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CHAPTER 2Literature ReviewSafety Performance Functions inthe Highway Safety Manual SPFs are statistical models that are used to predict annual crash frequency for a given roadwayelement (e.g., segment or intersection) as a function of site-specific features associated with thatroadway 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 integervalues) and the overdispersion that is commonly present in crash data. (In a negative binomialregression model, overdispersion means that the variance of the response is greater than whatâsassumed by the model.) Two types of SPFs exist in the HSM: Part B or Part C SPFs, each referringto the section of the HSM where they are described. Part B SPFs are high-level SPFs that are typically used for network screening purposes toidentify locations with higher-than-expected crash frequencies as sites with potential for safetyimprovement. These SPFs generally include only traffic volume and segment length (for roadwaysegments) 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 specificchanges to a facility). These generally include additional input variables compared to the Part BSPFs, such as roadway curvature and alignment, cross-sectional characteristics, roadside fea-tures, and the presence of other safety-influencing features. Often, these Part C SPFs providesafety predictions for sites that meet a set of base conditions, and other features are accommo-dated via a suite of adjustment factors (AFs) that modify the prediction for changes to these baseconditions. These are also referred to as project-level or design-level SPFs; the term design-levelSPFs is used for consistency throughout this report. The general form of an SPF for roadway segments is as follows:NSPF = AADT b AADT # Lb # b 0 L (1)where NSPF is the predicted annual crash frequency obtained from the SPF, assuming some baseconditions; AADT is the annual average daily traffic volume observed over the segment (vehicles/day);L is the segment length (miles); βAADT and βL are statistical model coefficients associated withAADT and segment length, respectively; and β0 is a constant. A similar equation exists for the general form of intersection SPFs:NSPF = Major AADT b Major # Minor AADT b Minor #b (2) 7
8ââ Calibration and Development of State-DOT-Specific Safety Performance Functions where NSPF 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 βMajor and βMinor are the respective model coefficients. The HSM further adjusts predictions obtained from SPFs using the following equation: N predicted = NSPF # ` AF1 # AF2 # . . . # AFn j # CF (3) where Npredicted is the predicted annual crash frequency for a given site, AFn 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) â Roadway segments â¾ Undivided roadway segments (2U) â Intersections â¾ Unsignalized three-leg (stop control on minor-road approaches) (3ST) â¾ Unsignalized four-leg (stop control on minor-road approaches) (4ST) â¾ Signalized four-leg (4SG) ⢠Multi-lane rural highways (Chapter 11) â Roadway segments â¾ Rural four-lane undivided segments (4U) â¾ Rural four-lane divided segments (4D) â Intersections â¾ Unsignalized three-leg (stop control on minor-road approaches) (3ST) â¾ Unsignalized four-leg (stop control on minor-road approaches) (4ST) â¾ Signalized four-leg (4SG) ⢠Urban and suburban arterials (Chapter 12) â Roadway segments â¾ Two-lane undivided arterials (2U) â¾ Three-lane arterials including a center two-way left-turn lane (TWLTL) (3T) â¾ Four-lane undivided arterials (4U) â¾ Four-lane divided arterials (i.e., including a raised or depressed median) (4D) â¾ Five-lane arterials including a center TWLTL (5T) â Intersections â¾ Unsignalized three-leg intersections (stop control on minor-road approaches) (3ST) â¾ Signalized three-leg intersections (3SG) â¾ Unsignalized four-leg intersections (stop control on minor-road approaches (4ST) â¾ 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,
Literature Reviewââ 9Table 2.ââ Summary of SPFs included in the HSM. Crash Types and Severity Facility Types Segments Based on SPFa Based on Crash Proportions/DistributionsbTwo-lane, two-way rural ⢠Undivided roadway segments (2U) Total Total, FI, or PDO (Single-Vehicle): (Chapter 10) Animal, bicycle, pedestrian, overturned, ran oï¬ road, other roads ⢠Unsignalized three-leg (stop control Intersections on minor-road approaches) (3ST) Total, FI, or PDO (Multi-Vehicle): ⢠Unsignalized four-leg (stop control on Total Angle, head-on, rear-end, sideswipe, other minor-road approaches) (4ST) ⢠Signalized four-leg (4SG) Total Segments Multi-lane rural highways ⢠Rural four-lane undivided segments (4U) KABC ⢠Rural four-lane divided segments (4D) KAB Total, KABC, KAB, or PDO: Head-on, sideswipe, rear-end, angle, single, ⢠Unsignalized three-leg (stop control Total (Chapter 11) Intersections other on minor-road approaches) (3ST) ⢠Unsignalized four-leg (stop control on KABC minor-road approaches) (4ST) ⢠Signalized four-leg (4SG) KAB FI or PDO (Multi-Vehicle Non-driveway): Total, FI, or PDO: Rear-end, head-on, angle, sideswipe (same ⢠Two-lane undivided arterials (2U) Multi-vehicle non-driveway, direction), sideswipe (opposite direction), ⢠Three-lane arterials including a center single-vehicle crashes other Segments two-way left-turn lane (TWLTL) (3T) Multi-vehicle driveway- ⢠Four-lane undivided arterials (4U) related FI or PDO (Single-Vehicle): Urban and suburban arterials ⢠Four-lane divided arterials (4D) Animal, ï¬xed object, other object, other ⢠Five-lane arterials including a center Total: (Chapter 12) TWLTL (5T) Vehicleâpedestrian FI or PDO (Multi-Vehicle Driveway- Vehicleâbicycle Related): Broken down by driveway type ⢠Unsignalized three-leg intersections (stop control on minor-road Total, FI, or PDO: FI or PDO (Single-Vehicle): approaches) (3ST) Intersections Single-vehicle crashes Parked vehicle, animal, ï¬xed object, other ⢠Signalized three-leg intersections Multi-vehicle collisions object, other, non-collision (3SG) Total: ⢠Unsignalized four-leg intersections Vehicleâpedestrian collisions FI or PDO (Multi-Vehicle): (stop control on minor-road Vehicleâbicycle collisions Read-end, head-on, angle, sideswipe, other approaches (4ST) ⢠Signalized four-leg intersections (4SG) FI or PDO (Multi-Vehicle): freeway segments Rural and urban ⢠Four-lane divided freeway Head-on, right-angle, rear-end, sideswipe, (Appendix C)Supplement) Freeways ⢠Six-lane divided freeway FI or PDO: other (HSM ⢠Eight-lane divided freeway Multi-vehicle ⢠Ten-lane divided freeway (urban Single-vehicle FI and PDO (Single-Vehicle): areas only) Animal, ï¬xed object, other object, parked vehicle, other (continued on next page)
10ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 2.ââ(Continued). Crash Types and Severity Facility Types Based on SPFa Based on Crash Proportions/Distributionsb ⢠Ramp entrance to four-lane divided Rural and urban freeway speed-change lanes freeway ⢠Ramp entrance to six-lane divided freeway ⢠Ramp entrance to eight-lane divided FI or PDO (Multi-Vehicle): freeway Head-on, right-angle, rear-end, sideswipe, (Appendix C) ⢠Ramp entrance to ten-lane divided other freeway (urban areas only) FI or PDO: ⢠Ramp exit from four-lane divided All crash types FI and PDO (Single-Vehicle): freeway Animal, ï¬xed object, other object, parked ⢠Ramp exit from six-lane divided vehicle, other freeway ⢠Ramp exit from eight-lane divided freeway ⢠Ramp exit from ten-lane divided freeway (urban areas only) segments and collectorâ Rural and urban ramp ⢠One-lane entrance ramp FI or PDO (Multi-Vehicle): distributor roads ⢠Two-lane entrance ramp (urban areas Head-on, right-angle, rear-end, sideswipe, (Appendix D) only) FI or PDO: other ⢠One-lane exit ramp Multi-vehicle ⢠Two-lane exit ramp (urban areas only) Single-vehicle FI and PDO (Single-Vehicle): ⢠One-lane C-D road Animal, ï¬xed object, other object, parked ⢠Two-lane C-D road (urban areas only) vehicle, other ⢠Three-leg terminals with diagonal exit Rural and urban crossroad ramp terminals (Appendix D) ramp (Signal control or one-way stop) ⢠Three-leg terminals with diagonal entrance ramp (Signal control or one- way stop) ⢠Four-leg terminals with diagonal ramps (Signal control or one-way stop) FI or PDO (Multi-Vehicle): ⢠Four-leg terminals at four-quadrant Head-on, right-angle, rear-end, sideswipe, parclo A (Signal control or one-way FI or PDO: other stop) All crash types ⢠Four-leg terminals at four-quadrant FI and PDO (Single-Vehicle): parclo B (Signal control or one-way Animal, ï¬xed object, other object, stop) parked vehicle, other ⢠Three-leg terminals at two-quadrant parclo A (Signal control or one-way stop) ⢠Three-leg terminals at two-quadrant parclo B (Signal control or one-way stop) a Unique SPF available to estimate crash frequencies. b Crash frequency estimates obtained by applying crash type or severity proportions to SPF outputs.
Literature Reviewââ 11note that these include both network-screening-level SPFs and design-level SPFs; the formerare 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 fromsome 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.CalibrationHSM Calibration Procedure The calibration factor (CF) in Equation (3) is intended to adapt the SPF to local conditions sincethe data used to estimate the crash frequency models were developed using information from onlya 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 frequen- cies 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). / n No,i / observed crash frequenciesCF = i = (4) / n i Nu,i / predicted crash frequencieswhere No,i is the observed number of crashes on site i, Nu,i is the unadjusted predicted number ofcrashes for site i, and n is the total number of sites used for calibration. As shown, this calculationis simply the ratio of total number of observed crashes for a sample of sites in a jurisdiction to thetotal number of predicted crashes for these same sites. The overdispersion parameter for the SPF can also be calibrated. This is typically done via anumerical maximum likelihood procedure using software such as the SPF Calibrator Tool (Lyonet al., 2016).Alternative Calibration Options/Forms The calibration factor definition in the HSM simply scales the predicted crash values toensure that the total number of crashes observed at all sites is the same as the total numberpredicted. However, many studies have found that calibration in this way does not accu-rately predict crashes since it assumes the same relationship between crash frequency andother factors that are inherent in the SPF that is applied. Thus, several research studies haveproposed alternative definitions of the calibration factor. A brief review of these is providedas 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: No,i = eln(CF1)+ln(Nu,i). Using this relationship, the calibration factor (CF1) simplifies to the following definition: / n No,i Nu,i CF1 = i (5) n
12ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 3.ââ Summary of design features for which adjustment factors exist in the HSM. Site Type Applicable SPF AF Descriptions Lane width Shoulder width and type Horizontal curves: length, radius, spiral transitions Horizontal curves: super-elevation Grades Roadway segments Driveway density Two-lane, two- Centerline rumble strips way rural roads Passing lanes (Chapter 10) Two-way left-turn lanes Roadside design Lighting Automated speed enforcement Intersection skew angle Three- and four-leg stop-controlled Intersection left-turn lanes intersections and four-leg signalized Intersection right-turn lanes intersections Lighting Lane width Shoulder width and type Undivided roadway segment Side slopes Lighting Automated speed enforcement Lane width Multi-lane rural Right shoulder width highways Divided roadway segment Median width (Chapter 11) Lighting Automated speed enforcement Intersection angle Three- and four-leg stop-controlled Left-turn lane on major road intersection Right-turn lane on major road Lighting Urban and On-street parking suburban arterials Roadside ï¬xed objects (Chapter 12) Roadway segments Median width Lighting Automated speed enforcement Intersection left-turn lanes Urban and Intersection left-turn signal phasing suburban arterials Multi-vehicle collisions and single- Intersection right-turn lanes (Chapter 12) vehicle crashes at intersections Right turn on red Lighting Red light cameras Bus stops Vehicleâpedestrian collisions at Schools signalized intersections Alcohol sales establishments
Literature Reviewââ 13 Table 3.ââ(Continued). Site Type Applicable SPF AF Descriptions Horizontal curve Lane width Freeway segments or speed-change Inside shoulder width lanes Median width Median barrier High volume Freeway segments Multi-vehicle crashes on freeway (Supplement Lane change segments Appendix C) Outside shoulder width Single-vehicle crashes on freeway Shoulder rumble strip presence segments Outside clearance Outside barrier Ramp entrances Ramp entrance Ramp exits Ramp exit Horizontal curve Lane width Right shoulder width Ramp or C-D road segments Left shoulder width Ramp segments Right side barrier (Supplement Left side barrier Appendix D) Lane add or drop Multi-vehicle crashes on ramp or C-D Ramp speed-change lanes segments C-D road segments Weaving section Thus, this study defines the calibration factor as the average of the individual âcalibration factorsâ computed for each site.⢠Rajabi et al. (2018) propose two additional calibration factors based on maximum likelihood estimation (CF2) and least squares estimation (CF3). â 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 relation- ship for CF2: No,i + { n = /i n (6) CF2 Nu,i + {l where Ï 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 pre- dicted crashes obtained from the SPF fit the observed crash data when a constant calibra- tion factor is applied. â 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 / N #N n o,i u,i CF3 = i (7) / `N j n i u,i 2
