occurred, as follows:

  $C{F}_5=\frac{{\displaystyle {\sum }_i^n{N}_{o,i}/L_i}}{{\displaystyle {\sum }_i^n{N}_{u,i}/L_i}}$

  (9)

Lastly, Srinivasan et al. (2016) propose a calibration function as an alternative to the calibration factor. This calibration function takes the following form:

where a and b are estimated using regression. This formulation is more flexible not only because it has more parameters (two—a and b—compared to just a single parameter estimated when applying a calibration factor), but also because the exponential term (b) can change the relationship between crash frequency and explanatory variables, like traffic volumes. For example, in the HSM SPF for two-lane rural roads, traffic volume is treated as a multiplicative term (e.g., the β_AADT coefficient is 1), which suggests a linear relationship. However, several studies have found that this exponent can differ from 1 in some regions. If the calibration function just described was applied to the HSM SPF for two-lane rural roads, it would allow crash frequency to vary non-linearly with traffic volume.

Martinelli et al. (2009) compared the performance of the HSM calibration factor with CF₄ and CF₅, while Rajabi et al. (2018) compared the performance of the HSM calibration factor with CF₁, CF₂, CF₃, and the calibration function proposed in Srinivasan et al. (2016). In general, these studies found that the HSM calibration factor does not perform as well as the alternate definitions. In particular, the segment length weighted calibration factor (CF₅) appeared to perform the best in the Martinelli et al. (2009) study. In the Rajabi et al. (2018) study, the best-performing calibration factor differed based on the metric used to assess its goodness of fit; however, the authors recommended that CF₂ be used based on its application of maximum likelihood, since this is the same technique used to estimate coefficients of the negative binomial regression models. Overall, however, the calibration function proposed in Srinivasan et al. (2016) was found to offer superior performance to the use of a single, constant calibration factor.

SPF Development

In addition to calibration, the HSM also suggests that jurisdiction- or state-specific SPFs can be developed using local data. Doing so should provide crash frequency estimates that are more reflective of local conditions compared with applying the calibration procedure. The SPFs in the HSM are developed using negative binomial regression (Miaou, 1994; Shankar et al., 1995). This is a regression technique specifically developed to deal with count data (i.e., the fact that crash

outcomes take non-negative integer values) and overdispersion in crash data when the variance exceeds the mean. Thus, the development of state-specific SPFs requires advanced statistical knowledge.

Two methods are described in the HSM to develop state-specific SPFs. The first method defines and estimates a model for a set of base conditions. Only sites that meet these conditions are considered in the SPF development process, and the only input variables considered are exposure-related variables (e.g., segment length and traffic volumes). Changes from these base conditions are then accommodated via crash modification factors (CMFs) that are either estimated using the appropriate methods from state-specific data or obtained from a trustworthy source (e.g., the FHWA CMF Clearinghouse). Sites should be selected randomly throughout the agency. If possible, selecting sites that are in close physical proximity should be avoided to reduce the correlation between other design features (Carter et al., 2012; Srinivasan and Bauer, 2013). If data from multiple regions or jurisdictions within the agency are included, then region-specific variables should be included to account for regional differences in safety performance (Carter et al., 2012).

The second method considers both exposure-related variables and additional input variables (such as roadway geometric or roadside characteristics). Model coefficients for all variables are estimated together. Once the SPF is obtained, a set of base conditions is prescribed and adjustment factors can be computed for the set of variables to describe changes from these base conditions directly from the SPF. Srinivasan and Bauer (2013) suggest that the variables considered should both be readily available to users of the SPF and describe features that are likely to have an influence on safety performance. However, care should be taken to avoid including too many variables in the model to avoid overfitting the data (Carter et al., 2012; Srinivasan and Bauer, 2013). Goodness-of-fit tools such as CURE plots (described later) can be used to assess the fit of the data and identify extraneous variables that may be omitted from the model.

Guidance on Calibration and State-Specific SPF Development

The choice between calibrating the HSM SPFs to reflect state-specific conditions and the development of state-specific SPFs depends on several factors, including available expertise and resources, desired accuracy, and data availability. In general, calibration requires less expertise and resources but provides less accurate predictions. However, in many cases, data availability is a key limiting factor in this decision.

Sample Size Requirements

Several sources in the literature provide guidance on the minimum number of sites of a given facility type to help practitioners determine if calibration or state-specific SPF development is feasible. The HSM suggests that a minimum sample size of 30–50 sites with at least 100 crashes per year be used for the calibration factor development process, based on expert judgment. Bahar and Hauer (2014) provide a scientific method to estimate the minimum sample size necessary for calibration based on the desired level of precision in the calibration factors. Precision is measured in terms of standard error and coefficient of variation in the calibration factor, and recommendations are provided for acceptable ranges. Alternatively, the Calibrator was developed by Lyon et al. (2016) and serves as an Excel-based tool that can be used to facilitate the calibration process.

The HSM also suggests that multiple region-specific calibration factors can be developed for a single SPF by larger DOTs with extreme differences in terrain, climate, driver population, or other factors related to geographic differences observed within that agency. As per Lyon et al. (2016), the number of regions considered for the development of unique calibration factors for

an agency depends on the difference between the values across individual regions and the desired level of accuracy needed.

The SPF Decision Guide proposes thresholds of 100–200 miles (for roadway segments) or 100–200 sites for intersections representing at least 300 crashes per year to develop SPFs (Srinivasan et al., 2013). These values were obtained by identifying the minimum sample sizes needed for count regression models.

Data Needs

Various data elements are needed to support the development of calibration factors and state-specific SPFs. In both cases, sufficient data elements are needed to identify specific facility types. These data elements typically include:

• Segments
  • Area type
  • Roadway functional classification
  • Number of lanes
  • Median divider presence and type
• Intersections
  • Area type
  • Roadway functional classification
  • Traffic control type
  • Number of approach legs on each of the major and minor approach
• Interchange and ramps
  • Area type (urban vs. rural)
  • Interchange configuration
  • Ramp terminal designation
  • Traffic control for ramp terminal

For network-screening-level SPFs, traffic volumes are needed as a measure of exposure. For segments, this refers to the AADT observed along the individual segment. For intersections, this includes AADT on both the major and minor approaches. Interchange and ramps would include the AADT on the ramp and the crossroad of ramp terminals. In all cases, observed crash data would also be needed. This includes the location of each crash (attributed to each site being considered), crash type and/or severity (if calibrating or developing SPFs to this level of specificity), and other relevant information (e.g., involvement of non-motorized user or number of vehicles involved in a crash, if relevant).

Additional data elements are also needed to support the calibration or development of project-level SPFs. For calibration, this includes the list of data elements required to apply the associated adjustment factors for the relevant SPF; a full list of these is provided in Table 3. For SPF development, the set of data elements will vary based on what is readily available or can be feasibly collected from that state DOT. This can include roadway geometric features (e.g., horizontal curvature and cross-sectional information such as lane, median, and shoulder widths); roadside features (such as roadside hazard rating or presence of barriers); and the presence of other safety-influencing features (e.g., passing zones or safety countermeasures such as rumble strips).

Assessing Accuracy

The fit of a state-specific SPF to observed data or of a calibrated SPF to observed data can be quantified using several measures. The first is the differences between observed and predicted crash outcomes. Ideally, this would be done for a set of sites that were not included in the SPF development or calibration process. Specific measures can include:

• Root mean square error (RMSE)
• Mean absolute error (MAE)
• Modified R² value
• Overdispersion parameter
• Coefficient of variation in the calibration factor

Details on how these measures are defined are provided in Lyon et al. (2016). The first two compare differences between observed crash frequencies and predicted values from the SPF, with RMSE weighing more strongly values with larger differences than MAE. Smaller numbers are indicative of a better fit. The modified R² value is a value between zero and 1 representing the amount of variation in the observed crash data that is explained by the model. Values closer to 1 represent a better fit. The overdispersion parameter quantifies how much the predicted estimates vary from the mean value. Smaller values indicate a better fit. Finally, the coefficient of variation of the calibration factor represents how much calibrated estimates of crash predictions vary from observed values for individual sites. Lower values represent a better fit.

Cumulative Residual (CURE) plots are also often used to assess the fit of a model to data used to estimate the model. Residuals are defined as the difference between observed and predicted outcomes, and these are accumulated with respect to a variable of interest, often one of the continuous input variables or predicted crash frequency. Hauer (2015) and Lyon et al. (2016) provide more details on how CURE plots can be developed, how a confidence interval can be estimated and used to assess if the observed trend is in line with randomness (good fit) or not, and specific trends that indicate issues in the model fit. CURE plots can also be used to determine when adding additional variables would cause overfitting. Specifically, no additional variables should be added if the cumulative residuals fall within the 95% confidence interval. Examples of CURE plots representing a good fit and a poor fit to the observed data are provided in Figures 2a and 2b, respectively.

SPF Calibration and Development Efforts by Individual State DOTs

This section documents specific SPF calibration and development activities undertaken by individual state DOTs that were found in the research literature. Only efforts sponsored or endorsed by state DOTs are summarized here; thus, purely academic research articles or studies

are not included. These efforts are organized by the respective state DOT. While this section provides research on calibration-factor and state-specific SPF development that were sponsored by state DOTs, the results do not reflect the degree to which the DOTs are using these specific models. Further, the results identified do not always match with the responses received from state DOTs to the survey performed as a part of this project (and described in Chapter 3). Any significant differences are noted herein. Lastly, note that no SPF calibration or development efforts are provided for individual cities or metropolitan planning organizations (MPOs) as the focus was on research performed for and used by the state DOTs.

Alabama

Summary

Mehta and Lou (2013) calibrated HSM SPFs and developed state-specific SPFs at the design level for total crashes on two-lane two-way rural roads (approximately 6,000 sites, each with a minimum length of 0.05 miles) and four-lane divided highways (4,000 sites, each with an average length of 0.36 miles) in Alabama using observed crash data from 2006 to 2009 obtained from the Critical Analysis Reporting Environment. Calibration was performed using a special case of a negative binomial (NB) regression model as well as the recommended HSM methodology. The results of this calibration are presented in Table 4.

Two network-screening-level and two design-level SPFs were estimated with four different model types, including an NB regression model and three model specifications from other studies. Ultimately, the calibrated models and SPFs were assessed for goodness of fit based on a validation dataset randomly selected from the original dataset, using measures such as log-likelihood and Akaike information criterion (AIC), mean absolute deviation (MAD), mean squared prediction error (MSPE), and mean prediction bias (MPB). The model found to best fit the data from Alabama was a state-specific SPF form originally developed by the Connecticut Transportation Institute considering variables such as AADT, segment length, lane width, and speed limit.

Kim et al. (2015) calibrated existing HSM SPFs and developed state-specific network screening-level SPFs using observed crash data from 2007 to 2009 on urban and suburban arterial segments. Calibration was performed for total crashes on two-lane undivided arterials (2,600 sites), three-lane arterials with a center two-way left turn-lane (TWLTL) (480 sites), four-lane undivided arterials (1,000 sites), four-lane divided arterials (3,100 sites), and five-lane arterials with TWLTL (1,600 sites). No minimum length was considered for each site included in the calibration analysis. The same site types had SPFs of different forms developed for multi-vehicle crashes and single-vehicle crashes. Based on AIC, Bayesian information criterion (BIC), MAD, and MPB, it was determined that a NB regression model, considering factors of AADT and segment length in non-logarithmic forms, performed the best of the models considered. The calibration factors are provided in Table 5; however, it was noted that there was not enough observed crash data to meet the HSM requirements for calibration, and, as a result, the factors were deemed unreliable.

Table 4. Calibration factors for Alabama from Mehta and Lou (2013).

Table 5. Calibration factors for Alabama from Kim et al. (2015).

^*Calibration factors noted as not reliable due to lack of adequate observed crashes on sites.

Alaska

Summary

Bowie et al. (2014) developed design-level calibration factors for HSM-published intersection SPFs using data from 2010 at urban intersections in Anchorage, Alaska. Calibrated intersection types included: three- and four-leg intersections with minor-road stop control, and signalized three- and four-leg intersections, all on urban and suburban arterials. Each intersection type was calibrated for total, fatal and injury, and property damage-only crashes. The results of the calibration are provided in Table 6. The report indicated that the calibration factors are based on a relatively small sample size (30 sites each), with the three-leg unsignalized intersections failing to meet HSM-recommended minimum observed total crashes (only 34 total crashes) and the three-leg signalized intersections failing to meet the recommended minimum number of locations studied (only 22 sites). The authors suggested that Alaska would benefit from state-specific SPF development due to Alaska’s high frequency of animal crashes, distinctly different vehicle fleet, and weather consistently different from the rest of the United States.

Arizona

Summary

Srinivasan et al. (2016) estimated calibration factors and functions for design-level SPFs of two-lane rural road segments in Arizona using observed crash data from 2008 to 2012. A total of 509 homogeneous segments were considered, which covered a total length of 187.5 miles.

Table 6. Calibration factors for Alaska from Bowie et al. (2014).

Table 7. Calibration factors for Arizona from Srinivasan et al. (2016).

An overall state-wide calibration factor was determined through the traditional HSM-recommended methodology for the HSM Part C SPF, resulting in the calibration factor presented in Table 7.

Calibration factors were also determined for a variety of AADT ranges, segment lengths, and alignment types; these are presented in Table 8.

Calibration functions were estimated by ordinary least squares (OLS), Poisson, and NB regression, resulting in functions following the form of Equation (10), with parameters presented in Table 9.

Based on CURE plots, it was determined that calibration functions estimated through NB regression based on AADT and segment length would outperform the calibration factors in jurisdictions where the calibration factors do not match local data.

Colety et al. (2016) expands on Srinivasan et al. (2016), using the same dataset by developing calibration factors to account for differences in regional terrain, highway classification type, and curve radius. The additional calibration factors are provided in Table 10. Colety et al. (2016) also provides a directly estimated statewide calibration function that provides a calibration factor as a function of the HSM-predicted crashes.

Arizona DOT (no date) developed a draft of state-specific design-level SPFs for total crashes occurring at roundabouts based on four years of observed crash data from 2018 to 2021. The screening-level SPF was developed using NB regression considering the natural logarithm of

Table 8. Additional calibration factors for Arizona from Srinivasan et al. (2016).

Table 9. Calibration function parameters from Srinivasan et al. (2016).

Table 10. Calibration factors for Arizona from Colety et al. (2016).

average entering AADT over the four years and the total number of entering lanes. A likelihood ratio test suggests that the developed model is significant at the 99.9% confidence level.

Arkansas

Summary

Gattis et al. (2017) developed project design-level calibration factors using observed crash data from 2011 to 2013. The study considered rural two-lane undivided roadways, four-lane divided roadways, and rural three- and four-leg stop-controlled intersections on both roadway types. Segments had a minimum length of 0.15 miles. Calibration for the rural segments also accounted for regional differences in terrain—namely, “flatter terrain” and “hilly terrain.” The results of these calibration efforts are presented in Table 11 and Table 12. The authors noted that local law enforcement agencies do not regularly forward crash reports to the statewide database as is required, resulting in underreporting. Additionally, there was an indication that the years analyzed had lower crash frequency than normal.

California

Summary

The findings of the literature review in this section differ from responses received from California as a part of the survey described in Chapter 3. Furthermore, the case example of

Table 11. Calibration factors for Arkansas from Gattis et al. (2017).

Table 12. Calibration factors for intersections in Arkansas from Gattis et al. (2017).

practices in California (Chapter 4) suggests that California currently applies uncalibrated versions of the HSM SPFs.

Shankar and Madanat (2015) developed both network-screening and design-level SPFs for California using observed crash data from 2005 to 2010. SPFs were developed for several crash severity categories, including all crashes, PDO, complaint of pain, visible injury, severe injury, and fatalities. The entire dataset consisted of over 13,000 centerline miles of roadway and 17,000 intersections. The following facility types were considered:

• Roadway segments
  • Two-lane rural (R2U)
  • Four-lane rural (R4)
  • Four+-lane rural (R4+)
  • Multi-lane undivided rural (RMU)
  • Two-lane urban (U2L)
  • Four-lane urban (U4L)
  • Five- to seven-lane urban (U57)
  • Eight+-lane urban (U8+)
  • Multi-lane undivided urban (UMU)
  • Multi-lane divided urban (UMD)
• All intersections (INT)
• Ramps (RP)
  • All ramps
  • Ramps with ramp meters

Design-level SPFs contained a range of input variables that covered different geometric and site-specific features, including indicator variables for crash year. A follow-up study (Shankar and Madanat, 2016) updated these SPFs to account for unobserved effects in crash data via the addition of random parameters to design-level SPF models.