14ââ Calibration and Development of State-DOT-Specific Safety Performance Functions ⢠Martinelli et al. (2009) propose two additional calibration factors: one that considers crash densities (CF4) and another that uses a weighted ratio (CF5). â 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: / n No,i L i (8) i CF4 = / n i Nu,i Lli where Li is the length of segment i. â Weighted ratio: this calibration factor weights each predicted and observed value by the length of the segment in which each crash occurred, as follows: / n No,i # L i CF5 = i (9) / n i Nu,i # L i Lastly, Srinivasan et al. (2016) propose a calibration function as an alternative to the calibration factor. This calibration function takes the following form: N p = a # ` Nu j b (10) where a and b are estimated using regression. This formulation is more flexible not only because it has more parameters (twoâa and bâcompared to just a single parameter estimated when applying a calibration factor), but also because the exponential term (b) can change the relation- ship 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 βAADT 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 calibra- tion 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
Literature Reviewââ 15outcomes take non-negative integer values) and overdispersion in crash data when the varianceexceeds the mean. Thus, the development of state-specific SPFs requires advanced statisticalknowledge. Two methods are described in the HSM to develop state-specific SPFs. The first method definesand estimates a model for a set of base conditions. Only sites that meet these conditions are con-sidered 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 conditionsare then accommodated via crash modification factors (CMFs) that are either estimated usingthe appropriate methods from state-specific data or obtained from a trustworthy source (e.g., theFHWA CMF Clearinghouse). Sites should be selected randomly throughout the agency. If pos-sible, selecting sites that are in close physical proximity should be avoided to reduce the correla-tion between other design features (Carter et al., 2012; Srinivasan and Bauer, 2013). If data frommultiple regions or jurisdictions within the agency are included, then region-specific variablesshould 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 areestimated together. Once the SPF is obtained, a set of base conditions is prescribed and adjustmentfactors can be computed for the set of variables to describe changes from these base conditionsdirectly from the SPF. Srinivasan and Bauer (2013) suggest that the variables considered shouldboth be readily available to users of the SPF and describe features that are likely to have an influ-ence on safety performance. However, care should be taken to avoid including too many vari-ables 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 dataand identify extraneous variables that may be omitted from the model.Guidance on Calibration and State-SpecificSPF Development The choice between calibrating the HSM SPFs to reflect state-specific conditions and thedevelopment of state-specific SPFs depends on several factors, including available expertise andresources, desired accuracy, and data availability. In general, calibration requires less expertiseand resources but provides less accurate predictions. However, in many cases, data availability is akey limiting factor in this decision.Sample Size Requirements Several sources in the literature provide guidance on the minimum number of sites of a givenfacility type to help practitioners determine if calibration or state-specific SPF development is fea-sible. The HSM suggests that a minimum sample size of 30â50 sites with at least 100 crashes peryear be used for the calibration factor development process, based on expert judgment. Baharand Hauer (2014) provide a scientific method to estimate the minimum sample size necessary forcalibration based on the desired level of precision in the calibration factors. Precision is measured interms of standard error and coefficient of variation in the calibration factor, and recommenda-tions 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 fora single SPF by larger DOTs with extreme differences in terrain, climate, driver population, orother 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
16ââ Calibration and Development of State-DOT-Specific Safety Performance Functions 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 100â200 miles (for roadway segments) or 100â200 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 â Area type â Roadway functional classification â Number of lanes â Median divider presence and type ⢠Intersections â Area type â Roadway functional classification â Traffic control type â Number of approach legs on each of the major and minor approach ⢠Interchange and ramps â Area type (urban vs. rural) â Interchange configuration â Ramp terminal designation â 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 asso- ciated 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:
Literature Reviewââ 17⢠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 twocompare differences between observed crash frequencies and predicted values from the SPF,with RMSE weighing more strongly values with larger differences than MAE. Smaller numbersare indicative of a better fit. The modified R2 value is a value between zero and 1 representingthe amount of variation in the observed crash data that is explained by the model. Values closerto 1 represent a better fit. The overdispersion parameter quantifies how much the predictedestimates vary from the mean value. Smaller values indicate a better fit. Finally, the coefficient ofvariation of the calibration factor represents how much calibrated estimates of crash predictionsvary 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 usedto estimate the model. Residuals are defined as the difference between observed and predicted out-comes, and these are accumulated with respect to a variable of interest, often one of the continuousinput variables or predicted crash frequency. Hauer (2015) and Lyon et al. (2016) provide moredetails on how CURE plots can be developed, how a confidence interval can be estimated andused to assess if the observed trend is in line with randomness (good fit) or not, and specific trendsthat indicate issues in the model fit. CURE plots can also be used to determine when adding addi-tional variables would cause overfitting. Specifically, no additional variables should be added if thecumulative residuals fall within the 95% confidence interval. Examples of CURE plots representinga good fit and a poor fit to the observed data are provided in Figures 2a and 2b, respectively.SPF Calibration and Development Effortsby Individual State DOTs This section documents specific SPF calibration and development activities undertaken byindividual state DOTs that were found in the research literature. Only efforts sponsored orendorsed by state DOTs are summarized here; thus, purely academic research articles or studies (a) (b)Figure 2.ââ CURE plot examples: (a) good fit to observed data and (b) poor fit to observed data.
18ââ Calibration and Development of State-DOT-Specific Safety Performance Functions 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 Calibrated SPFs? Design-level State-specific SPFs? Network-screening-level, design-level 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 valida- tion 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.ââ Calibration factors for Alabama from Mehta and Lou (2013). Calibration Factors by Method Facility Type Sample Size NB Regression HSM Methodology Model Two-lane two-way rural roads 6,000 sites 1.392 1.522 (R2U) Rural four-lane divided highways 4,000 sites 1.103 1.863 (R4D)
Literature Reviewââ 19 Table 5.ââ Calibration factors for Alabama from Kim et al. (2015). Sample Calibration Factors by Year Arterial Type Size 2007 2008 2009 Two-lane undivided (U2U) 2,600 sites 0.08* 0.53* 0.24* Three-lane arterials with TWLTL (U3T) 480 sites 0.99* 0.94* 0.52* Four-lane undivided arterials (U4U) 1,000 sites 0.34* 0.36* 0.42* Four-lane divided arterials (U4D) 3,100 sites 0.95* 1.12* 1.36* Five-lane arterials with TWLTL (U5T) 1,600 sites 0.35* 0.26* 0.34* *Calibration factors noted as not reliable due to lack of adequate observed crashes on sites.AlaskaSummary Calibrated SPFs? Design-level State-specific SPFs? None Bowie et al. (2014) developed design-level calibration factors for HSM-published intersectionSPFs using data from 2010 at urban intersections in Anchorage, Alaska. Calibrated intersectiontypes included: three- and four-leg intersections with minor-road stop control, and signalizedthree- and four-leg intersections, all on urban and suburban arterials. Each intersection type wascalibrated for total, fatal and injury, and property damage-only crashes. The results of the cali-bration are provided in Table 6. The report indicated that the calibration factors are based on arelatively small sample size (30 sites each), with the three-leg unsignalized intersections failingto meet HSM-recommended minimum observed total crashes (only 34 total crashes) and thethree-leg signalized intersections failing to meet the recommended minimum number of loca-tions studied (only 22 sites). The authors suggested that Alaska would benefit from state-specificSPF development due to Alaskaâs high frequency of animal crashes, distinctly different vehiclefleet, and weather consistently different from the rest of the United States.ArizonaSummary Calibrated SPFs? Design-level State-specific SPFs? Design-level Srinivasan et al. (2016) estimated calibration factors and functions for design-level SPFs oftwo-lane rural road segments in Arizona using observed crash data from 2008 to 2012. A totalof 509 hom*ogeneous segments were considered, which covered a total length of 187.5 miles. Table 6.ââ Calibration factors for Alaska from Bowie et al. (2014). Calibration Factors Fatal Property Sample Intersection Type Total and Damage- Size Crashes Injury Only Crashes Crashes Three-leg intersection with stop control on 30 1.48 1.05 1.75 minor approach (U3ST) Three-leg intersection with signal control 22 3.94 3.51 4.20 (U3SG) Four-leg intersection with stop control on 30 3.46 3.22 3.60 minor approaches (U4ST) Four-leg intersection with signal control 30 4.65 4.16 4.97 (U4ST)
20ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 7.ââ Calibration factors for Arizona from Srinivasan et al. (2016). Calibration Facility Type Sample Size Factor Two-lane two-way rural road segments 509 segments 1.079 (R2U) (187.5 miles) 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 regres- sion, 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.ââ Additional calibration factors for Arizona from Srinivasan et al. (2016). Sample Facility Type Variable Range Calibration Factor Size 0â2,500 1.292 AADT 2,501â5,000 1.014 509 > 5,000 0.933 Two-lane two- segments 0â0.4 1.408 way rural road Segment length (187.5 0.4â0.8 0.99 segments (R2U) (miles) miles) 0.8â1.2 0.867 Curve 1.197 Alignment Tangent 1.038 Table 9.ââ Calibration function parameters from Srinivasan et al. (2016). Regression Method Facility Type Sample Size Parameter OLS Poisson NB 1.417 1.385 1.380 Two-lane two-way 509 segments 0.650 0.689 0.694 rural road (187.5 miles) Overdispersion parameter (Ï) n/a n/a 3.869 segments (R2U) Abridged log likelihood n/a -186.4 -108.8
Literature Reviewââ 21 Table 10.ââ Calibration factors for Arizona from Colety et al. (2016). Sample Facility Type Variable Range Calibration Factor Size Flat and rolling 1.103 Region Mountainous 1.054 2- rural principal arterial 1.054 Highway 6 - rural principal arterial 0.969 Two-lane two- 509 functional code 7 - rural minor collector 1.179 way rural segments 8 - rural major collector 1.753 road segments (187.5 (R2U) miles) ⤠500 1.593 501â1,000 1.279 Curve radius 1,001â2,000 1.473 (feet) 2,001â3,000 1.114 >3,000 1.023average entering AADT over the four years and the total number of entering lanes. A likelihoodratio test suggests that the developed model is significant at the 99.9% confidence level.ArkansasSummary Calibrated SPFs? Design-level State-specific SPFs? None Gattis et al. (2017) developed project design-level calibration factors using observed crash datafrom 2011 to 2013. The study considered rural two-lane undivided roadways, four-lane dividedroadways, 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 accountedfor regional differences in terrainânamely, âflatter terrainâ and âhilly terrain.â The results of thesecalibration efforts are presented in Table 11 and Table 12. The authors noted that local law enforce-ment 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 hadlower crash frequency than normal.CaliforniaSummary Calibrated SPFs? None State-specific SPFs? Design-level The findings of the literature review in this section differ from responses received fromCalifornia as a part of the survey described in Chapter 3. Furthermore, the case example of Table 11.ââ Calibration factors for Arkansas from Gattis et al. (2017). Sample Size Flatter Terrain Hilly Terrain Facility Type (Number of Calibration Calibration Segments) Factor Factor Rural two-lane undivided roads (R2U) 322 (ï¬atter), 0.54 0.73 244 (hilly) Rural four-lane divided roads (R4D) 106 (ï¬atter), 0.66 0.75 36 (hilly)
22ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 12.ââ Calibration factors for intersections in Arkansas from Gattis et al. (2017). Sample Calibration Facility Type Size Factor Rural three-leg stop-controlled on R2U facilities (R2 207 0.65 3ST) Rural three-leg stop-controlled on R4D facilities (R4 36 0.70 3ST) Rural four-leg stop-controlled on R2U facilities (R2 172 0.46 4ST) Rural four-leg stop-controlled on R4D facilities (R4 49 0.74 4ST) 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 â Two-lane rural (R2U) â Four-lane rural (R4) â Four+-lane rural (R4+) â Multi-lane undivided rural (RMU) â Two-lane urban (U2L) â Four-lane urban (U4L) â Five- to seven-lane urban (U57) â Eight+-lane urban (U8+) â Multi-lane undivided urban (UMU) â Multi-lane divided urban (UMD) ⢠All intersections (INT) ⢠Ramps (RP) â All ramps â 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 Calibrated SPFs? None State-specific SPFs? Network-screening-level 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:
Literature Reviewââ 23⢠Four-leg signalized intersection (4SG) on: â Four-lane divided roads â Six-lane divided roads⢠Four-leg unsignalized intersections on: â Two-lane undivided roads â Four-lane divided roads â Four-lane undivided roads⢠Three-leg signalized intersections (3SG) on: â Four-lane divided roads⢠Three-leg unsignalized intersections on: â Two-lane divided roads â Two-lane undivided roads â Four-lane divided roads â Four-lane undivided roads Sample sizes ranged from 34 to 101 intersections of each type. SPFs were developed for totalcrash frequency and fatal and injury crash frequency. Kononov (2018) developed network-screening-level SPFs for total crashes and fatal and injurycrashes at 20 different intersection types based on data from 2011 to 2015. Sample sizes were notprovided. The SPFs follow Sigmoidal and ho*rl functional forms and consider only the AADTfor the major and minor approaches. The SPFs developed are presented in the following list:⢠Urban Intersections â Urban two-lane divided unsignalized three-leg (U2xDU3) â Urban two-lane divided unsignalized four-leg (U2Xdu3) â Urban two-lane undivided unsignalized three-leg (U2Xuu3) â Urban two-lane undivided unsignalized four-leg (U2Xuu4) â Urban four-lane divided signalized three-leg (U4Xds3) â Urban four-lane divided signalized four-leg (U4Xds4) â stratified norms for two ranges of AADT â Urban four-lane divided unsignalized three-leg (U4Xdu3) â Urban four-lane divided unsignalized four-leg (U4Xdu4) â stratified norms for two ranges of AADT â Urban four-lane undivided unsignalized three-leg (U4Xuu3) â Urban four-lane undivided unsignalized four-leg (U4Xuu4) â Urban six-lane divided signalized four-leg (U6Xds4) â stratified norms for two ranges of AADT⢠One-Way Intersections â One-way main line with N lanes, two-way side-road, unsignalized four-leg (Unx1W2WUU4) â One-way main line with two to three lanes, one-way side-road signalized four-leg (U23x1W1WUS4) â One-way main line with four to five lanes, one-way side-road signalized four-leg (U45x1W1WUS4) â One-way main line with N lanes, two-way side-road signalized four-leg (Unx1W2WUS4)⢠Rural Intersections â Rural two-lane divided unsignalized three-leg (R2Xdu3) â Rural two-lane divided unsignalized four-leg (R2Xdu4) â Rural two-lane undivided unsignalized three-leg (R2Xuu3) â Rural two-lane undivided unsignalized four-leg (R2Xuu4) â stratified norms for two ranges of AADT â Rural four-lane divided unsignalized three-leg (R4Xdu4)
24ââ Calibration and Development of State-DOT-Specific Safety Performance Functions 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 Calibrated SPFs? None State-specific SPFs? Network-screening-level 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 â Rural freeway divided two or more lanes (R2+F) â Rural non-freeway divided two or more lanes (R2+D) â Rural non-freeway undivided two or more lanes (R2+U) â Rural speed-change lane four or six lanes â Urban freeway divided two or three lanes (U2F, U3F) â Urban freeway divided four lanes (U4F) â Urban freeway divided five or more lanes (U5+F) â Urban non-freeway divided two lanes (U2D) â Urban non-freeway divided three lanes (U3D) â Urban non-freeway divided four or more lanes (U4+D) â Urban non-freeway one-way one or more lanes â Urban non-freeway undivided two lanes (U2U) â Urban non-freeway undivided three lanes (U3U) â Urban non-freeway undivided four or more lanes (U4U) â Urban speed-change lane four or fewer lanes â Urban speed-change lane five or more lanes ⢠Town-Maintained Roadway Segments â Rural arterial or collector â Rural local one or more lanes â Urban arterial two lanes â Urban arterial three or more lanes â Urban arterial one-way one or more lanes â Urban collector two lanes â Urban collector three or more lanes â Urban collector one-way one or more lanes â Urban local two lanes â Urban local three or more lanes â Urban local one-way one â Urban local one-way two or more lanes ⢠Freeway Ramp Segments â Rural ramps â Urban entrance ramps â Urban exit ramps â Urban other ramps Intersection facility types include: ⢠State-Maintained Intersections with Full Traffic Volume Information â Rural three-leg sign controlled (R3ST) â Rural three-leg signalized (R3SG)
Literature Reviewââ 25 â Rural four-leg sign controlled (R4ST) â Rural four-leg signalized (R4SG) â Urban two-lane three-leg sign controlled (U2 3ST) â Urban two-lane three-leg signalized (U2 3SG) â Urban two-lane four-leg sign controlled (U2 4ST) â Urban two-lane four-leg signalized (U2 4SG) â Urban multi-lane three-leg sign controlled (UM 3ST) â Urban multi-lane three-leg signalized (UM 3SG) â Urban multi-lane four-leg sign controlled (UM 4ST) â Urban multi-lane four-leg signalized (UM 4SG)⢠State-Maintained Intersection with Partial Traffic Volume Information â Rural three-leg sign controlled (R3ST) â Rural three-leg signalized (R4ST) â Rural four-leg sign controlled (R4ST) â Rural four-leg signalized (R4SG) â Urban two-lane three-leg sign controlled (U2 3ST) â Urban two-lane three-leg signalized (U2 3SG) â Urban two-lane four-leg sign controlled (U2 4ST) â Urban two-lane four-leg signalized (U2 4SG) â Urban multi-lane three-leg sign controlled (UM 3ST) â Urban multi-lane three-leg signalized (UM 3SG) â Urban multi-lane four-leg sign controlled (UM 4ST) â Urban multi-lane four-leg signalized (UM 4SG) A variety of crash type/severity combinations are included:⢠Total crashes⢠Multi-vehicle crashes â Angle â Front to front â Front to rear â Sideswipe opposite direction â Sideswipe same direction â Multi other⢠Single-vehicle crashes â Fixed objects â Non-fixed objects â Overturn/rollover â Jackknife â Non-collision other â Single other⢠Severity â KABC â KAB â KA â PDO⢠Emphasis area â DUI related â Aggressive driving related â Roadway departure â Young driver involved â Motorcycle involved
26ââ Calibration and Development of State-DOT-Specific Safety Performance Functions â Qualifying commercial vehicle involved â Adverse weather â Wet road surfaces â Pedestrian involved â Bicycle involved Further information on SPF development was not available. Delaware Summary Calibrated SPFs? None State-specific SPFs? None 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 Calibrated SPFs? None State-specific SPFs? None The authors did not find any documentation of state customization of HSM tools or SPFs for the District of Columbia. Florida Summary Calibrated SPFs? Design-level State-specific SPFs? Network-screening-level Srinivasan et al. (2011) developed calibration factors for design-level segment and inter- section 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 calibra- tion 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)âthe range represents annual calibration factors that were developed for each year in the 2005â2008 period. Some data col- lection 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 seg- ments 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.
Literature Reviewââ 27 Table 13.ââ Calibration factors for Florida from Srinivasan et al. (2011). KABC KAB Calibration Calibration Facility Type Sample Size Factor Factor Range Range Roadway Segments Rural two-lane two-way roads (R2U) 4,811 0.980â1.069 1.217â1.372 (2,121.0 miles) Rural multi-lane highways (RMD, RMU) 1,376 0.655â0.719 n/a (550.8 miles) Urban two-lane undivided roads (U2U) 5,076 0.928â1.119 n/a (628.4 miles) Urban three-lane roads with TWLTL (U3T) 709 0.952â1.126 n/a (66.3 miles) Urban four-lane undivided roads (U4U) 1,251 0.641â0.749 n/a (96.1 miles) Urban four-lane divided roads (U4D) 7,506 1.602â1.750 n/a (970.6 miles) Urban ï¬ve-lane roads with TWLTL (U5T) 2,868 0.695â0.726 n/a (253.6 miles) Intersections Three-leg stop-controlled intersections on two-lane 39 0.65â0.80 0.58â1.06 rural roads (R2 3ST) Four-leg stop-controlled intersections on two-lane 24 0.47â0.80 0.54â1.21 rural roads (R2 4ST) Four-leg signalized intersections on two-lane rural 28 0.89â1.44 1.22â2.02 roads (R2 4SG) Four-leg signalized intersections on rural multi-lane 25 0.35â0.44 0.40â0.50 highways (RM 4SG) Three-leg signalized intersections on urban arterials 45 1.41â2.10 n/a (U3SG) Four-leg signalized intersections on urban arterials 121 1.79â2.05 n/a (U4SG) 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, rampvolumes, and indicators for context-specific classifications and interchange types. Details onthe years of observed crash data used, sample sizes, or the development of the SPFs were notprovided. 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 typebefore implementing them more widely in Florida. Ozguyen et al. (2019) developed design-levelSPFs for both signalized and unsignalized restricted RCUT intersections using data from Alabama,Georgia, Louisiana, Maryland, Michigan, Minnesota, Mississippi, North Carolina, Ohio, SouthCarolina, Tennessee, Texas, and Washington. Data were available for a total of 225 unique inter-sections. SPFs were developed for total and fatal/injury crashes. SPF input variables and CMFsestimated 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, offsetdistance, deceleration lane length, acceleration lane length, number of nearby driveways, numberof left-turn lanes, and major-road speed limit. SPFs of various complexity were estimated, and thesimplest ones (i.e., those with the fewest input variables) were recommended since they providedsimilar prediction accuracy with lower data requirements.
28ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Georgia Summary Calibrated SPFs? Network-screening-level State-specific SPFs? Network-screening-level 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 Calibrated SPFs? None State-specific SPFs? None The authors did not find any documentation of state customization of HSM tools or SPFs for Hawaii. Table 14.ââ Calibration factors for Georgia from Alluri and Ogle (2011). Calibration Factor Calibration Factor Sample Size Facility Type for Fatal + Injury for Total Crash (Miles) Crash Frequency Frequency Rural two-lane roads (R2U) 79,586 0.295 0.268 Rural multi-lane undivided roads (RMU) 475 0.729 0.997 Rural multi-lane divided roads (RMD) 1,433 1.553 0.698 Rural freeways â four lanes (R4F) 393 1.255 1.162 Rural freeways â six+ lanes (R6+F) 121 1.083 1.372 Rural freeways within interchange area â 159 0.613 0.573 four lanes Rural freeways within interchange area â 59 1.480 1.653 six+ lanes Urban two-lane arterial streets (U2U) 34,651 1.623 2.300 Urban multi-lane undivided arterial 1,534 1.149 2.121 streets (UMU) Urban multi-lane divided arterial streets 1,397 2.714 3.293 (UMD) Urban one-way arterial streets (UOA) 684 0.418 0.147 Urban freeways â four lanes (U4F) 285 0.408 0.752 Urban freeways â six lanes (U6F) 121 0.885 1.638 Urban freeways â eight+ lanes (U8+F) 25 0.703 1.450 Urban freeways within interchange area â 245 0.600 0.815 four lanes Urban freeways within interchange area â 131 0.651 1.259 six lanes Urban freeways within interchange area â 189 0.576 1.087 eight+ lanes
Literature Reviewââ 29IdahoSummary Calibrated SPFs? Network-screening-level State-specific SPFs? Network-screening-level Abdel-Rahim and Sipple (2015) calibrated network-screening-level HSM SPFs and developedstate-specific network-screening-level SPFs for total crashes on rural two-lane two-way highwaysegments (approximately 220 miles), rural three-leg stop-controlled intersections (43 interÂsections), and rural four-leg stop-controlled intersections (41 intersections) in Idaho using observedcrash 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 lengthand 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 observationswere held out for validation purposes. Both the calibrated SPFs and the state-specific SPFs wereanalyzed based on Pearsonâs R, MSPE, and Freeman-Tukey R-squared. The authorsâ comparisonsdemonstrated 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 signifi-cant improvement for rural four-leg stop-controlled intersections.IllinoisSummary Calibrated SPFs? Design-level State-specific SPFs? Network-screening-level Tegge et al. (2010) developed statewide screening-level SPFs for fatal and injury crashes andcrashes of severity levels K, A, and B on the KABCO scale for 12 segment facility types and eightintersection types using observed crash data from 2001 to 2005. The facility types were included:⢠Segments â Rural two-lane highway (R2U) â Rural multi-lane undivided highway (RMU) â Rural freeway, four lanes (R4F) â Rural freeway, six+ lanes (R6+F) â Urban two-lane highway (U2L) â Urban one-way arterial (UOA) â Urban multi-lane undivided highway (UMU) â Urban multi-lane divided highway (UMD) â Urban freeway, four lanes (U4F) â Urban freeway, six lanes (U6F) â Urban freeway, eight+ lanes (U8+F) Table 15.ââ Calibration factors for Idaho from Abdel-Rahim and Sipple (2015). Facility Type Sample Size Calibration Factor Two-lane, two-way rural highways (R2U) 220 miles 0.87 Rural three-leg stop-controlled intersections 43 intersections 0.56 (R3ST) Rural four-leg stop-controlled intersections 41 intersections 0.62 (R4ST)
30ââ Calibration and Development of State-DOT-Specific Safety Performance Functions ⢠Intersections â Rural minor leg stop control (R3ST, R4ST) â Rural all-way stop control (R3aST, R4aST) â Rural signalized intersection (R3SG, R4ST) â Rural undetermined (RUI) â Urban minor leg stop control (U3ST, U4ST) â Urban all-way stop control (U3aST, U4aST) â Urban signalized intersection (U3SG, U4SG) â Urban undetermined (UUI) Sample sizes ranged from 33.2 miles to 7,968.1 miles for segments (with one exceptionâsix+ 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 Calibrated SPFs? None State-specific SPFs? Design-level 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 devel- oped 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 Calibrated SPFs? Design-level State-specific SPFs? Design-level 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
Literature Reviewââ 31Table 16.ââ Calibration factors for Illinois from Illinois DOT (2014). 2006â2008 Calibration 2009â2011 Calibration Facility Type Factor Factor Two-Lane Two-Way Rural Roads Undivided roadway segments (R2U) 1.78 1.47 Three-leg stop-controlled intersections (R3ST) 0.24 0.24 Four-leg stop-controlled intersections (R4ST) 0.28 0.31 Multi-Lane Rural Roads Four-lane divided roadway segments (R4D) 1.72 1.30 Three-leg stop-controlled intersections (R3ST) 0.55 0.37 Four-leg stop-controlled intersections (R4ST) 0.66 0.60 UrbanâSuburban Arterials Two-lane undivided roadway segments (U2U) 1.22 0.92 posted speed ⤠30 mph Three-lane roadway segment (U3T) .154 1.15 posted speed ⤠30 mph Four-lane undivided roadway segment (U4U) .162 1.35 posted speed ⤠30 mph Four-lane divided roadway segment (U4D) 1.42 1.22 posted speed ⤠30 mph Five-lane roadway segment (U5T) 1.57 1.17 posted speed ⤠30 mph Two-lane undivided roadway segments (U2U) 1.33 1.13 posted speed > 30 mph Three-lane roadway segment (U3T) 1.99 1.36 posted speed > 30 mph Four-lane undivided roadway segment (U4U) 2.55 2.04 posted speed > 30 mph Four-lane divided roadway segment (U4D) 1.18 0.97 posted speed > 30 mph Five-lane roadway segment (U5T) 1.09 0.88 posted speed > 30 mph Three-leg stop-controlled intersections (R3ST) 0.59 0.32 Three-leg signalized intersections (R3SG) 2.21 1.68 Four-leg stop-controlled intersections (R4ST) 0.68 0.63 Four-leg signalized intersections (R4SG) 3.22 2.32 Table 17.ââ Calibration factors for Iowa from Iowa DOT (2017). Facility State-Speciï¬c SPF Crash Type Type Calibration Factor Multi-vehicle fatal and injury 1.26 Urban Multi-vehicle property damage only 1.79 freeways Single-vehicle fatal and injury 0.85 Single-vehicle property damage only 1.17 Multi-vehicle fatal and injury 1.08 Rural Multi-vehicle property damage only 1.67 freeways Single-vehicle fatal and injury 0.64 Single-vehicle property damage only 1.16
32ââ Calibration and Development of State-DOT-Specific Safety Performance Functions 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 â Rural two-lane, two-way roads â¾ Two-way undivided (R2U) â Rural multi-lane highways â¾ Four-lane undivided (R4U) â¾ Four-lane divided (R4D) ⢠Intersections â Rural two-lane, two-way roads â¾ Unsignalized three-leg, minor stop (R2 3ST) â¾ Unsignalized four-leg, minor stop (R2 4ST) â¾ Signalized four-leg (R2 4SG) â Rural multi-lane highways â¾ Unsignalized three-leg, minor stop (RM 3ST) â¾ Unsignalized four-leg, minor stop (RM 4ST) â¾ Signalized four-leg (RM 4SG) â Urban and suburban arterials â¾ Unsignalized three-leg, minor stop (UA 3ST) â¾ Signalized three-leg (UA 3SG) â¾ Unsignalized four-leg, minor stop (UA 4ST) â¾ 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.ââ Calibration factors for Iowa from Kimley-Horn and Associates (2021). Facility Type Calibration Factor Urban two-lane undivided arterial 1.63 (U2U) Urban three-lane arterial with two- 1.53 way left-turn lane (U3T) Urban four-lane undivided arterial 1.70 (U4U) Urban four-lane divided arterial 2.44 (U4D) Urban ï¬ve-lane arterial with two- 1.14 way left-turn lane (U5T)
Literature Reviewââ 33limits (45â50 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 ofbetween 342.21 miles and 10,688.68 miles of roadway.KansasSummary Calibrated SPFs? Design-level State-specific SPFs? Design-level 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 froma random statewide sample of 41 sections were calibrated, resulting in factors between 0.78 and3.23, 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 regionaldifferences and the high proportion of observed animal-related crashes. Calibration factors andfunctions were assessed for goodness of fit based on the following: Pearsonâs product moment cor-relation 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 crashprediction was also assessed with and without an Empirical Bayes adjustment. The study concludedthat the Empirical Bayes adjustment universally improved prediction ability, and that county-levelcalibration functions and statewide calibration factors provided the most accurate predictions. Bornheimer et al. (2011) developed state-specific design-level SPFs for animal-related crashesand non-animal-related crashes on two-lane rural roads using observed crash data from 2005 to2007 and approximately 300 miles of roadway data. NB regression was used to estimate modelparameters for seven different model specifications accounting for variables such as AADT, seg-ment length, roadside hazard rating (RHR), and exposure. Based on goodness of fit (as assessedby a paired t-test, Pearsonâs R, BIC, MPB, and MAD), a model predicting non-animal-relatedcrashes considering AADT, segment length, and roadside hazard rating was determined to be thebest 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 develop-ment of calibration factors and SPFs relied on observed crash data from 2011 to 2013. Calibra-tion factors were calculated via the HSM methodology, while the SPFs were developed usingthe same form as SPFs published in the HSM with new parameter estimates derived from NBregression using Kansas data. Proportions for crash types were also reported for the specifiedperiod, including the following types:⢠Single-vehicle â Animal-related â Ran off road Table 19.ââ Calibration factor for Kansas from Lubliner and Schrock (2011). Facility Type Sample Size Calibration Factor Rural two-lane two-way roads (R2U) 41 segments 1.48
34ââ Calibration and Development of State-DOT-Specific Safety Performance Functions â Moving vehicle â Rollover â Other â Pedestrian â Pedal cyclist ⢠Multi-vehicle â Head-on â Rear-end â Angle â Sideswipe (opposite direction) â Sideswipe (same direction) â Backed-into â Other ⢠Light condition â Daylight â Dawn â Dusk â Dark (streetlights on) â Dark (no streetlights) â Other A summary of the calibration factors developed in this study is provided in Table 20 and Table 21. Table 20.ââ Calibration factors for Kansas highways from Dissanayake and Aziz (2016). State- HSM Fatal State- HSM Total Speciï¬c SPF Sample and Injury Speciï¬c SPF Crash Fatal and Facility Type Size Crash Total Crash Calibration Injury Crash (Segments) Calibration Calibration Factor Calibration Factor Factor Factor Rural four-lane divided 281 1.436 0.524 0.956 1.002 highway (R4D) Rural four-lane undivided highway 83 1.495 0.359 1.019 0.858 (R4U) Table 21.ââ Calibration factors for Kansas rural intersections from Dissanayake and Aziz (2016). HSM Intersection-Box HSM Intersection-Related Method Method Sample Size Fatal and Fatal and Facility Type Total Crash Total Crash (Intersections) Injury Crash Injury Crash Calibration Calibration Calibration Calibration Factor Factor Factor Factor Rural four-leg stop- controlled 199 0.91 0.74 0.44 0.21 intersections (R4ST) Rural three-leg stop- controlled 65 2.87 1.16 0.92 0.47 intersections (R3ST)
Literature Reviewââ 35 Table 22.ââ Calibration factors for Kansas from Dissanayake and Karmacharya (2020). Sample Size Calibration Facility Type (No. of Severity Type Factor Sites) Urban three-leg stop Total 0.51 controlled intersections 347 Fatal + injury 0.40 (U3ST) Urban three-leg signalized Total 0.64 89 intersections (U3SG) Fatal + injury 0.52 Urban four-leg stop Total 0.61 controlled intersections 167 Fatal + injury 0.73 (U4ST) Urban four-leg signalized Total 1.17 198 intersections (U4SG) Fatal + injury 2.00 Dissanayake and Karmacharya (2020) developed calibration factors for HSM design-levelSPFs at various urban intersection types using observed crash data from 2013 to 2016 (2013 to 2015for three intersection types and 2014 to 2016 for one). A summary of the calibration factors andsample sizes is provided in Table 22. Dissanayake and Matarage (2020) developed design-level calibration factors and functions forsingle- and multi-vehicle fatal and injury and property damage-only crashes on freeway segmentsand speed-change lanes using observed crash data from 2013 to 2015. Calibration factors werealso estimated for observed crashes on ramp segments and ramp terminal facilities from 2014 to2016. Goodness of fit for both the calibration factors and calibration functions was determinedbased on CURE plots generated based on a holdout sample of observed crash data. A summaryof the calibration factors developed is provided in Table 23. Sample sizes used were 521 segmentsbetween 0.1 and 1 mile in length (freeway segments), 351 to 366 segments between 0.02 and0.30 mile in length (entrance- and exit-related speed-change lanes), 156 to 184 ramps (entranceand exit), and 74 to 120 signal- and stop-controlled ramp terminals.KentuckySummary Calibrated SPFs? None State-specific SPFs? Network-screening-level Green et al. (2015) developed network-screening-level SPFs for total crashes and KAB crashesoccurring at urban and rural intersections using observed crash data from 2009 to 2014. The SPFswere developed using NB regression in the R statistical software and account only for the AADTof major and minor approaches of the intersections. The intersections studied were classified asfollows in Table 24. Ross et al. (2022) developed screening-level SPFs for KAB and CO severity crashes occurringon 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 datafrom 2015 to 2019. Sample sizes were not explicitly defined for any facility type. CURE plots weregenerated for each SPF developed. Blanford et al. (2022) developed screening-level SPFs for total crashes, aggressive drivingcrashes, distracted driving crashes, impaired driving crashes, and unrestrained driving crasheson 13 segment facility types using observed crash data from 2014 to 2018. Sample sizes ranged
Table 23.ââ Calibration factors for Kansas from Dissanayake and Matarage (2020). Sample Size Calibration Facility Type (No. of Crash Type Crash Severity Factor Sites) Fatal and injury 0.952 Multiple vehicle Property damage only 1.982 Freeway segments 521 Fatal and injury 0.936 Single vehicle Property damage only 1.843 Fatal and injury 1.452 351 Entrance-related Property damage only 1.943 Speed-change lanes Fatal and injury 1.416 366 Exit-related Property damage only 1.720 Fatal and injury 0.957 Multiple vehicle Property damage only 2.737 Entrance ramp segments 184 Fatal and injury 0.165 Single vehicle Property damage only 0.368 Fatal and injury 5.426 Multiple vehicle Property damage only 7.973 Exit ramp segments 156 Fatal and injury 0.179 Single vehicle Property damage only 0.55 Stop-controlled ramp Fatal and injury 0.884 120 Total terminals Property damage only 1.353 Signal-controlled ramp Fatal and injury 0.626 74 Total terminals Property damage only 1.242 D4 stop-controlled ramp Fatal and injury 1.118 102 Total terminals Property damage only 1.269 D4 signal-controlled Fatal and injury 0.671 57 Total ramp terminals Property damage only 1.515 Table 24.ââ SPFs developed for Kentucky from Green et al. (2015). Sample Facility Description Code Size Undivided three-leg rural full stop U3rF 78 Undivided three-leg rural (at least) partial stop U3rP 37,256 Undivided three-leg rural signal U3rS 96 Undivided three-leg urban full stop U3uF 68 Undivided three-leg urban (at least) partial stop U3uP 10,252 Undivided three-leg urban signal U3uS 583 Undivided four+ leg rural full stop U4rF 77 Undivided four+ leg rural (at least) partial stop U4rP 4,202 Undivided four+ leg rural signal U4rS 166 Undivided four+ leg urban full stop U4uF 89 Undivided four+ leg urban (at least) partial stop U4uP 2,484 Undivided four+ leg urban signal U4uS 1,492 Divided three-leg rural (at least) partial stop D3rP 729 Divided three-leg rural signal D3rS 26 Divided three-leg urban (at least) partial stop D3uP 1,292 Divided three-leg urban signal D3uS 335 Divided four+ leg rural (at least) partial stop D4rP 459 Divided four+ leg rural signal D4rS 66 Divided four+ leg urban (at least) partial stop D4uP 560 Divided four+ leg urban signal D4uS 832
Literature Reviewââ 37from 19 to 12,525 segments, and four to 127,107 crashes. Facilities included in the study are thefollowing:⢠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 eachmodel to analyze goodness of fit. The parameters of each model are not provided in the report.LouisianaSummary Calibrated SPFs? Design-level State-specific SPFs? Network-screening-level Sun et al. (2011) calibrated design-level HSM SPFs for total crashes on rural divided andundivided multi-lane highways using observed crash data from 2003 to 2007. Sample sizes wereapproximately 60 to 80 miles per year for undivided roads and 450 to 600 miles per year fordivided roads. The HSM methodology was followed exclusively, and the only validation of thecalibration factors were simple comparisons of observed crashes, predicted crashes, and pre-dicted crashes with calibration. The calibration factors developed are presented in Table 25. Robicheaux and Wolshon (2015) calibrated HSM design-level SPFs for total crashes onLouisiana road and highway segments using observed crash data from 2009 to 2011. A totalof 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, urbantwo-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 road-way segments were used in the calibration factor development. The values of the eight calibrationfactors are provided in Table 26. Calibration factors were calculated based on random samplesfrom the statewide dataset, and crashes influenced by intersection effects were removed from thedataset if the crash occurred within 150 feet of an intersection. The authors acknowledged thatthe study was lacking in statistical analysis of the calibration factors, and they questioned thelong-term applicability of these factors. Table 25.ââ Calibration factors for Louisiana from Sun et al. (2011). Sample Size HSM SPF Facility Type (Miles) Calibration Factor Rural two-lane road (RMU) 58.26â79.24 0.98 Rural multi-lane divided highway (RMD) 454.36â603.56 1.27
38ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 26.ââ Calibration factors for Louisiana from Robicheaux and Wolshon (2015). Sample Size HSM SPF Facility Type (No. of Calibration Factor Segments) Rural two-lane road (R2U) 99 0.97 Rural multi-lane divided highway (RMD) 80 0.62 Rural multi-lane undivided highway (RMU) 50 1.92 Urban two-lane roads (U2U) 30 1.91 Urban three-lane roads with TWLTL (U3T) 32 0.26 Urban four-lane divided highways (U4D) 49 1.59 Urban four-lane undivided highways (U4U) 49 2.54 Urban ï¬ve-lane highways with TWLTL (U5T) 145 0.06 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 âflatâ or ârolling.â SPFs all take Sigmoidal or ho*rl 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 â Two-lane undivided highways (R2U) â Four-lane divided highways (R4D) â Four-lane undivided highways (R4U) ⢠Urban segments â Four-lane divided freeways (U4D) â Six-lane divided freeways (U6D) ⢠Rural intersections â Two-lane divided unsignalized three-leg intersections (R2D 3ST) â Two-lane divided unsignalized four-leg intersections (R2D 4ST) â Two-lane undivided unsignalized three-leg intersections (R2U 3ST) â Two-lane undivided unsignalized four-leg intersections (R2U 4ST) â Four-lane divided unsignalized three-leg intersections (R4D 3ST) â Four-lane divided unsignalized four-leg intersections (R4D 4ST) ⢠Urban intersections â Two-lane divided signalized three-leg intersections (U2D 3SG) â Two-lane divided signalized four-leg intersections (U2D 4SG) â Two-lane divided unsignalized three-leg intersections (U2D 3ST) â Two-lane divided unsignalized four-leg intersections (U2D 4ST) â Two-lane undivided signalized three-leg intersections (U2U 3SG) â Two-lane undivided signalized four-leg intersections (U2U 4SG) â Two-lane undivided unsignalized three-leg intersections (U2U 3ST) â Two-lane undivided unsignalized four-leg intersections (U2U 4ST) â Four-lane divided signalized three-leg intersections (U4D 3SG) â Four-lane divided signalized four-leg intersections (U4D 4SG) â Four-lane divided unsignalized three-leg intersections (U4D 3ST) â Four-lane divided unsignalized four-leg intersections (U4D 4ST) â Four-lane undivided signalized three-leg intersections (U4U 3SG) â Four-lane undivided signalized four-leg intersections (U4U 4SG)