Colorado

Summary

Persaud and Lyon, Inc., and Felsburg Holt & Ullevig (2009) developed network-screening-level SPFs for various urban intersection types in Colorado using observed crash data from 2000 to 2004. SPFs were developed for:

• Four-leg signalized intersection (4SG) on:
  • Four-lane divided roads
  • Six-lane divided roads

• Four-leg unsignalized intersections on:
  • Two-lane undivided roads
  • Four-lane divided roads
  • Four-lane undivided roads
• Three-leg signalized intersections (3SG) on:
  • Four-lane divided roads
• Three-leg unsignalized intersections on:
  • Two-lane divided roads
  • Two-lane undivided roads
  • Four-lane divided roads
  • Four-lane undivided roads

Sample sizes ranged from 34 to 101 intersections of each type. SPFs were developed for total crash frequency and fatal and injury crash frequency.

Kononov (2018) developed network-screening-level SPFs for total crashes and fatal and injury crashes at 20 different intersection types based on data from 2011 to 2015. Sample sizes were not provided. The SPFs follow Sigmoidal and Hoerl functional forms and consider only the AADT for the major and minor approaches. The SPFs developed are presented in the following list:

• Urban Intersections
  • Urban two-lane divided unsignalized three-leg (U2xDU3)
  • Urban two-lane divided unsignalized four-leg (U2Xdu3)
  • Urban two-lane undivided unsignalized three-leg (U2Xuu3)
  • Urban two-lane undivided unsignalized four-leg (U2Xuu4)
  • Urban four-lane divided signalized three-leg (U4Xds3)
  • Urban four-lane divided signalized four-leg (U4Xds4) – stratified norms for two ranges of AADT
  • Urban four-lane divided unsignalized three-leg (U4Xdu3)
  • Urban four-lane divided unsignalized four-leg (U4Xdu4) – stratified norms for two ranges of AADT
  • Urban four-lane undivided unsignalized three-leg (U4Xuu3)
  • Urban four-lane undivided unsignalized four-leg (U4Xuu4)
  • Urban six-lane divided signalized four-leg (U6Xds4) – stratified norms for two ranges of AADT
• One-Way Intersections
  • One-way main line with N lanes, two-way side-road, unsignalized four-leg (Unx1W2WUU4)
  • One-way main line with two to three lanes, one-way side-road signalized four-leg (U23x1W1WUS4)
  • One-way main line with four to five lanes, one-way side-road signalized four-leg (U45x1W1WUS4)
  • One-way main line with N lanes, two-way side-road signalized four-leg (Unx1W2WUS4)
• Rural Intersections
  • Rural two-lane divided unsignalized three-leg (R2Xdu3)
  • Rural two-lane divided unsignalized four-leg (R2Xdu4)
  • Rural two-lane undivided unsignalized three-leg (R2Xuu3)
  • Rural two-lane undivided unsignalized four-leg (R2Xuu4) – stratified norms for two ranges of AADT
  • Rural four-lane divided unsignalized three-leg (R4Xdu4)

The SPFs were developed using a generalized linear modeling methodology, assuming an NB distribution, and an EB method was applied to correct for regression to the mean bias.

Connecticut

Summary

CTSRC (2020) developed a state-specific network-screening-level crash prediction analytical tool that uses developed SPFs in combination with observed crash proportions for 32 segment and 24 intersection types. Segment facility types include:

• State-Maintained Roadway Segments
  • Rural freeway divided two or more lanes (R2+F)
  • Rural non-freeway divided two or more lanes (R2+D)
  • Rural non-freeway undivided two or more lanes (R2+U)
  • Rural speed-change lane four or six lanes
  • Urban freeway divided two or three lanes (U2F, U3F)
  • Urban freeway divided four lanes (U4F)
  • Urban freeway divided five or more lanes (U5+F)
  • Urban non-freeway divided two lanes (U2D)
  • Urban non-freeway divided three lanes (U3D)
  • Urban non-freeway divided four or more lanes (U4+D)
  • Urban non-freeway one-way one or more lanes
  • Urban non-freeway undivided two lanes (U2U)
  • Urban non-freeway undivided three lanes (U3U)
  • Urban non-freeway undivided four or more lanes (U4U)
  • Urban speed-change lane four or fewer lanes
  • Urban speed-change lane five or more lanes
• Town-Maintained Roadway Segments
  • Rural arterial or collector
  • Rural local one or more lanes
  • Urban arterial two lanes
  • Urban arterial three or more lanes
  • Urban arterial one-way one or more lanes
  • Urban collector two lanes
  • Urban collector three or more lanes
  • Urban collector one-way one or more lanes
  • Urban local two lanes
  • Urban local three or more lanes
  • Urban local one-way one
  • Urban local one-way two or more lanes
• Freeway Ramp Segments
  • Rural ramps
  • Urban entrance ramps
  • Urban exit ramps
  • Urban other ramps

Intersection facility types include:

• State-Maintained Intersections with Full Traffic Volume Information
  • Rural three-leg sign controlled (R3ST)
  • Rural three-leg signalized (R3SG)

• Rural four-leg sign controlled (R4ST)
• Rural four-leg signalized (R4SG)
• Urban two-lane three-leg sign controlled (U2 3ST)
• Urban two-lane three-leg signalized (U2 3SG)
• Urban two-lane four-leg sign controlled (U2 4ST)
• Urban two-lane four-leg signalized (U2 4SG)
• Urban multi-lane three-leg sign controlled (UM 3ST)
• Urban multi-lane three-leg signalized (UM 3SG)
• Urban multi-lane four-leg sign controlled (UM 4ST)
• Urban multi-lane four-leg signalized (UM 4SG)
• State-Maintained Intersection with Partial Traffic Volume Information
  • Rural three-leg sign controlled (R3ST)
  • Rural three-leg signalized (R4ST)
  • Rural four-leg sign controlled (R4ST)
  • Rural four-leg signalized (R4SG)
  • Urban two-lane three-leg sign controlled (U2 3ST)
  • Urban two-lane three-leg signalized (U2 3SG)
  • Urban two-lane four-leg sign controlled (U2 4ST)
  • Urban two-lane four-leg signalized (U2 4SG)
  • Urban multi-lane three-leg sign controlled (UM 3ST)
  • Urban multi-lane three-leg signalized (UM 3SG)
  • Urban multi-lane four-leg sign controlled (UM 4ST)
  • Urban multi-lane four-leg signalized (UM 4SG)

A variety of crash type/severity combinations are included:

• Total crashes
• Multi-vehicle crashes
  • Angle
  • Front to front
  • Front to rear
  • Sideswipe opposite direction
  • Sideswipe same direction
  • Multi other
• Single-vehicle crashes
  • Fixed objects
  • Non-fixed objects
  • Overturn/rollover
  • Jackknife
  • Non-collision other
  • Single other
• Severity
  • KABC
  • KAB
  • KA
  • PDO
• Emphasis area
  • DUI related
  • Aggressive driving related
  • Roadway departure
  • Young driver involved
  • Motorcycle involved

• Qualifying commercial vehicle involved
• Adverse weather
• Wet road surfaces
• Pedestrian involved
• Bicycle involved

Further information on SPF development was not available.

Delaware

Summary

The authors did not find any documentation of state customization of HSM tools or SPFs for Delaware. Note that this differs from responses received from Delaware as a part of the survey described in Chapter 3. The responses to the survey indicated calibration factors are currently being developed.

District of Columbia

Summary

The authors did not find any documentation of state customization of HSM tools or SPFs for the District of Columbia.

Florida

Summary

Srinivasan et al. (2011) developed calibration factors for design-level segment and intersection SPFs in the HSM using observed crash data from 2005 to 2009 (only intersections used 2009 crash data). Between 66.3 and 2121.0 miles of sites were used for segment calibration factors, while 25 to 121 intersections were included for intersection calibration factors. Table 13 provides a summary of the range of calibration factors developed for both fatal and injury crashes (KABC) and fatal and major injury crashes (KAB)—the range represents annual calibration factors that were developed for each year in the 2005–2008 period. Some data collection issues were noted. For example, base values in the HSM for adjustment factors used in the SPFs were assumed when data were not available. Curves were also removed from segment databases since detailed curvature information was not available. The calibration factors were developed using HSM collision-type distributions and Florida-specific values; however, the calibration factors were relatively insensitive to this change. Region-specific calibration factors were also developed for individual Florida DOT (FDOT) districts. Finally, state-specific SPFs were developed using only traffic volumes as input variables for rural two-lane roadway segments and urban four-lane divided roadway segments. The state-specific SPFs were not shown to provide an improvement in prediction accuracy as the HSM-calibrated SPFs provided better predictions.

Table 13. Calibration factors for Florida from Srinivasan et al. (2011).