Literature Reviewââ 39 â Four-lane undivided unsignalized three-leg intersections (U4U 3ST) â Four-lane undivided unsignalized four-leg intersections (U4U 4ST) â Six-lane divided signalized four-leg intersections (U6D 4SG) â Six-lane divided unsignalized four-leg intersections (U6D 4ST)MaineSummary Calibrated SPFs? Design-level State-specific SPFs? None Belz and Aguilar (2015) developed state-specific calibration factors for HSM design-level SPFsfor rural two-lane road segments and intersections, as well as urban and suburban arterialsand intersections. The calibration factors for each of the 13 different facility types are listed inTable 27, along with sample sizes.MarylandSummary Calibrated SPFs? Design-level State-specific SPFs? None Shin et al. (2014) developed state-specific calibration factors for HSM design-level SPFs forroadway segment and intersection facility types using observed crash data from 2008 to 2010across the network of Maryland State Highway Administration roads (excluding the City ofBaltimore). Between 19 and 252 roadway sites (minimum length of 0.1 miles for rural and 0.04 milesfor urban) were used for segment-level calibration, and between 10 and 244 sites were used forintersection calibration. The calibration factors were calculated for total, KABC, KAB, and PDOseverities, and the observed crash proportions for various single- and multi-vehicle crash typesin Maryland were presented allowing for state-specific prediction of those crash types. The cali-bration factors calculated are presented in Table 28. Table 27.ââ Calibration factors for Maine from Maine DOT (2014). Sample Size Facility Type Calibration Factor (No. of Sites or Miles) Intersections on Rural Two-Lane Roads Three-leg stop controlled (R2 3ST) 0.54 169 Four-leg signalized (R2 4SG) 0.55 107 Four-leg stop controlled (R2 4ST) 0.38 44 Intersections on Urban and Suburban Arterials Three-leg stop controlled (U3ST) 0.65 325 Three-leg signalized (U3SG) 1.36 44 Four-leg stop controlled (U4ST) 0.77 118 Four-leg signalized (U4SG) 1.53 25 Rural Two-Lane Road Segments Two-lane undivided (R2U) 1.08 90.81 Urban and Suburban Arterial Segments Two-lane undivided (U2U) 2.11 25.82 Three-lane including a TWLTL (U3T) 1.62 15.76 Four-lane undivided (U4U) 1.77 7.36 Four-lane divided (U4D) 2.56 9.21 Five-lane including a TWLTL (U5T) 1.22 8.31
40ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 28.ââ Calibration factors for Maryland from Shin et al. (2014). Sample Calibration Calibration Calibration Calibration Size Factor for Factor for Factor for Factor for Facility Type (No. of Total KABC KAB PDO Sites) Crashes Crashes Crashes Crashes Two-lane two-way undivided rural roads 251 0.6956 â â â (R2U) Four-lane undivided rural roads (R4U)* 19 2.3408 1.949861 1.9231 â Four-lane divided rural roads (R4D) 160 0.5838 0.4193 0.4565 â Two-lane two-way undivided urban 252 0.6814 0.6125 â 0.7313 roads (U2U) Two lane urban roads with TWLTL (U3T) 138 1.0785 1.3053 â 0.9362 Four-lane undivided urban roads (U4U) 145 0.8788 0.7696 â 0.9611 Four-lane divided urban roads (U4D) 244 0.8269 1.0665 â 1.1874 Four lane urban roads with TWLTL (U5T) 115 1.1891 1.1918 â 1.1874 Three-leg stop-controlled intersections on 162 0.1645 â â â two-lane rural roads (R2 3ST)* Four-leg stop-controlled intersections on 115 0.2011 â â â two-lane rural roads (R2 4ST)* Three-leg signalized intersections on two- 67 0.2634 â â â lane rural roads (R2 4SG)* Three-leg stop-controlled intersections on 26 0.1788 0.2550 0.2664 â multi-lane rural roads (RM3ST)* Four-leg stop-controlled intersections on 10 0.3667 0.3923 0.3953 â multi-lane rural roads (RM4ST)* Four-leg signalized intersections on 35 0.1086 0.1327 0.1879 â multi-lane rural roads (RM4SG)* Urban three-leg stop-controlled 152 0.1562 0.2273 â 0.1138 intersections (U3ST)* Urban four-leg stop-controlled 90 0.3824 0.4964 â 0.3003 intersections (U4ST)* Urban three-leg signalized intersections 167 0.3982 0.5967 â 0.3427 (U3SG) Urban four-leg signalized intersections 244 0.4782 0.6285 â 0.3994 (U4SG) *Denotes that the facility did not meet the HSM minimum sample size criteria of 30â50 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, calibra- tion 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 Calibrated SPFs? Design-level State-specific SPFs? Network-screening-level 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
Literature Reviewââ 41 Table 29.ââ Calibration factors for Maryland from Shin et al. (2020). Calibration Facility Type Sample Size Crash Type Crash Severity Factor Fatal and injury 0.455 Multiple vehicle Property damage only 0.286 Freeway segments 317 miles Fatal and injury 0.627 Single vehicle Property damage only 0.641 Fatal and injury 0.591 Entrance related Speed-change 80.73 miles Property damage only 0.527 lanes Fatal and injury 0.767 Exit related Property damage only 0.881 Fatal and injury 0.676 147 segments Stop-controlled Property damage only 0.378 Ramp terminals Fatal and injury 0.350 172 segments Signalized Property damage only 0.30286 intersections of each type were considered in this project. SPFs were also developed for thesesame intersection types for multi-vehicle crashes (only); however, due to data limitations, onlytraffic volumes on the major- and minor-road approaches were considered as input variables. Theauthors suggested that the HSM adjustment factors could be applied to these SPFs to accountfor specific design features. Calibration factors were then developed for these state-specific SPFswith HSM adjustment factors applied; these are also provided in Table 30. A follow-up study (Xie and Wen, 2021) developed updated calibration factors and SPFsfor these same intersection types using observed crash data from 2015 to 2018. Between 51 and118 intersections of each type were considered in the sample used for calibration. The calibra-tion factors obtained are shown in Table 31. Traffic volumes were estimated using data fromthe MassDOT Roadway Inventory and Streetlight; two sets of calibration factors were developedbased on these different traffic volume sources. SPFs were developed for total crashes, fatal andinjury crashes, PDO crashes, multi-vehicle crashes, single-vehicle crashes, and vehicleâpedestriancrashes using Bayesian NB regression. Only traffic volumes were considered as input variablesto the SPFs. The two methods (calibration and state-specific SPFs) were compared using errorsbetween observed crash frequencies and predicted values, as well as CURE plots. VHB (2020) developed SPFs for rural and urban arterials and collectors to support networkscreening using observed crash data from 2013 to 2017. SPFs were developed for roadway seg-ments 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 tostatewide SPFs, region-specific SPFs were estimated at the MassDOT district level for several ofthese facility types. Unique SPFs were estimated considering and ignoring traffic volumes; the latteronly included segment length as an input variable. Additionally, the SPFs with traffic volumes Table 30.ââ Calibration factors for Massachusetts from Xie and Chen (2016). Sample Size HSM Calibration State-Speciï¬c SPF Intersection Type (No. of Sites) Factor Calibration Factor Three-leg signalized (U3SG) 48 1.50 0.95 Three-leg stop controlled 86 0.77 1.13 (U3ST) Four-leg signalized (U4SG) 52 1.49 1.00 Four-leg stop controlled 59 1.03 1.04 (U4ST)
42ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 31.ââ Calibration factors Massachusetts from Xie and Chen (2021). HSM HSM State-Speciï¬c State- Sample Calibration Calibration SPF Speciï¬c SPF Facility Type Size Factor Factor Calibration Calibration (No. of (AADT (AADT Factor Factor Sites) from from (AADT from (AADT from MassDOT) Streetlight) MassDOT) Streetlight) Three-leg signalized 51 1.58 1.23 0.98 0.98 (U3SG) Three-leg stop controlled 118 0.87 0.55 0.98 1.00 (U3ST) Four-leg signalized (U4SG) 59 1.87 1.51 0.98 0.96 Four-leg stop controlled 75 1.23 0.76 1.01 0.99 (U4ST) 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 Calibrated SPFs? Design-level State-specific SPFs? Design-level 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 Michiganâs 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.ââ Calibration factors for Michigan from Savolainen et al. (2015). Sample Calibration Factor by Crash Type Size Single Vehicle Multiple Vehicle Facility Type (No. of Fatal and Fatal and Sites) Total PDO Total PDO Injury Injury Urban three-leg signalized 485 0.95 0.825 1.338 0.876 1.1 0.561 intersections (U3SG) Urban three-leg stop-controlled 5,731 0.266 0.232 0.353 0.294 0.34 0.171 intersections (U3ST) Urban four-leg signalized 1,710 0.977 0.648 2.002 1.094 1.331 0.75 intersections (U4SG) Urban four-leg stop-controlled 2,695 0.333 0.311 0.512 0.469 0.563 0.301 intersections (U4ST)
Literature Reviewââ 43 Table 33.ââ Calibration factors for Michigan from Savolainen et al. (2016). Crash Type Sample Single Vehicle Multiple Vehicle Size Facility Type Fatal (No. of Fatal and Sites) Total PDO and Total PDO Injury Injury Two-lane two-way undivided 489 3.498 4.372 1.302 1.529 1.555 1.26 urban roads (U2U) Two-lane urban roads with 236 4.224 5.472 1.506 1.874 2.061 1.443 TWLTL (U3T) Four-lane undivided urban 373 2.133 2.301 1.059 1.943 2.431 1.156 roads (U4U) Four-lane urban roads with 239 1.099 1.31 0.628 1.466 1.53 1.066 TWLTL (U5T) Four-lane divided urban roads 439 1.971 2.092 1.396 0.579 0.621 0.104 (U4D)period. Sample sizes ranged from 239 to 489 segments, each with average lengths between 0.6and 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 crashdata from 2011 to 2015. Observed crash proportions for a variety of single- and multi-vehiclecrashes and crash severities were provided for Michigan, allowing for estimation of these crashtypes. The calibration factors were calculated via the HSM methodology, and SPFs weredeveloped through a generalized linear modeling technique assuming a Poisson distribution.Intersection sample sizes ranged from 175 to 2,513, while segment sample sizes ranged from95.2 miles to 5,351.6 miles. Due to a high proportion of deer-related crashes, calibration factorswere calculated for both total crashes and non-deer-related crashes on segments. Both cali-bration factors and developed SPFs attempted to capture regional differences across the state;calibration factors were estimated both statewide and for individual regions, while newlydeveloped SPFs included variables to account for regional differences. The calculated calibra-tion factors are provided in Tables 34 and 35, and SPFs were estimated for the same facilitytypes as calibration factors. Geedipally et al. (2019) developed design-level state-specific SPFs for two-lane two-way ruralroads using observed crash data from 2011 to 2015. Sample sizes ranged from approximately1,450 to 4,500 miles. Separate single- and multi-vehicle crash SPFs were developed for fataland injury crashes and PDO crashes on paved roads funded through federal aid, and for fatal andinjury crashes and PDO crashes on paved roads with other sources of funding. SPFs consideredvariables such as AADT, lane widths, presence of horizontal curves, driveway density, roadwaysurface (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.MinnesotaSummary Calibrated SPFs? Design-level State-specific SPFs? None Storm and Richfield (2014) used three years of observed crash data to develop calibrationfactors for design-level HSM SPFs for total crashes on rural roadway segments and intersections.
44ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 34.ââ Calibration factors for roadway segments in Michigan from Gates et al. (2018). Sample Sample Calibration Calibration Facility Type Region Size Size Factor for Total Factor for Non- (Sites) (Miles) Crashes Deer Crashes Statewide 946 3,003 2.16 0.64 Superior 185 658 2.35 0.59 Two-lane two- North 210 705 2.33 0.63 way undivided Grand 161 458 2.13 0.69 rural roads Bay 204 677 2.25 0.63 (R2U) Southwest 99 236 1.75 0.67 University 87 269 1.85 0.62 Metro 0 0 â Statewide 106 200 2.05 1.02 Superior 12 17 2.83 1.35 Four-lane North 0 0 â divided rural Grand 17 41 1.51 0.92 roads Bay 36 71 2.19 0.97 (R4D) Southwest 28 40 1.49 1.00 University 14 31 3.33 1.21 Metro 0 0 â Statewide 55 91 1.28 0.56 Superior 17 17 1.58 0.64 Four-lane North 4 6 2.58 0.73 undivided Grand 5 7 1.60 0.77 rural roads Bay 20 45 1.08 0.51 (R4U) Southwest 6 7 0.95 0.48 University 4 9 1.84 0.67 Metro 0 0 â Statewide 8,318 3,558 2.12 0.75 Superior 634 303 2.90 0.89 Two-lane North 1,496 636 2.39 0.8 federal-aid Grand 2,032 845 2.63 0.96 paved roads Bay 1,085 465 2.27 0.63 (2PF) Southwest 332 159 1.65 0.69 University 2,403 1,033 1.87 0.70 Metro 336 118 1.36 0.63 Statewide 2,525 1,293.7 2.14 0.78 Superior 15 6.2 â Two-lane non- North 203 76.1 1.65 0.53 federal-aid Grand 418 212.0 1.85 0.85 paved roads Bay 321 139.4 1.54 0.55 (2PN) 513 270.6 Southwest 2.07 0.93 University 1,061 582.7 2.68 0.83 Metro 14 6.8 â Statewide 3,054 1,436 2.73 1.67 Superior 2 3 â Gravel two- North 120 46 1.64 1.00 lane non- Grand 268 132 3.41 2.36 federal-aid Bay 156 72 3.32 1.19 roads Southwest 135 67 2.34 1.33 (2GN) University 2,056 939 2.76 1.63 Metro 317 177 2.40 1.83 â Cells indicate calibration factors that were not calculated due to small sample sizes.
Literature Reviewââ 45 Table 35.ââ Calibration factors for intersections in Michigan from Gates et al. (2018). Sample Size Calibration Factor for Facility Type Region (No. of Sites) Total Crashes Statewide 175 1.22 Superior 5 0.60 Four-leg North 32 1.09 signalized Grand 30 1.37 intersections Bay 63 1.35 (4SG) Southwest 17 1.12 University 26 1.11 Metro 2 1.06 Statewide 2,513 0.70 Superior 198 0.84 Four-leg stop- North 360 0.69 controlled Grand 521 0.68 intersections Bay 516 0.68 (4ST) Southwest 278 0.72 University 583 0.71 Metro 57 0.85 Statewide 2,297 0.85 Superior 287 1.17 Three-leg stop- North 381 0.89 controlled Grand 388 0.87 intersections Bay 229 0.76 (3ST) Southwest 381 0.78 University 564 0.78 Metro 67 0.85Calibration factors were calculated both for statewide crashes and for those crashes occurringin the Minneapolis/St. Paul (Metro) area, the values of which are presented in Table 36. Forintersections, 100 sites were randomly selected except for 4SG intersections, which only had31 available across the state. For segments, approximately 300 miles were used for each calibra-tion factor. Additional information regarding the proportion of crash types including variousforms of single- and multi-vehicle crashes, severity levels (fatal and injury and PDO), and night-time crashes were published to allow prediction of those crash types in conjunction with thecalibration factors.MississippiSummary Calibrated SPFs? Design-level State-specific SPFs? Design-level 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 inter-sections on rural two-lane two-way roads, rural multi-lane highways, and urban and suburbanarterials at severity levels ranging from total crashes to PDO. The authors also recommendedthe development of state-specific SPFs for urban three-leg and urban four-leg intersections dueto the large calibration factors observed. Calibration factors were calculated using the FHWA
46ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 36.ââ Calibration factors for Minnesota from Storm and Richfield (2014). Greater Metro Minnesota Greater Minnesota Metro Sample Minnesota Sample Minnesota Facility Type Size Calibration Size Calibration (# of Factor (# of Factor sites) sites) Rural Two-Lane, Two-Way Highways 42 73 R2U - Roadway Segments (326 0.41 (276 0.58 miles) miles) R3ST - Three-leg intersection with minor-road 100 0.71 100 0.63 stop control R4ST - Four-leg intersection with minor-road 100 0.45 100 0.69 stop control R4SG - Four-leg signalized intersections 31* 1.22* 31* 1.22* Rural Expressway (Rural Multi-Lane Divided) R4U - Roadway Segments 423 miles 0.69 108 miles 0.53 R3ST - Three-leg intersection with minor-road 93 2.32 31 0.74 stop control R4ST - Four-leg intersection with minor-road 75 1.87 36 0.88 stop control RMD 4SG - Four-leg signalized intersections 40* 0.39* 40* 0.39* *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 variationâ 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 Calibrated SPFs? Design-level State-specific SPFs? None 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 pro- vided 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.ââ Calibration factors for Mississippi from Walker et al. (2020). Number of Calibration Facility Type Severity Miles or Factor Intersections KABCO 1.18 Divided segments (RMD) KABC 0.64 1,380 KAB 0.41 Rural multi-lane KABCO 0.36 Three-leg intersections with minor- divided road KABC 0.36 490 road stop control (R3ST) (HSM) KAB 0.23 KABCO 0.69 Four-leg signalized intersections KABC 0.53 46 (R4SG) KAB 0.36 KABCO 2.68 Three-leg signalized intersections KABC 1.80 50 (U3SG) PDO 3.34 Urban two- to ï¬ve- KABCO 1.04 lane arterial Four-leg intersections with minor-road KABC 0.87 706 (HSM) stop control (U4ST) PDO 1.10 Four-leg signalized intersections KABC 2.25 147 (U4SG) Urban six-lane Four-leg signalized intersections arterial KABC 1.27 54 (U6 4SG) (NCHRP 17-58) Four-leg all way stop-control Rural two-lane two- KABCO 0.215 129 intersections (R2 4ST) way highway Three-leg all way stop-control (NCHRP 17-68) KABCO 0.893 19 intersections (R2 3ST) Table 38.ââ Summary of calibration factors estimated in Sun et al. (2013). Sample Calibration Facility Type Size (No. of Factor Sites) Rural two-lane undivided highway segments (R2U) 196 0.82 Rural multi-lane divided highway segments (RMD) 37 0.98 Urban two-lane undivided arterial segments (U2U) 73 0.84 Urban four-lane divided arterial segments (U4D) 66 0.98 Urban five-lane undivided arterial segments (U5T) 59 0.73 Rural four-lane freeway segments (R4D) (PDO SV) 47 1.51 Rural four-lane freeway segments (R4D) (PDO MV) 47 1.98 Rural four-lane freeway segments (R4D) (FI SV) 47 0.77 Rural four-lane freeway segments (R4D) (FI MV) 47 0.91 Urban four-lane freeway segments (U4D) (PDO SV) 39 1.62 Urban four-lane freeway segments (U4D) (PDO MV) 39 3.59 Urban four-lane freeway segments (U4D) (FI SV) 39 0.70 Urban four-lane freeway segments (U4D) (FI MV) 39 1.40 Urban six-lane freeway segments (U6D) (PDO SV) 54 0.88 Urban six-lane freeway segments (U6D) (PDO MV) 54 1.63 Urban six-lane freeway segments (U6D) (FI SV) 54 1.01 Urban six-lane freeway segments (U6D) (FI MV) 54 1.20 Urban three-leg signalized intersections (U3SG) 35 3.03 Urban four-leg signalized intersections (U4SG) 35 4.91 Urban three-leg stop-controlled intersections (U3ST) 70 1.06 Urban four-leg stop-controlled intersections (U4ST) 70 1.30 Rural two-lane three-leg stop-controlled intersections (R23ST) 70 0.77 Rural two-lane four-leg stop-controlled intersections (R24ST) 70 0.49 Rural multi-lane three-leg stop-controlled intersections (RM3ST) 70 0.28 Rural multi-lane four-leg stop-controlled intersections (RM4ST) 70 0.39 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.
48ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 39.ââ Summary of calibration factors estimated in Sun et al. (2017). Sample Size Current Facility Type (No. of Calibration Factor Sites) Rural two-lane undivided highway segments (R2U) 36 0.97 Rural multi-lane divided highway segments (RMD) 37 0.74 Urban two-lane undivided arterial segments (U2U) 75 1.48 Urban four-lane divided arterial segments (U4D) 66 0.91 Urban five-lane undivided arterial segments (U5T) 59 0.84 Rural four-lane freeway segments (R4D) (PDO SV) 45 1.29 Rural four-lane freeway segments (R4D) (PDO MV) 45 2.14 Rural four-lane freeway segments (R4D) (FI SV) 45 0.50 Rural four-lane freeway segments (R4D) (FI MV) 45 0.84 Urban four-lane freeway segments (U4D) (PDO SV) 41 1.20 Urban four-lane freeway segments (U4D) (PDO MV) 41 1.46 Urban four-lane freeway segments (U4D) (FI SV) 41 0.60 Urban four-lane freeway segments (U4D) (FI MV) 41 0.71 Urban six-lane freeway segments (U6D) (PDO SV) 54 0.85 Urban six-lane freeway segments (U6D) (PDO MV) 54 1.22 Urban six-lane freeway segments (U6D) (FI SV) 54 0.96 Urban six-lane freeway segments (U6D) (FI MV) 54 0.85 Urban three-leg signalized intersections (U3SG) 35 2.95 Urban four-leg signalized intersections (U4SG) 35 5.21 Urban three-leg stop-controlled intersections (U3ST) 70 1.28 Urban four-leg stop-controlled intersections (U4ST) 70 1.27 Rural two-lane three-leg stop-controlled intersections (R23ST) 70 0.69 Rural two-lane four-leg stop-controlled intersections (R24ST) 66 0.41 Rural multi-lane three-leg stop-controlled intersections (RM3ST) 70 0.95 Rural multi-lane four-leg stop-controlled intersections (RM4ST) 70 0.65 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 Calibrated SPFs? None State-specific SPFs? Yes, but no details on network-screening-level vs. design-level 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 Transportationâs Safety Program. Nebraska Summary Calibrated SPFs? None State-specific SPFs? None The authors did not find any documentation of state customization of HSM tools or SPFs for Nebraska.
Literature Reviewââ 49NevadaSummary Calibrated SPFs? Yes but no details on network-screening-level vs. design-level State-specific SPFs? Design-level Tian et al. (2013) calibrated the design-level two-lane, two-way rural road SPF, using observedcrash data in Nevada from 2007 to 2011. Approximately 680 miles of roadway was used for thisanalysis 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 DOTresearch report with any additional information was not found.New HampshireSummary Calibrated SPFs? None State-specific SPFs? Network-screening-level Gross et al. (2016) developed state-specific SPFs for New Hampshire for network screen-ing purposes as part of a larger study to compare the outcomes of different network screeningmethods using observed crash data from 2010 to 2014. SPFs were developed for the followingsite types and included either total entering traffic volume or traffic volume on major/minorintersection 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 incor-porating SPFs into the network screening process and using either the EB expected excess crashfrequency or EB expected crash frequency better identified sites with the highest potential overalleconomic benefit.New JerseySummary Calibrated SPFs? Design-level State-specific SPFs? Network-screening-level 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.ââ Calibration factor for Nevada estimated in Tian et al. (2013). Facility Type Calibration Factor Rural two-way two-lane roads (R2U) 1.21
50ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 41.ââ Calibration factors for New Jersey from Ozbay et al. (2019). Sample Size Calibration Facility Type (No. of Sites) Factor Roadway Segments Rural two-lane, two-way (R2U) 756 1.55 Rural four-lane undivided (R4U) 27 1.10 Rural four-lane divided (R4D) 45 1.70 Urban two-lane undivided (U2U) 459 1.264 Urban four-lane undivided (U4U) 514 1.097 Urban four-lane divided (U4D) 387 1.596 Intersections Rural two-lane, unsignalized three-leg intersections (R2 3ST) 314 0.88 Rural two-lane, unsignalized four-leg intersections (R2 4ST) 149 0.88 Rural two-lane, signalized four-leg intersections (R2 4SG) 45 0.85 Urban two-lane undivided, unsignalized three-leg 227 2.61 intersections (U2 3ST) Urban four-lane undivided, signalized three-leg intersections 164 3.60 (U4 3SG) Urban three-lane undivided with two-way left-turn lane, 121 1.66 unsignalized four-leg intersections (U3 4SG) Urban four-lane, signalized four-leg intersections (U4 4SG) 209 4.25 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 inter- sections 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.ââ Adjustment factors considered in New Jersey for SPF calibration. Facility Type Adjustment Factors Two-lane, two-way rural roadway segments ⢠Horizontal curvature (both length and radius) ⢠Shoulder type ⢠Shoulder width Urban roadway segments ⢠On-street parking ⢠Roadside ï¬xed objects ⢠Median width ⢠Lighting ⢠Automated speed enforcement Rural intersections on two-lane, two-way roads ⢠Intersection skew angle ⢠Presence of left-turn lanes ⢠Right-turn lanes ⢠Lightning Urban intersections ⢠Left-turn lanes ⢠Left-turn signal phasing ⢠Right-turn lanes ⢠Right turn on red ⢠Lighting ⢠Red-light cameras
Literature Reviewââ 51were not considered in the SPF development process; thus, these SPFs were network-screening-levelSPFs and only included traffic volumes (either AADT for a segment or on incoming intersectionapproaches) and segment lengths (for roadway segments) as input variables. The lone exceptionswere SPFs developed for vehicleâpedestrian crashes on U3SG and U4SG intersections, whichincluded both vehicular traffic volume and pedestrian volume as input variables. No recommen-dations were provided on which of these SPFs should be used for a given site type (calibrated orstate-specific); both were made available for use in a spreadsheet tool for New Jersey.New MexicoSummary Calibrated SPFs? None State-specific SPFs? None The authors did not find any documentation of state customization of HSM tools or SPFsfor New Mexico.New YorkSummary Calibrated SPFs? None State-specific SPFs? Network-screening-level Note that responses to the survey described in Chapter 3 indicate that New York both appliescalibration factors and state-specific SPFs. However, the authors did not find any documentationrelated 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 YorkState. 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 includetraffic volumes and segment lengths (for roadway segments) as input variables. In general,segment lengths are included so that predicted crash frequency increases proportionally withsegment length. Further, different functional forms were considered for traffic volume, includingthe traditional HSM form, ho*rl form, and polynomial form. Average crash rates are also includedfor 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 CarolinaSummary Calibrated SPFs? Design-level State-specific SPFs? Network-screening-level The summary here differs from responses received from North Carolina as a part of the surveydescribed in Chapter 3; see the case example in Chapter 4 for more details. Srinivasan and Carter (2011) developed network-screening-level SPFs (considering only trafficvolumes) 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 â Divided roadway segments (RMD) â Undivided roadway segments (RMU)
52ââ Calibration and Development of State-DOT-Specific Safety Performance Functions ⢠Multi-lane urban roadways â Divided roadway segments (UMD) â Undivided roadway segments (UMU) ⢠Rural freeways â Four-lane freeways outside of the influence of interchanges â Six+-lane freeways outside of the influence of interchanges â Four-lane freeways within the influence of interchanges â Six+-lane freeways within the influence of interchanges ⢠Urban freeways â Four-lane freeways outside of the influence of interchanges â Six-lane freeways outside of the influence of interchanges â Eight+-lane freeways outside of the influence of interchanges â Four-lane freeways within the influence of interchanges â Six-lane freeways within the influence of interchanges â 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
Literature Reviewââ 53 Table 43.ââ Calibration factors for North Carolina from Srinivasan and Carter (2011). Sample Size Calibration Facility Type (No. of Sites Factor or Miles) Roadway Segments Rural four-lane divided (R4D) 49.77 0.97 Urban two-lane undivided (U2U) 59.39 1.54 Urban two-lane with TWLTL (U3T) 7.57 3.62 Urban four-lane divided (U4D) 15.50 3.87 Urban four-lane undivided (U4U) 15.29 4.04 Urban four-lane with TWLTL (U5T) 12.46 1.72 Intersections Rural two-lane, minor stop-controlled three-leg 133 0.57 (R2 3ST) Rural two-lane, signalized four-leg (R2 4SG) 19 1.04 Rural two-lane, minor stop-controlled four-leg (R2 59 0.68 4ST) Rural four-lane, signalized four-leg (R4 4SG) 23 0.49 Urban arterial, signalized three-leg (U3SG) 31 2.47 Urban arterial, minor stop-controlled three-leg 73 1.72 (U3ST) Urban arterial, signalized four-leg (U4SG) 122 2.79 Urban arterial, minor stop-controlled four-leg 20 1.32 (U4ST)updated to provide frequency estimates for individual crash types. A summary of the calibrationfactors is provided in Table 46 and Table 47.North DakotaSummary Calibrated SPFs? None State-specific SPFs? None The authors did not find any documentation of state customization of HSM tools or SPFs forNorth Dakota.OhioSummary Calibrated SPFs? Design-level State-specific SPFs? Design-level Troyer et al. (2015) developed calibration factors for design-level HSM SPFs in Ohio usingobserved crash data from 2009 to 2011. The set of SPFs and associated calibration factors isprovided in Table 48. These SPFs were design-level SPFs that included adjustment factors forvarious site-specific features for each facility type; however, the set of adjustment factors con-sidered was not reported. The calibration process started with a fixed number of sites per facilitytype (50) and then additional sites were added to ensure a minimum of 100 crashes observedper year across that facility type. CURE plots were used to assess the fit of the calibration SPFpredictions to Ohio data, and the results suggested a good fit. Using this information, the OhioDOT prioritized site types for the development of state-specific SPFs based on the fit, trafficvolumes, and site type frequency.