FDOT (2023) provides state-specific SPFs developed for three-leg signalized intersections, four-leg signalized intersections, and crossroad ramp terminal intersections. These are network-screening-level SPFs that consider traffic volumes on the major and minor approaches, ramp volumes, and indicators for context-specific classifications and interchange types. Details on the years of observed crash data used, sample sizes, or the development of the SPFs were not provided.

Additionally, the Florida DOT funded a project to estimate SPF for restricted U-turn (RCUT) intersections using data from other states to better understand the safety impacts of this site type before implementing them more widely in Florida. Ozguyen et al. (2019) developed design-level SPFs for both signalized and unsignalized restricted RCUT intersections using data from Alabama, Georgia, Louisiana, Maryland, Michigan, Minnesota, Mississippi, North Carolina, Ohio, South Carolina, Tennessee, Texas, and Washington. Data were available for a total of 225 unique intersections. SPFs were developed for total and fatal/injury crashes. SPF input variables and CMFs estimated as a part of this project included major-road traffic volume, minor-road traffic volume, number of U-turns, number of lanes on the major and minor approaches, median width, offset distance, deceleration lane length, acceleration lane length, number of nearby driveways, number of left-turn lanes, and major-road speed limit. SPFs of various complexity were estimated, and the simplest ones (i.e., those with the fewest input variables) were recommended since they provided similar prediction accuracy with lower data requirements.

Georgia

Summary

Alluri and Ogle (2011) both calibrated and developed state-specific network-screening-level SPFs for total and fatal and injury crashes with data collected in Georgia from 2004 to 2006. The SPFs that were calibrated were obtained from the SafetyAnalyst software. Sample sizes ranged from 25 miles (urban freeways with eight+ lanes) to 79,586 miles (rural two-lane roads). The study found that state-specific SPFs performed better than calibrated SPFs for predicting fatal and injury crashes; however, the relatively low overdispersion parameter associated with the HSM SPFs made them preferable for predicting total crashes. Table 14 shows the site types studied and respective calibration factors applied to the HSM SPFs.

Hawaii

Summary

The authors did not find any documentation of state customization of HSM tools or SPFs for Hawaii.

Table 14. Calibration factors for Georgia from Alluri and Ogle (2011).

Idaho

Summary

Abdel-Rahim and Sipple (2015) calibrated network-screening-level HSM SPFs and developed state-specific network-screening-level SPFs for total crashes on rural two-lane two-way highway segments (approximately 220 miles), rural three-leg stop-controlled intersections (43 intersections), and rural four-leg stop-controlled intersections (41 intersections) in Idaho using observed crash data from 2003 to 2012. The calibration factors developed are provided in Table 15.

An NB regression model was used to develop the state-specific SPFs considering segment length and AADT for the highway segments, and major and minor approach AADT for intersections. Each SPF model was trained on 70% of the available data, while the remaining 30% of observations were held out for validation purposes. Both the calibrated SPFs and the state-specific SPFs were analyzed based on Pearson’s R, MSPE, and Freeman-Tukey R-squared. The authors’ comparisons demonstrated that state-specific SPFs outperform the calibrated HSM SPFs for rural two-lane two-way highway segments and rural three-leg stop-controlled intersections, but there was no significant improvement for rural four-leg stop-controlled intersections.

Illinois

Summary

Tegge et al. (2010) developed statewide screening-level SPFs for fatal and injury crashes and crashes of severity levels K, A, and B on the KABCO scale for 12 segment facility types and eight intersection types using observed crash data from 2001 to 2005. The facility types were included:

• Segments
  • Rural two-lane highway (R2U)
  • Rural multi-lane undivided highway (RMU)
  • Rural freeway, four lanes (R4F)
  • Rural freeway, six+ lanes (R6+F)
  • Urban two-lane highway (U2L)
  • Urban one-way arterial (UOA)
  • Urban multi-lane undivided highway (UMU)
  • Urban multi-lane divided highway (UMD)
  • Urban freeway, four lanes (U4F)
  • Urban freeway, six lanes (U6F)
  • Urban freeway, eight+ lanes (U8+F)

Table 15. Calibration factors for Idaho from Abdel-Rahim and Sipple (2015).

• Intersections
  • Rural minor leg stop control (R3ST, R4ST)
  • Rural all-way stop control (R3aST, R4aST)
  • Rural signalized intersection (R3SG, R4ST)
  • Rural undetermined (RUI)
  • Urban minor leg stop control (U3ST, U4ST)
  • Urban all-way stop control (U3aST, U4aST)
  • Urban signalized intersection (U3SG, U4SG)
  • Urban undetermined (UUI)

Sample sizes ranged from 33.2 miles to 7,968.1 miles for segments (with one exception—six+ lane rural freeways, which had just 25.3 miles) and 199 to 14,933 intersections. The authors indicated that there was an inability to identify interchange areas, potentially influencing the results of the SPF estimation by considering interchange-influenced crashes with the rest of the segment crashes. SPFs were estimated using generalized linear modeling techniques for NB and Poisson regression, and the authors stated that they intended to implement the new SPFs in SafetyAnalyst.

Illinois DOT (2014) developed calibration factors for design-level SPFs in the HSM. Two sets of calibration factors were estimated: one using observed crash data from 2006 to 2008 and one using data from 2009 to 2011. Table 16 provides a summary of these calibrations; sample sizes were not provided. Crash severity distributions were also computed using Illinois data.

Indiana

Summary

Tarko et al. (2018) developed a total of eight design-level state-specific SPFs for total crashes and property damage-only crashes using crash data from 2009 to 2011. The SPFs were developed via NB regression for segments of the following facilities: rural two-lane roads (5,355 sites with an average length of 1.33 miles), rural multi-lane roads (581 sites with an average, length of 1.30 miles), urban two-lane roads (2,594 sites with an average length of 0.42 miles), and urban multi-lane roads (1,351 sites with an average length of 0.50 miles). Development of these SPFs considered segment length and traffic volumes, and also considered variables such as lane width, shoulder width and type, border zone, signalized and unsignalized intersection density, functional classification, and presence of curbs.

Tarko et al. (2019) calibrated over 80 CMFs for various road and control improvements to local conditions using observed crash data from 2013 to 2015. CMFs were applied to rural two-lane segments (5,774 sites), rural divided multi-lane segments (782 sites), and urban/suburban arterial segments (820 sites). Local crash type and severity distributions were also estimated as a part of this project.

Iowa

Summary

Iowa DOT (2017) developed calibration factors to be applied to HSM design-level SPFs for single- and multi-vehicle fatal and injury or property damage-only crashes for urban and rural freeway segments. The published calibration factors are presented in Table 17. A calibration

Table 16. Calibration factors for Illinois from Illinois DOT (2014).

Table 17. Calibration factors for Iowa from Iowa DOT (2017).

factor of 0.837 for total crashes on rural, primary, two-lane road segments was also included. Sample sizes were not provided for the data used to estimate these calibration factors.

Kimley-Horn and Associates (2021) provided additional calibration factors for design-level HSM SPFs for total crashes on urban and suburban arterial segments. The published results included calibration factors presented in Table 18.

The report also indicated that calibration factors for the following facility types were under development at the time of publication, though the authors did not find any updates on their development:

• Segments
  • Rural two-lane, two-way roads
    • Two-way undivided (R2U)
  • Rural multi-lane highways
    • Four-lane undivided (R4U)
    • Four-lane divided (R4D)
• Intersections
  • Rural two-lane, two-way roads
    • Unsignalized three-leg, minor stop (R2 3ST)
    • Unsignalized four-leg, minor stop (R2 4ST)
    • Signalized four-leg (R2 4SG)
  • Rural multi-lane highways
    • Unsignalized three-leg, minor stop (RM 3ST)
    • Unsignalized four-leg, minor stop (RM 4ST)
    • Signalized four-leg (RM 4SG)
  • Urban and suburban arterials
    • Unsignalized three-leg, minor stop (UA 3ST)
    • Signalized three-leg (UA 3SG)
    • Unsignalized four-leg, minor stop (UA 4ST)
    • Signalized four-leg (UA 4SG)

Oneyear et al. (2023) developed state-specific network-screening-level SPFs for high-speed (posted speed limits greater than or equal to 45 mph) paved secondary roads in Iowa using observed crash data from 2016 to 2020. The fit of the SPFs to the observed data was assessed using CURE plots and other statistical measures. Separate SPFs were developed for tangent sections and sections with curves (though these were not fully curve segments), and these were further disaggregated based on volumes (high versus low, using an AADT of 400 as the threshold), speed

Table 18. Calibration factors for Iowa from Kimley-Horn and Associates (2021).

limits (45–50 mph versus 55+ mph) and amount of curvature within the segment (<25% versus >25%). Sample sizes ranged from 558 to 7,459 sites for each SPF, representing a total length of between 342.21 miles and 10,688.68 miles of roadway.