Table 44.ââ Roadway segment calibration factors for North Carolina from Smith et al. (2017). Sample Size Facility Type Calibration Factor (Miles) Two-lane, two-way rural (R2U) 476* [144C, 160M, 1.09* [1.78C, 0.78M, 172P] 1.21P] Rural four-lane divided (R4D) 202* [64C, 78M, 60P] 0.93* [1.27C, 0.78M, 0.83P] Urban two-lane undivided (U2U) 30 1.17 Urban two-lane with TWLTL (U3T) [1.55] 15 1.55 Urban four-lane divided (U4D) [2.25] 11 2.25 Urban four-lane undivided (U4U) [2.14] 4 2.14 Urban four-lane with TWLTL (U5T) [1.40] 11 1.40 Rural four-lane freeways (multi-vehicle, fatal + injury 28 1.29 crashes) Rural four-lane freeways (single-vehicle and fatal + 28 0.65 injury crashes) Rural four-lane freeways (multi-vehicle PDO crashes) 28 1.57 Rural four-lane freeways (single-vehicle PDO crashes) 28 1.48 Urban four-lane freeways (multi-vehicle, fatal + injury 13 0.79 crashes) Urban four-lane freeways (single-vehicle and fatal + 13 0.59 injury crashes) Urban four-lane freeways (multi-vehicle PDO crashes) 13 0.84 Urban four-lane freeways (single-vehicle PDO crashes) 13 0.69 Urban six-lane freeways (multi-vehicle, fatal + injury 14 0.78 crashes) Urban six-lane freeways (single-vehicle and fatal + 14 0.84 injury crashes) Urban six-lane freeways (multi-vehicle PDO crashes) 14 0.78 Urban six-lane freeways (single-vehicle PDO crashes) 14 1.16 Urban eight-lane freeways (multi-vehicle, fatal + injury 5 0.59 crashes) Urban eight-lane freeways (single-vehicle and fatal + 5 0.65 injury crashes) Urban eight-lane freeways (multi-vehicle PDO 5 0.76 crashes) Urban eight-lane freeways (single-vehicle PDO 5 0.86 crashes) *Regionalized calibration factors available for Coastal (C), Piedmont (P), and Mountain (M).Table 45.ââ Intersection calibration factors for North Carolina from Smith et al. (2017). Sample Size Facility Type Calibration Factor (No. of Sites) Intersections on two-lane, two-way rural roads Three-leg minor stop controlled (R2 3ST) 173* [35C, 37M, 101P] 0.58* [0.51C, 0.69M, 0.55P] Four-leg signalized (R2 4SG) 85* [26C, 14M, 45P] 0.77* [0.99C, 0.63M, 0.71P] Four-leg minor stop controlled (R2 4ST) 203* [91C, 28M, 84P] 0.63* [0.65C, 0.50M, 0.67P] Intersections on rural multi-lane roads Three-leg minor stop-controlled intersections (RM 3ST) 15 0.36 Four-leg signalized intersections (RM 4SG) 27 0.41 Four-leg minor stop-controlled intersections (RM 4ST) 22 1.44 Intersections on urban arterials Three-leg minor stop controlled (U3ST) 52 1.61 Three-leg signalized intersection (U3SG) 33 2.17 Four-leg signalized (U4SG) 102 1.79 Four-leg minor stop controlled (U4ST) 56 3.07*Regionalized calibration factors available for Coastal (C), Piedmont (P), and Mountain (M).
Table 46.ââ Segment calibration factors for North Carolina from Saleem et al. (2021). Sample Size Facility Type Calibration Factor (Miles) Rural two-lane undivided (R2U) 732.74 [193.78C, 1.29* [1.55C, 1.21M, 277.8M, 261.08P] 1.21P] Rural four-lane divided (R4U) 197.27 [60.21C, 1.39* [1.53C, 1.33M, 77.28M, 59.78P] 1.32P] Urban two-lane undivided (U2U) 42.01 1.54 Urban two-lane with TWLTL (U3T) 19.16 2.02 Urban four-lane undivided (U4U) 7.51 2.08 Urban four-lane divided (U4D) 4.17 1.67 Urban four-lane with TWLTL (U5T) 15.71 1.22 Rural four-lane freeways (multi-vehicle, fatal + injury 1.23 crashes) Rural four-lane freeways (single-vehicle and fatal + 0.73 30.12 injury crashes) Rural four-lane freeways (multi-vehicle PDO crashes) 1.48 Rural four-lane freeways (single-vehicle PDO crashes) 1.09 Urban four-lane freeways (multi-vehicle, fatal + injury 1.20 crashes) Urban four-lane freeways (single-vehicle and fatal + 19.79 0.76 injury crashes) Urban four-lane freeways (multi-vehicle PDO crashes) 1.74 Urban four-lane freeways (single-vehicle PDO crashes) 0.89 Urban six-lane freeways (multi-vehicle, fatal + injury 1.19 crashes) Urban six-lane freeways (single-vehicle and fatal + 18.84 0.78 injury crashes) Urban six-lane freeways (multi-vehicle PDO crashes) 1.44 Urban six-lane freeways (single-vehicle PDO crashes) 0.98 Urban eight-lane freeways (multi-vehicle, fatal + injury 1.06 crashes) Urban eight-lane freeways (single-vehicle and fatal + 0.66 12.52 injury crashes) Urban eight-lane freeways (multi-vehicle PDO crashes) 1.42 Urban eight-lane freeways (single-vehicle PDO crashes) 0.83*Regionalized calibration factors available for Coastal (C), Piedmont (P), and Mountain (M). Table 47.ââ Intersection calibration factors for North Carolina from Saleem et al. (2021). Sample Size Facility Type Calibration Factor (Intersections) Intersections on two-lane, two-way rural roads Three-leg minor stop controlled (R2 3ST) 208 [47C, 51M, 110P] 0.67* [0.63C, 0.64M, 0.70P] Four-leg signalized (R2 4SG) 105 [28C, 18M, 59P] 0.87* [1.17C, 0.60M, 0.83P] Four-leg minor stop controlled (R2 4ST) 234 [103C, 32M, 99P] 0.73* [0.86C, 0.58M, 0.69P] Intersections on rural-multi-lane roads Three-leg minor stop-controlled intersections (RM 14 0.58 3ST) Four-leg signalized intersections (RM 4SG) 28 0.32 Four-leg minor stop-controlled intersections (RM 4ST) 21 1.15 Intersections on urban arterials Three-leg minor stop controlled (U3ST) 7 2.26 Three-leg signalized intersection (U3SG) 53 2.40 Four-leg signalized (U4SG) 117 3.23 Four-leg minor stop controlled (U4ST) 18 1.31 *Regionalized calibration factors available for Coastal (C), Piedmont (P), and Mountain (M)
56ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 48.ââ Calibration factors for Ohio from Troyer et al. (2015). Sample Size Calibration Facility Type (No. of Sites) Factor Rural two-way, two-lane roads Road segments (R2U) 350 1.20 Three-leg minor stop-controlled intersections (R2 200 1.51 3ST) Four-leg minor stop-controlled intersections (R2 200 1.50 4ST) Four-leg signalized intersections (R2 4SG) 200 1.86 Rural multi-lane highways Divided road segments (RMD) 150 1.31 Undivided road segments (RMU) 150 1.61 Three-leg minor stop-controlled intersections (RM 200 1.66 3ST) Four-leg minor stop-controlled intersections (RM 250 1.73 4ST) Four-leg signalized intersections (RM 4SG) 50 1.33 Urban and suburban arterials Two-lane undivided road segments (U2U) 150 1.02 Three-lane segments with TWLTL (U3T) 150 0.45 Four-lane undivided road segments (U4U) 150 0.24 Four-lane divided road segments (U4D) 150 0.79 Five-lane road segments with TWLTL (U5T) 150 0.36 Three-leg minor stop-controlled intersections 50 1.34 (U3ST) Three-leg signalized intersections (U3SG) 50 3.35 Four-leg minor stop-controlled intersections 125 1.60 (U4ST) Four-leg signalized intersections (U4SG) 50 3.71 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 â Rural four-lane â Rural six-lane â Urban four-lane â Urban six-lane â Urban eight+-lane â Urban seven+ lanes (within interchange influence areas) ⢠Interchange segments â Rural four-lane â Rural six-lane â Urban four-lane â 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
Literature Reviewââ 57outside shoulder widths, depressed median widths, presence of weaving, lane addition or lanedrop, degree of curvature, proportion of a segment that was a curve, presence of median andoutside barriers, and posted speed limit. Maistros (2022) documents the calibration of design-level SPFs for three additional site typesincluded in the ECAT (Economic Crash Analysis Tool) used in Ohio to implement predictivesafety analysis. These site types included: urban four-leg signalized intersections on high-speedarterials (10 sites), urban four-leg single-lane roundabouts (51 sites), and urban four-leg multi-lane roundabouts (33 sites). The specific calibration factors were not provided. Two other sitetypes were identified as having sufficient sample size for calibration but lacked observed crashdata: rural four-leg all-way stop-controlled intersections (81 sites) and urban four-leg all-waystop-controlled intersections (27 sites).OklahomaSummary Calibrated SPFs? None State-specific SPFs? Design-level Responses received from Oklahoma to the survey described in Chapter 3 indicate that Oklahomaboth applies calibration factors and state-specific SPFs. However, no documentation was foundon the development of calibration factors for Oklahoma. Li and Yu (2021) developed design-level SPFs for total crash frequency on roadway segmentsof U.S. interstates and state highways in Oklahoma using crash data from 2012 to 2016, considering5,626 segments comprising 5,643 lane miles. Specific features accounted for within this SPFincluded: 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 fornetwork screening purposes.OregonSummary Calibrated SPFs? Design-level State-specific SPFs? Design-level Monsere et al. (2011) used crash data from 2005 to 2007 to develop design-level SPFs to predicttotal crash frequency on rural three-leg stop-controlled intersections and urban four-leg signal-ized intersections. Approximately 200 rural and 300 urban intersections were considered in thesample. Many explanatory variables were considered in the SPF development process, includingtraffic 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. How-ever, 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 withcalibrated versions of the associated SPFs in the HSM. The calibration factors developed arepresented in Table 49. The state-specific SPFs were found to provide better predictions and thuswere ultimately recommended for use in Oregon. Table 49.ââ Calibration factors for Oregon from Monsere et al. (2011). Facility Type Calibration Factor Rural three-leg stop-controlled intersections (R3ST) 0.32 Urban four-leg signalized intersections (U4SG) 1.054
58ââ Calibration and Development of State-DOT-Specific Safety Performance Functions 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 cali- brated SPF predictions. Calibration factors for urban arterials were also estimated separately for specific regions (âclimate zonesâ) 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. The authors specifically mentioned that property damage-only crashes in Oregon are self- reported (with a threshold of $1,500 damage for reporting); thus, this might contribute to the calibration factors that are significantly different from 1.0 in most cases. Additionally, rural minor-road traffic volumes were estimated for many sites using a regression model that con- sidered several factors, including (a) county population, (b) population of nearest city, (c) aver- age per capita income of the region, (d) distance to nearest freeway, (e) roadway type, (f) if the location was within a city limit, (g) presence of turn lanes, (h) centerline presence, (i) if adjacent lane use was developed, and (j) presence of striped edge lines. Table 50.ââ Calibration factors for Oregon from Dixon et al. (2012). Calibration Regionalized Calibration Factor Calibration Calibration Factor Facility Type (Fatal + Factor Factor Range (Total Injury (PDO Crashes) (Total Crashes) Crashes) Crashes) Roadway Segments Rural two-lane (R2U) 0.74 1.15 n/a n/a Rural multi-lane undivided (UMU) 0.37 0.26 n/a n/a Rural multi-lane divided (UMD) 0.77 0.68 n/a n/a Urban two-lane undivided (U2U) 0.62 1.00 0.47 0.434â0.955 Urban three-lane with TWLTL (U3T) 0.81 1.16 0.68 0.411â1.484 Urban four-lane divided (U4D) 1.41 1.93 1.23 1.042â2.311 Urban four-lane undivided (U4U) 0.63 0.96 0.50 0.218â0.994 Urban ï¬ve-lane with TWLTL (U5T) 0.64 0.92 0.52 0.000â0.811 Intersections Rural two-lane, three-leg stop controlled 0.31 0.41 n/a n/a (R2 3ST) Rural two-lane, four-leg stop controlled (R2 0.31 0.48 n/a n/a 4ST) Rural two-lane, four-leg signalized (R2 0.45 0.67 n/a n/a 4SG) Rural multi-lane, three-leg stop controlled 0.15 0.23 n/a n/a (RM 3ST) Rural multi-lane, four-leg stop controlled 0.39 0.48 n/a n/a (RM 4ST) Rural multi-lane, three-leg stop signalized 0.15 0.17 n/a n/a (RM 4SG) Urban arterial, three-leg stop controlled 0.35 0.51 0.26 n/a (U3ST) Urban arterial, four-leg stop controlled 0.44 0.54 0.38 n/a (U4ST) Urban arterial, three-leg signalized (U3SG) 0.73 1.07 0.58 n/a Urban arterial, four-leg signalized (U4SG) 1.05 1.36 0.94 n/a