Kansas

Summary

Lubliner and Schrock (2011) calibrated HSM SPFs at the design level for total crashes on two-lane rural roads using observed crash data from 2005 to 2007. Nineteen 10-mile sections from a random statewide sample of 41 sections were calibrated, resulting in factors between 0.78 and 3.23, with an overall statewide calibration factor of 1.48 as presented in Table 19.

Jurisdiction-specific linear calibration models were also developed to account for regional differences and the high proportion of observed animal-related crashes. Calibration factors and functions were assessed for goodness of fit based on the following: Pearson’s product moment correlation coefficients between observed and predicted crash frequencies, MPB, MAD, a paired t-test, and percent difference between observed and predicted values. Each method proposed for crash prediction was also assessed with and without an Empirical Bayes adjustment. The study concluded that the Empirical Bayes adjustment universally improved prediction ability, and that county-level calibration functions and statewide calibration factors provided the most accurate predictions.

Bornheimer et al. (2011) developed state-specific design-level SPFs for animal-related crashes and non-animal-related crashes on two-lane rural roads using observed crash data from 2005 to 2007 and approximately 300 miles of roadway data. NB regression was used to estimate model parameters for seven different model specifications accounting for variables such as AADT, segment length, roadside hazard rating (RHR), and exposure. Based on goodness of fit (as assessed by a paired t-test, Pearson’s R, BIC, MPB, and MAD), a model predicting non-animal-related crashes considering AADT, segment length, and roadside hazard rating was determined to be the best model.

Dissanayake and Aziz (2016) calibrated HSM SPFs and developed new state-specific design-level SPFs for total and fatal and injury crash severities on rural four-lane divided (281 segments) and undivided (83 segments) highways. Calibration factors for rural three- (65 intersections) and four-leg (199 intersections) stop-controlled intersections were also developed. The development of calibration factors and SPFs relied on observed crash data from 2011 to 2013. Calibration factors were calculated via the HSM methodology, while the SPFs were developed using the same form as SPFs published in the HSM with new parameter estimates derived from NB regression using Kansas data. Proportions for crash types were also reported for the specified period, including the following types:

• Single-vehicle
  • Animal-related
  • Ran off road

Table 19. Calibration factor for Kansas from Lubliner and Schrock (2011).

• Moving vehicle
• Rollover
• Other
• Pedestrian
• Pedal cyclist
• Multi-vehicle
  • Head-on
  • Rear-end
  • Angle
  • Sideswipe (opposite direction)
  • Sideswipe (same direction)
  • Backed-into
  • Other
• Light condition
  • Daylight
  • Dawn
  • Dusk
  • Dark (streetlights on)
  • Dark (no streetlights)
  • Other

A summary of the calibration factors developed in this study is provided in Table 20 and Table 21.

Table 20. Calibration factors for Kansas highways from Dissanayake and Aziz (2016).

Table 21. Calibration factors for Kansas rural intersections from Dissanayake and Aziz (2016).

Table 22. Calibration factors for Kansas from Dissanayake and Karmacharya (2020).

Dissanayake and Karmacharya (2020) developed calibration factors for HSM design-level SPFs at various urban intersection types using observed crash data from 2013 to 2016 (2013 to 2015 for three intersection types and 2014 to 2016 for one). A summary of the calibration factors and sample sizes is provided in Table 22.

Dissanayake and Matarage (2020) developed design-level calibration factors and functions for single- and multi-vehicle fatal and injury and property damage-only crashes on freeway segments and speed-change lanes using observed crash data from 2013 to 2015. Calibration factors were also estimated for observed crashes on ramp segments and ramp terminal facilities from 2014 to 2016. Goodness of fit for both the calibration factors and calibration functions was determined based on CURE plots generated based on a holdout sample of observed crash data. A summary of the calibration factors developed is provided in Table 23. Sample sizes used were 521 segments between 0.1 and 1 mile in length (freeway segments), 351 to 366 segments between 0.02 and 0.30 mile in length (entrance- and exit-related speed-change lanes), 156 to 184 ramps (entrance and exit), and 74 to 120 signal- and stop-controlled ramp terminals.

Kentucky

Summary

Green et al. (2015) developed network-screening-level SPFs for total crashes and KAB crashes occurring at urban and rural intersections using observed crash data from 2009 to 2014. The SPFs were developed using NB regression in the R statistical software and account only for the AADT of major and minor approaches of the intersections. The intersections studied were classified as follows in Table 24.

Ross et al. (2022) developed screening-level SPFs for KAB and CO severity crashes occurring on urban and rural two-lane facilities, interstates and parkways, multi-lane divided facilities, multi-lane undivided facilities, and 36 different intersection types using observed crash data from 2015 to 2019. Sample sizes were not explicitly defined for any facility type. CURE plots were generated for each SPF developed.

Blanford et al. (2022) developed screening-level SPFs for total crashes, aggressive driving crashes, distracted driving crashes, impaired driving crashes, and unrestrained driving crashes on 13 segment facility types using observed crash data from 2014 to 2018. Sample sizes ranged

Table 23. Calibration factors for Kansas from Dissanayake and Matarage (2020).

Table 24. SPFs developed for Kentucky from Green et al. (2015).

from 19 to 12,525 segments, and four to 127,107 crashes. Facilities included in the study are the following:

• Interstates and parkways
• Rural two-lane; shoulder < 4 feet
• Rural two-lane; shoulder > 4 feet
• Rural three+ lanes; shoulder < 4 feet divided
• Rural three+ lanes; shoulder > 4 feet divided
• Rural three+ lanes; shoulder < 4 feet undivided
• Rural three+ lanes; shoulder > 4 feet undivided
• Urban two-lane; shoulder < 4 feet
• Urban two-lane; shoulder > 4 feet
• Urban three+ lanes; shoulder < 4 feet divided
• Urban three+ lanes; shoulder > 4 feet divided
• Urban three+ lanes; shoulder < 4 feet undivided
• Urban three+ lanes; shoulder > 4 feet undivided

SPFs were developed using the SPF-R package in RStudio. CURE plots were generated for each model to analyze goodness of fit. The parameters of each model are not provided in the report.

Louisiana

Summary

Sun et al. (2011) calibrated design-level HSM SPFs for total crashes on rural divided and undivided multi-lane highways using observed crash data from 2003 to 2007. Sample sizes were approximately 60 to 80 miles per year for undivided roads and 450 to 600 miles per year for divided roads. The HSM methodology was followed exclusively, and the only validation of the calibration factors were simple comparisons of observed crashes, predicted crashes, and predicted crashes with calibration. The calibration factors developed are presented in Table 25.

Robicheaux and Wolshon (2015) calibrated HSM design-level SPFs for total crashes on Louisiana road and highway segments using observed crash data from 2009 to 2011. A total of eight calibration factors were calculated, one for each of the following segment types: rural two-lane roads, rural multi-lane divided highways, rural multi-lane undivided highways, urban two-lane roads, urban three-lane roads with TWLTL, urban four-lane divided highways, urban four-lane undivided highways, and urban five-lane highways with TWLTL. Between 30 and 145 roadway segments were used in the calibration factor development. The values of the eight calibration factors are provided in Table 26. Calibration factors were calculated based on random samples from the statewide dataset, and crashes influenced by intersection effects were removed from the dataset if the crash occurred within 150 feet of an intersection. The authors acknowledged that the study was lacking in statistical analysis of the calibration factors, and they questioned the long-term applicability of these factors.

Table 25. Calibration factors for Louisiana from Sun et al. (2011).

Table 26. Calibration factors for Louisiana from Robicheaux and Wolshon (2015).

Kononov (2017) developed total crash and fatal and injury crash network-screening-level SPFs for five different segment types and 27 intersection types using five years of observed crash data. Sample size information was not available. SPFs for segments included consideration of terrain in that the SPFs are specifically applicable to segments in terrain deemed “flat” or “rolling.” SPFs all take Sigmoidal or Hoerl functional forms and were developed using a generalized linear modeling methodology assuming NB or Poisson distributions. An Empirical Bayes adjustment was performed to account for regression to the mean bias, and goodness of fit was measured by CURE plots. A list of the facilities for which SPFs were developed is presented below:

• Rural segments
  • Two-lane undivided highways (R2U)
  • Four-lane divided highways (R4D)
  • Four-lane undivided highways (R4U)
• Urban segments
  • Four-lane divided freeways (U4D)
  • Six-lane divided freeways (U6D)
• Rural intersections
  • Two-lane divided unsignalized three-leg intersections (R2D 3ST)
  • Two-lane divided unsignalized four-leg intersections (R2D 4ST)
  • Two-lane undivided unsignalized three-leg intersections (R2U 3ST)
  • Two-lane undivided unsignalized four-leg intersections (R2U 4ST)
  • Four-lane divided unsignalized three-leg intersections (R4D 3ST)
  • Four-lane divided unsignalized four-leg intersections (R4D 4ST)
• Urban intersections
  • Two-lane divided signalized three-leg intersections (U2D 3SG)
  • Two-lane divided signalized four-leg intersections (U2D 4SG)
  • Two-lane divided unsignalized three-leg intersections (U2D 3ST)
  • Two-lane divided unsignalized four-leg intersections (U2D 4ST)
  • Two-lane undivided signalized three-leg intersections (U2U 3SG)
  • Two-lane undivided signalized four-leg intersections (U2U 4SG)
  • Two-lane undivided unsignalized three-leg intersections (U2U 3ST)
  • Two-lane undivided unsignalized four-leg intersections (U2U 4ST)
  • Four-lane divided signalized three-leg intersections (U4D 3SG)
  • Four-lane divided signalized four-leg intersections (U4D 4SG)
  • Four-lane divided unsignalized three-leg intersections (U4D 3ST)
  • Four-lane divided unsignalized four-leg intersections (U4D 4ST)
  • Four-lane undivided signalized three-leg intersections (U4U 3SG)
  • Four-lane undivided signalized four-leg intersections (U4U 4SG)

• Four-lane undivided unsignalized three-leg intersections (U4U 3ST)
• Four-lane undivided unsignalized four-leg intersections (U4U 4ST)
• Six-lane divided signalized four-leg intersections (U6D 4SG)
• Six-lane divided unsignalized four-leg intersections (U6D 4ST)

Maine

Summary

Belz and Aguilar (2015) developed state-specific calibration factors for HSM design-level SPFs for rural two-lane road segments and intersections, as well as urban and suburban arterials and intersections. The calibration factors for each of the 13 different facility types are listed in Table 27, along with sample sizes.

Maryland

Summary

Shin et al. (2014) developed state-specific calibration factors for HSM design-level SPFs for roadway segment and intersection facility types using observed crash data from 2008 to 2010 across the network of Maryland State Highway Administration roads (excluding the City of Baltimore). Between 19 and 252 roadway sites (minimum length of 0.1 miles for rural and 0.04 miles for urban) were used for segment-level calibration, and between 10 and 244 sites were used for intersection calibration. The calibration factors were calculated for total, KABC, KAB, and PDO severities, and the observed crash proportions for various single- and multi-vehicle crash types in Maryland were presented allowing for state-specific prediction of those crash types. The calibration factors calculated are presented in Table 28.

Table 27. Calibration factors for Maine from Maine DOT (2014).

Table 28. Calibration factors for Maryland from Shin et al. (2014).

^*Denotes that the facility did not meet the HSM minimum sample size criteria of 30–50 sites or the minimum annual crash threshold of 100.

Shin et al. (2022) developed state-specific calibration factors for HSM design-level SPFs for single- and multi-vehicle fatal and injury and PDO crashes on freeways, speed-change lanes, and ramp terminals using observed crash data from 2008 to 2010. Due to sample size limitations, calibration factors were not disaggregated by area type (urban/rural) or number of lanes. The total sample size available for calibration was 317 miles of freeway segments, 80.73 miles of speed-change lanes, 172 signalized ramp terminals, and 147 stop-controlled ramp terminals. This study excluded sites in the City of Baltimore due to a difference in data collection schemes. The calculated calibration factors are provided in Table 29.

Massachusetts

Summary

Xie and Chen (2016) calibrated design-level HSM SPFs and developed state-specific network-screening-level SPFs using observed crash data from 2010 to 2012 for several intersection types on urban roads. Calibration factors for design-level SPFs are provided in Table 29. Between 48 and

Table 29. Calibration factors for Maryland from Shin et al. (2020).

86 intersections of each type were considered in this project. SPFs were also developed for these same intersection types for multi-vehicle crashes (only); however, due to data limitations, only traffic volumes on the major- and minor-road approaches were considered as input variables. The authors suggested that the HSM adjustment factors could be applied to these SPFs to account for specific design features. Calibration factors were then developed for these state-specific SPFs with HSM adjustment factors applied; these are also provided in Table 30.

A follow-up study (Xie and Wen, 2021) developed updated calibration factors and SPFs for these same intersection types using observed crash data from 2015 to 2018. Between 51 and 118 intersections of each type were considered in the sample used for calibration. The calibration factors obtained are shown in Table 31. Traffic volumes were estimated using data from the MassDOT Roadway Inventory and Streetlight; two sets of calibration factors were developed based on these different traffic volume sources. SPFs were developed for total crashes, fatal and injury crashes, PDO crashes, multi-vehicle crashes, single-vehicle crashes, and vehicle–pedestrian crashes using Bayesian NB regression. Only traffic volumes were considered as input variables to the SPFs. The two methods (calibration and state-specific SPFs) were compared using errors between observed crash frequencies and predicted values, as well as CURE plots.

VHB (2020) developed SPFs for rural and urban arterials and collectors to support network screening using observed crash data from 2013 to 2017. SPFs were developed for roadway segments on two-lane divided roads, two-lane undivided roads, four-lane divided roads, and four-lane undivided roads; sample sizes ranged from 34.4 miles to over 2,000 miles. In addition to statewide SPFs, region-specific SPFs were estimated at the MassDOT district level for several of these facility types. Unique SPFs were estimated considering and ignoring traffic volumes; the latter only included segment length as an input variable. Additionally, the SPFs with traffic volumes

Table 30. Calibration factors for Massachusetts from Xie and Chen (2016).

Table 31. Calibration factors Massachusetts from Xie and Chen (2021).

considered both total vehicle miles traveled along the roadway segment and adjustments for specific traffic volume ranges. Default AADT values were assumed for roadway segments with no traffic volumes available.

Michigan

Summary

Savolainen et al. (2015) calculated statewide design-level calibration factors for total, fatal and injury, and PDO single- and multi-vehicle crashes at urban three- and four-leg stop-controlled and signalized intersections using observed crash data from 2008 to 2012. Between 485 and 5,731 intersections were available for each specific facility type. SPFs were also developed for the same site and crash types with indicator variables to account for regional differences across the state, and additional new SPFs were estimated for pedestrian crashes, bicycle crashes, and one-way-street intersections. The results of the calibration factor estimation are presented in Table 32. The authors used the calibration factors as evidence that HSM-default SPFs do not adequately represent Michigan conditions; in addition, state-specific SPFs would better reflect Michigan’s crash data.

Savolainen et al. (2016) mimics the previous report in both calibration and development of state-specific SPFs at the design level but for urban segment site types over the same study

Table 32. Calibration factors for Michigan from Savolainen et al. (2015).

Table 33. Calibration factors for Michigan from Savolainen et al. (2016).

period. Sample sizes ranged from 239 to 489 segments, each with average lengths between 0.6 and 0.75 miles. The results of the calibration factor estimation are provided in Table 33.

Gates et al. (2018) calibrated HSM design-level SPFs and developed state-specific design-level SPFs for total crashes on rural road segments and intersections using observed crash data from 2011 to 2015. Observed crash proportions for a variety of single- and multi-vehicle crashes and crash severities were provided for Michigan, allowing for estimation of these crash types. The calibration factors were calculated via the HSM methodology, and SPFs were developed through a generalized linear modeling technique assuming a Poisson distribution. Intersection sample sizes ranged from 175 to 2,513, while segment sample sizes ranged from 95.2 miles to 5,351.6 miles. Due to a high proportion of deer-related crashes, calibration factors were calculated for both total crashes and non-deer-related crashes on segments. Both calibration factors and developed SPFs attempted to capture regional differences across the state; calibration factors were estimated both statewide and for individual regions, while newly developed SPFs included variables to account for regional differences. The calculated calibration factors are provided in Tables 34 and 35, and SPFs were estimated for the same facility types as calibration factors.

Geedipally et al. (2019) developed design-level state-specific SPFs for two-lane two-way rural roads using observed crash data from 2011 to 2015. Sample sizes ranged from approximately 1,450 to 4,500 miles. Separate single- and multi-vehicle crash SPFs were developed for fatal and injury crashes and PDO crashes on paved roads funded through federal aid, and for fatal and injury crashes and PDO crashes on paved roads with other sources of funding. SPFs considered variables such as AADT, lane widths, presence of horizontal curves, driveway density, roadway surface (paved versus gravel), and a variable to account for regional differences between counties. The SPFs were developed using NB regression with crash data that did not include animal-related crashes.

Minnesota

Summary

Storm and Richfield (2014) used three years of observed crash data to develop calibration factors for design-level HSM SPFs for total crashes on rural roadway segments and intersections.

Table 34. Calibration factors for roadway segments in Michigan from Gates et al. (2018).

— Cells indicate calibration factors that were not calculated due to small sample sizes.

Table 35. Calibration factors for intersections in Michigan from Gates et al. (2018).

Calibration factors were calculated both for statewide crashes and for those crashes occurring in the Minneapolis/St. Paul (Metro) area, the values of which are presented in Table 36. For intersections, 100 sites were randomly selected except for 4SG intersections, which only had 31 available across the state. For segments, approximately 300 miles were used for each calibration factor. Additional information regarding the proportion of crash types including various forms of single- and multi-vehicle crashes, severity levels (fatal and injury and PDO), and nighttime crashes were published to allow prediction of those crash types in conjunction with the calibration factors.

Mississippi

Summary

Walker et al. (2020) developed calibration factors for design-level SPFs from the HSM, NCHRP Project 17-58, and NCHRP Project 17-68. These included SPFs for segments and intersections on rural two-lane two-way roads, rural multi-lane highways, and urban and suburban arterials at severity levels ranging from total crashes to PDO. The authors also recommended the development of state-specific SPFs for urban three-leg and urban four-leg intersections due to the large calibration factors observed. Calibration factors were calculated using the FHWA

Table 36. Calibration factors for Minnesota from Storm and Richfield (2014).

^*Calibration factor is statewide.

Calibrator, except in the case of the SPFs from NCHRP projects, which were estimated using the R statistical software. The two new design-level SPFs for four-leg minor-road stop-controlled intersections on rural multi-lane divided highways and rural two-lane two-way segments were developed using NB regression. Calibration factors and SPFs were assessed for goodness of fit based on CURE plots, MAD, modified R², dispersion parameter, and coefficient of variation—and a goodness-of-fit scoring system was used to recommend calibration factors for use by MDOT. The calibration factors recommended for use by MDOT, as well as sample sizes, are provided in Table 37.

Missouri

Summary

Sun et al. (2013) estimated calibration factors for various design-level SPFs using observed crash data from 2009 to 2011. A summary of the calibration factors that were estimated is provided in Table 38. Notable data collection issues that were mentioned included a lack of traffic volumes for ramps and a lack of consistent crash data from within the state. The former was solved by assuming values from nearby locations or estimating traffic volumes based on mainline volumes. The latter included missing PDO crash data from one jurisdiction within the state and was solved by excluding data from that jurisdiction. With the exception of rural two-lane undivided highway segments (which had approximately 200 sites), between 40 and 70 sites were used for each site type to develop the calibration factor. For roadway segments, these sites were a minimum of 0.25 miles (urban) and 0.5 miles (rural) long.

Sun et al. (2017) developed updated calibration factors for most of these site types using observed crash data from 2012 to 2014. These updated calibration factors are provided in

Table 37. Calibration factors for Mississippi from Walker et al. (2020).

Table 38. Summary of calibration factors estimated in Sun et al. (2013).

PDO indicates property damage-only crashes, FI indicates fatal and injury crashes, SV indicates crashes involving a single vehicle, and MV indicates crashes involving multiple vehicles.

Table 39. Summary of calibration factors estimated in Sun et al. (2017).

Table 39. The same set of sites was used as the previous calibration effort, although some sites were replaced if significant changes occurred. Additionally, crash severity and type distributions were calculated using available crash data.

Montana

Summary

The authors did not find any documentation of state customization of HSM tools or SPFs for Montana. Note that this lack of documentation differs from responses received from Montana as a part of the survey described in Chapter 3; however, the responses to the survey also indicated that the reports documenting SPFs developed for Montana are kept internal to the Montana Department of Transportation’s Safety Program.

Nebraska

Summary

The authors did not find any documentation of state customization of HSM tools or SPFs for Nebraska.

Nevada

Summary

Tian et al. (2013) calibrated the design-level two-lane, two-way rural road SPF, using observed crash data in Nevada from 2007 to 2011. Approximately 680 miles of roadway was used for this analysis and a calibration factor of 1.21 was obtained, as shown in Table 40.

Paz et al. (2015) reported that calibration factors were estimated for the following site types:

• Urban freeway segments with four and six lanes (U4D and U6D)
• Urban freeway segments in interchange areas with four and six lanes
• Urban signalized four-leg and three-leg intersections (U3SG and U4SG)
• Urban stop-controlled four-leg and three-leg intersections (U3ST and U4ST)
• Arterial segments with two, four, and six lanes

However, calibration factors were not provided in Paz et al. (2015), and a Nevada DOT research report with any additional information was not found.

New Hampshire

Summary

Gross et al. (2016) developed state-specific SPFs for New Hampshire for network screening purposes as part of a larger study to compare the outcomes of different network screening methods using observed crash data from 2010 to 2014. SPFs were developed for the following site types and included either total entering traffic volume or traffic volume on major/minor intersection legs as input variables:

• Three-leg signalized intersections (3SG) (sample of 108 intersections)
• Four-leg signalized intersections (4SG) (sample of 190 intersections)
• Three-leg stop-controlled intersections (3ST) (sample of 824 intersections)
• Four-leg stop-controlled intersections (4ST) (sample of 276 intersections)

A mix of rural and urban intersections was included in each SPF. The results revealed that incorporating SPFs into the network screening process and using either the EB expected excess crash frequency or EB expected crash frequency better identified sites with the highest potential overall economic benefit.

New Jersey

Summary

Ozbay et al. (2019) developed calibration factors for design-level HSM SPFs and state-specific network-screening-level SPFs for New Jersey using observed crash data from 2011 to 2015.

Table 40. Calibration factor for Nevada estimated in Tian et al. (2013).

Table 41. Calibration factors for New Jersey from Ozbay et al. (2019).

Table 41 provides a summary of the calibration factors that were obtained. Between 387 and 756 segments were used for segment-level calibration factors, and between 45 and 314 intersections were included in the intersection samples. Several adjustment factors were applied to the SPFs in the calibration process; these are summarized in Table 42. Additionally, for some intersections, traffic volumes were not directly available and were estimated using volumes from neighboring links.

SPFs were also developed for several site types for which sufficient observations were available. However, while data for adjustment factors were considered in the SPF calibration process, these

Table 42. Adjustment factors considered in New Jersey for SPF calibration.

were not considered in the SPF development process; thus, these SPFs were network-screening-level SPFs and only included traffic volumes (either AADT for a segment or on incoming intersection approaches) and segment lengths (for roadway segments) as input variables. The lone exceptions were SPFs developed for vehicle–pedestrian crashes on U3SG and U4SG intersections, which included both vehicular traffic volume and pedestrian volume as input variables. No recommendations were provided on which of these SPFs should be used for a given site type (calibrated or state-specific); both were made available for use in a spreadsheet tool for New Jersey.

New Mexico

Summary

The authors did not find any documentation of state customization of HSM tools or SPFs for New Mexico.

New York

Summary

Note that responses to the survey described in Chapter 3 indicate that New York both applies calibration factors and state-specific SPFs. However, the authors did not find any documentation related to the use of calibration factors in the literature for New York.

The New York State DOT Red Book (New York DOT, 2023) provides state-specific network-screening-level SPFs to predict total crash frequency for various facility types for use in New York State. There are over 100 SPFs included for roadway segments and intersections on rural two-lane, two-way roads, rural multi-lane highways, urban arterials, freeways, ramps, and ramp terminals; for brevity, a complete list is not provided. These are network-screening-level SPFs that include traffic volumes and segment lengths (for roadway segments) as input variables. In general, segment lengths are included so that predicted crash frequency increases proportionally with segment length. Further, different functional forms were considered for traffic volume, including the traditional HSM form, Hoerl form, and polynomial form. Average crash rates are also included for each site type for comparison with the predicted values obtained from the SPF. No details on, or references to, the development of these SPFs were provided.

North Carolina

Summary

The summary here differs from responses received from North Carolina as a part of the survey described in Chapter 3; see the case example in Chapter 4 for more details.

Srinivasan and Carter (2011) developed network-screening-level SPFs (considering only traffic volumes) for the following facility types using observed crash data from 2007 to 2009:

• Two-lane, two-way rural roadway segments (R2U)
• Multi-lane rural highways
  • Divided roadway segments (RMD)
  • Undivided roadway segments (RMU)

• Multi-lane urban roadways
  • Divided roadway segments (UMD)
  • Undivided roadway segments (UMU)
• Rural freeways
  • Four-lane freeways outside of the influence of interchanges
  • Six+-lane freeways outside of the influence of interchanges
  • Four-lane freeways within the influence of interchanges
  • Six+-lane freeways within the influence of interchanges
• Urban freeways
  • Four-lane freeways outside of the influence of interchanges
  • Six-lane freeways outside of the influence of interchanges
  • Eight+-lane freeways outside of the influence of interchanges
  • Four-lane freeways within the influence of interchanges
  • Six-lane freeways within the influence of interchanges
  • Eight+-lane freeways within the influence of interchanges

SPFs were developed for nine crash types of primary importance to North Carolina, including:

• Total crashes
• KABC crashes
• KAB crashes
• PDO crashes
• Lane departure crashes
• Single-vehicle crashes
• Multi-vehicle crashes
• Wet-road crashes
• Nighttime crashes

In addition, more detailed SPFs were developed for two-lane, two-way rural roadway segments that included shoulder width, shoulder type, and terrain.

The study also developed calibration factors for SPFs included in the HSM. Table 43 provides a summary of the roadway segment and intersection SPFs that were calibrated, as well as the average calibration factors for the entire study period. Sample sizes for both calibration and SPF development consisted of ranges of 7.57 to 59.39 miles for segments and 19 to 133 sites for intersections.

A follow-up study (Smith et al., 2017) developed updated calibration factors for design-level SPFs in North Carolina using observed crash data from 2010 to 2015. A summary of the facility types/SPFs that were considered and the associated calibration factors for the entire study period is provided in Table 44 and Table 45 for roadway segments and intersections, respectively. Sample sizes for segments ranged from 4 to 476 miles of roadway, while intersection sample sizes ranged from 15 to 102 sites. Regionalized calibration factors (defined as coastal, mountain, and piedmont regions) were also developed for some SPFs. State-specific crash type proportions were also computed to be used with the calibrated SPF predictions for total crash frequency, to provide crash frequency estimates by type. Calibration functions were also estimated for two-lane, two-way rural roadway segments.

Saleem et al. (2021) provided updated calibration factors for the design-level HSM SPFs as well as freeway SPFs that were slated for inclusion in the HSM based on observed crashes from 2016 to 2019. For intersections, sample sizes ranged from 7 to 234 sites, while segment sample sizes ranged from 4.17 to 732.74 miles. Like the previous study, crash type proportions were also

Table 43. Calibration factors for North Carolina from Srinivasan and Carter (2011).

updated to provide frequency estimates for individual crash types. A summary of the calibration factors is provided in Table 46 and Table 47.

North Dakota

Summary

The authors did not find any documentation of state customization of HSM tools or SPFs for North Dakota.

Ohio

Summary

Troyer et al. (2015) developed calibration factors for design-level HSM SPFs in Ohio using observed crash data from 2009 to 2011. The set of SPFs and associated calibration factors is provided in Table 48. These SPFs were design-level SPFs that included adjustment factors for various site-specific features for each facility type; however, the set of adjustment factors considered was not reported. The calibration process started with a fixed number of sites per facility type (50) and then additional sites were added to ensure a minimum of 100 crashes observed per year across that facility type. CURE plots were used to assess the fit of the calibration SPF predictions to Ohio data, and the results suggested a good fit. Using this information, the Ohio DOT prioritized site types for the development of state-specific SPFs based on the fit, traffic volumes, and site type frequency.

Table 44. Roadway segment calibration factors for North Carolina from Smith et al. (2017).

^*Regionalized calibration factors available for Coastal (C), Piedmont (P), and Mountain (M).

Table 45. Intersection calibration factors for North Carolina from Smith et al. (2017).

^*Regionalized calibration factors available for Coastal (C), Piedmont (P), and Mountain (M).

Table 46. Segment calibration factors for North Carolina from Saleem et al. (2021).

^*Regionalized calibration factors available for Coastal (C), Piedmont (P), and Mountain (M).

Table 47. Intersection calibration factors for North Carolina from Saleem et al. (2021).

^*Regionalized calibration factors available for Coastal (C), Piedmont (P), and Mountain (M)

Table 48. Calibration factors for Ohio from Troyer et al. (2015).

Himes et al. (2021) developed design-level SPFs for freeway segments in Ohio using observed crash data from 2014 to 2018, considering sample sizes ranging from 36 to 1,355 segments (12.00 to 592.44 miles). Network screening-level SPFs were developed for total crash frequency and fatal + injury crash frequency for the following site types:

• Freeway segments
  • Rural four-lane
  • Rural six-lane
  • Urban four-lane
  • Urban six-lane
  • Urban eight+-lane
  • Urban seven+ lanes (within interchange influence areas)
• Interchange segments
  • Rural four-lane
  • Rural six-lane
  • Urban four-lane
  • Urban five/six-lane

Additionally, both bi-directional and one-directional design-level SPFs were developed for freeway segments, entry speed-change lanes, and exit speed-change lanes. SPFs were developed to predict fatal and injury multi-vehicle crashes, fatal and injury single-vehicle crashes, PDO multi-vehicle crashes, and PDO single-vehicle crashes. Adjustment factors considered included area type (urban versus rural), number of lanes, ramp location (left versus right), inside and

outside shoulder widths, depressed median widths, presence of weaving, lane addition or lane drop, degree of curvature, proportion of a segment that was a curve, presence of median and outside barriers, and posted speed limit.

Maistros (2022) documents the calibration of design-level SPFs for three additional site types included in the ECAT (Economic Crash Analysis Tool) used in Ohio to implement predictive safety analysis. These site types included: urban four-leg signalized intersections on high-speed arterials (10 sites), urban four-leg single-lane roundabouts (51 sites), and urban four-leg multilane roundabouts (33 sites). The specific calibration factors were not provided. Two other site types were identified as having sufficient sample size for calibration but lacked observed crash data: rural four-leg all-way stop-controlled intersections (81 sites) and urban four-leg all-way stop-controlled intersections (27 sites).

Oklahoma

Summary

Responses received from Oklahoma to the survey described in Chapter 3 indicate that Oklahoma both applies calibration factors and state-specific SPFs. However, no documentation was found on the development of calibration factors for Oklahoma.

Li and Yu (2021) developed design-level SPFs for total crash frequency on roadway segments of U.S. interstates and state highways in Oklahoma using crash data from 2012 to 2016, considering 5,626 segments comprising 5,643 lane miles. Specific features accounted for within this SPF included: traffic volume, pavement friction condition, pavement type, grade, degree of curvature, number of lanes, presence of median, and presence of shoulder. These SPFs were developed for network screening purposes.

Oregon

Summary

Monsere et al. (2011) used crash data from 2005 to 2007 to develop design-level SPFs to predict total crash frequency on rural three-leg stop-controlled intersections and urban four-leg signalized intersections. Approximately 200 rural and 300 urban intersections were considered in the sample. Many explanatory variables were considered in the SPF development process, including traffic volumes on the major and minor approaches, posted speed limit on the major approach, intersection skew angle, presence of lighting, and number of turn lanes on each approach. However, only traffic volumes were considered in the final model, and thus these resulted in network-screening-level SPFs. The report also compared predictions from these state-specific SPFs with calibrated versions of the associated SPFs in the HSM. The calibration factors developed are presented in Table 49. The state-specific SPFs were found to provide better predictions and thus were ultimately recommended for use in Oregon.

Table 49. Calibration factors for Oregon from Monsere et al. (2011).

Dixon et al. (2012) developed calibration factors for segment and intersection design-level SPFs in the HSM using observed crash data from 2004 to 2006. Segment sample sizes ranged from 50 to 491 and intersection sample sizes ranged from 25 to 200. Table 50 provides a summary of the calibration factors obtained for total crash frequency and fatal + injury crash frequency. State-specific crash severity and crash type proportions were also provided for use with the calibrated SPF predictions. Calibration factors for urban arterials were also estimated separately for specific regions (“climate zones”) within Oregon, and differences were observed across the state; the ranges of these are also shown in the table. Separate calibration factors were developed using the HSM default crash type/severity proportions and the locally derived values; however, the two methods did not result in statistically different calibration factors; thus, the calibration factors provided are those estimated using HSM crash type/severity proportions.