Literature Reviewââ 59 Dixon et al. (2015) developed design-level SPFs for signalized intersections in Oregon usingobserved crash data from 2010 to 2012, considering 66 unique intersections and an additional25 sites used for validation. Unique SPFs were estimated for total crash frequency and KABcrash frequency. In both cases, the set of intersections considered included four-leg signalizedintersections on rural two-lane roads, signalized intersections on rural multi-lane highways,and both three- and four-leg intersections on urban/suburban arterials (combined together).Network-screening-level SPFs were estimated where only major- and minor-road volumes wereconsidered as input variables for total crash frequency and traffic volumes and major-roadspeed limit for KAB crash frequency. Similar to the previous study, minor-road volumes wereestimated for intersections where actual values were not available; explanatory variables con-sidered included (a) major-road volumes, (b) parallel road volumes, (c) the number of throughlanes on the approach, and (d) functional and roadway functional classification. However,the project finally recommended applying a crash type proportion model to the predictedtotal crash frequency value to estimate the frequency of KAB crashes. This model included,as inputs, a major-road speed limit and speed limit difference between the major and minorapproaches.PennsylvaniaSummary Calibrated SPFs? Network-screening-level State-specific SPFs? Design-level Donnell et al. (2014) developed design-level SPFs for total crashes and fatal + injury crasheson both roadway segments and intersections of two-lane, two-way rural roads in Pennsylvaniausing observed crash data from 2005 to 2012, considering 21,340 unique roadway segmentsand 683 unique intersections. The SPFs for roadway segments included adjustment factors for(a) roadside hazard rating, (b) presence of shoulder rumble strips and passing zones, (c) accessdensity, horizontal curve density, and (d) degree of horizontal curvature. Intersection SPFs andthe associated adjustment factors considered are provided in Table 51. Table 51.ââ Summary of adjustment factors included in Pennsylvania SPFs in Donnell et al. (2014). Facility Type Adjustment Factors Four-leg signalized intersections (R2 4SG) ⢠Posted speed limit on major approach ⢠Posted speed limit on minor approach ⢠Presence of exclusive right-turn lane on either major approach Three-leg signalized intersections (R2 3SG) ⢠Posted speed limit on major approach ⢠Presence of a crosswalk on the major approach ⢠Presence of a crosswalk on the minor approach Four-leg all-way stop-controlled intersections (R2 ⢠Posted speed limit on major approach 4aST) Four-leg minor stop-controlled intersections (R2 ⢠Intersection skew angle 4ST) Three-leg minor stop-controlled intersections (R2 ⢠Presence of exclusive right-turn lane on 3ST) major approach ⢠Presence of exclusive left-turn lane on major approach
60ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Donnell et al. (2016) updated the design-level SPFs developed in the previous report to reflect more observed crash data (2005 to 2014) and to account for regional differences in the state. Sample sizes for each facility remained the same between the two reports. Additionally, new design-level SPFs were developed for roadway segments and intersections on rural multi-lane highways and urbanâsuburban arterials using observed crash data from 2010 to 2014, consider- ing 1,362 rural multi-lane highway segments, 168 rural multi-lane intersection sites, 16,780 urbanâ suburban arterial segments, and 4,472 unique intersections on urbanâsuburban arterials. This project also specifically focused on the development of regionalized SPFs within Pennsylvania. Three regionalization levels were considered: (1) unique SPFs developed for individual PennDOT engineering districts with adjustments for individual counties within that district; (2) statewide SPFs with adjustments for engineering districts within Pennsylvania; and (3) a statewide SPF. Table 52 summarizes the set of SPFs developed, the associated regionalization level, and the adjustment factors considered. Donnell et al. (2019) developed design-level SPFs for roadway segments and intersections of urbanâsuburban collector roadways in Pennsylvania using observed crash data from 2013 to 2017, considering 7,492 unique segments and 783 unique intersection sites. The same regional- ization process from the 2016 report was also used to consider variation in safety performance throughout the state. Table 53 summarizes the specific SPFs that were developed, the level of regionalization, and the adjustment factors that were considered. Jenior (2020) developed calibration factors for several ramp and freeway SPFs included in the HSM supplement using crash data from 2013 to 2017. This was done as a part of a larger network screening process. Sample sizes were not provided. Table 54 provides a summary of the calibration factors that were obtained. Rhode Island Summary Calibrated SPFs? None State-specific SPFs? None The authors did not find any documentation of state customization of HSM tools or SPFs for Rhode Island. South Carolina Summary Calibrated SPFs? Design-level State-specific SPFs? Design-level Ogle and Rajabi (2018) developed calibration factors and state-specific design-level SPFs for total crashes on 21 different facilities including both rural and urban segments and intersections using observed crash data from 2013 to 2015. Sample sizes ranged from 73 to 1,841 segments totaling between 15.73 to 1,117.73 miles for roadways segments, 80 to 7,000 sites for intersections, and 105 to 138 segments totaling 36.34 to 59.38 miles for freeways. Calibration factors were developed using the HSM methodology and are provided in Table 55. SPFs were developed using NB regression considering variables of (a) AADT, (b) lighting, (c) presence of turning lanes, (d) intersection skew angles, (e) lane width, (f) shoulder width, (g) median width, (h) grade, (i) horizontal curves, (j) driveway density, and (k) roadside hazard rating. Crash distribution tables were provided to allow for the prediction of other crash types and severities. The authors suggested that the state-specific SPFs would be more accurate than the calibrated national SPFs.
Literature Reviewââ 61Table 52.ââ Summary of adjustment factors included in Pennsylvania SPFsin Donnell et al. (2014). RegionalizationFacility Type Adjustment Factors LevelTwo-lane, two-way rural roadsRoad segments District-level with ⢠Roadside hazard rating(R2U) county-speciï¬c ⢠Passing zone adjustments ⢠Shoulder rumble strips ⢠Access density ⢠Horizontal curve density ⢠Degree of curvature per mileThree-leg Statewide ⢠Exclusive right-turn lane on major approachintersections with ⢠Exclusive left-turn lane on major approachminor-street stopcontrol(R2 3ST)Four-leg Statewide ⢠Intersection skew angleintersections withminor-street stopcontrol(R2 4ST)Four-leg Statewide ⢠Posted speed limit on major approachintersections withall-way stopcontrol (R2 4aST)Three-leg Statewide ⢠Posted speed limit on major approachintersections with ⢠Crosswalk on the major approachsignal control (R2 ⢠Crosswalk on the minor approach3SG)Four-leg Statewide ⢠Posted speed limit on major approachintersections with ⢠Posted speed limit on minor approachsignal control (R2 ⢠Exclusive right-turn lane on either major approach4SG)Rural multi-lane highwaysRoadway segments Statewide with ⢠Presence of a median barrier(RMU, RMD) district-speciï¬c ⢠Degree of curvature per mile adjustments ⢠Roadside hazard rating ⢠Access density ⢠Posted speed limit ⢠Centerline rumble strips ⢠Shoulder rumble stripsThree-leg Statewide ⢠noneintersections withminor-street stopcontrol(RM 3ST)Four-leg Statewide ⢠noneintersections withminor-street stopcontrol(RM 4ST)Four-leg Statewide ⢠noneintersections withsignal control (RM4SG) (continued on next page)
62ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 52.ââ(Continued). Regionalization Facility Type Adjustment Factors Level Urbanâsuburban arterials Two-lane District-level with ⢠Posted speed limit undivided arterials county-speciï¬c ⢠Center two-way left turn lane (U2U) adjustments ⢠Parking lane Four-lane Statewide with ⢠Posted speed limit undivided arterials district-speciï¬c ⢠Center two-way left turn lane (U4U) adjustments ⢠Parking lane Four-lane divided Statewide with ⢠Posted speed limit arterials (U4D) district-speciï¬c ⢠Center two-way left turn lane adjustments ⢠Median barrier Three-leg District-level with ⢠Posted speed limit on major road intersections with county-speciï¬c ⢠Posted speed limit on minor road minor-street stop adjustments control (U3ST) Four-leg Statewide with ⢠Posted speed limit on major road intersections with district-speciï¬c ⢠Posted speed limit on minor road minor-street stop adjustments control (U4ST) Three-leg Statewide with ⢠Posted speed limit on major road signalized district-speciï¬c ⢠Exclusive left-turn lane on major approach intersections adjustments ⢠Exclusive left-turn lane on minor approach (U3SG) Four-leg signalized Statewide with ⢠Posted speed limit on major road intersections district-speciï¬c ⢠Posted speed limit on minor road (U4SG) adjustments ⢠Exclusive left-turn lane on major approach ⢠Exclusive left-turn lane on minor approach ⢠Exclusive right-turn lane on major approach ⢠Exclusive right-turn lane on minor approach Table 53.ââ Summary of adjustment factors included in Pennsylvania SPFs in Donnell et al. (2019). Regionalization Facility Type Adjustment Factors Level Roadway segments Two-lane District-level with ⢠Degree of curvature per mile undivided (U2U) county-speciï¬c ⢠On-street parking adjustments ⢠Raised curb ⢠Posted speed limit ⢠Short segment Intersections Three-leg minor- Statewide with ⢠Crosswalk on major approach street stop district-speciï¬c ⢠Major posted speed limit controlled (U3ST) adjustments Three-leg all-way Statewide ⢠None stop controlled (U3aST) Four-leg minor- Statewide ⢠None street stop controlled (U4ST) Four-leg all-way Statewide ⢠None stop controlled (U4aST) Four-leg signalized Statewide ⢠None (U4SG)
Literature Reviewââ 63Table 54.ââ Freeway site calibration factors for Pennsylvania from Jenior (2020). Fatal + Injury Fatal + Injury PDO PDO Facility Type (Multi- (Single- (Multi- (Single- Vehicle) Vehicle) Vehicle) Vehicle)Basic freeway segment 1.07 0.93 0.43 0.66Signalized ramp terminal 0.49 (multi + single 0.67 (multi + single vehicle) vehicle)Stop-controlled ramp terminal 1.04 (multi + single 1.37 (multi + single vehicle) vehicle)Ramps (entrance, exit, and connector) 1.00 1.00 0.49 0.49Speed-change lanes and collector distributor roads 1.00 (all crashes) Table 55.ââ Calibration factors for South Carolina from Ogle and Rajabi (2018). Sample Size Sample Size Calibration Facility Type (No. of Sites) (Miles) Factor Segments Two-lane two-way undivided rural roads 1,841 1,117.73 0.99 (R2U) Four-lane divided rural roads (R4D) 508 161.16 0.61 Four-lane undivided rural roads (R4U) 484 126.25 0.31 Two-lane two-way undivided urban roads 667 201.65 1.66 (U2U) Two-lane two-way urban roads with TWLTL 73 15.73 1.47 (U3T) Four-lane undivided urban roads (U4U) 349 76.57 0.75 Four-lane divided urban roads (U4D) 352 85.02 0.83 Four-lane urban roads with TWLTL (U5T) 673 155.59 0.77 Intersections Rural three-leg stop-controlled intersection 7,000 n/a 0.40 (R3ST) Rural four-leg stop-controlled intersection 2,785 n/a 0.47 (R4ST) Rural four-leg signalized intersection (R4SG) 97 n/a 0.46 Three-leg stop-controlled intersection on rural 613 n/a 0.55 multi-lane highway (RM3ST) Four-leg stop-controlled intersection on rural 284 n/a 0.26 multi-lane highway (RM4ST) Four-leg signalized intersection on rural 80 n/a 0.40 multi-lane highway (RM4SG) Urban three-leg stop-controlled intersection 5,607 n/a 1.20 (U3ST) Urban four-leg stop-controlled intersection 2,992 n/a 0.96 (U4ST) Urban three-leg signalized intersection 299 n/a 2.00 (U3SG) Urban four-leg signalized intersection (U4SG) 538 n/a 2.45 Interstates Rural four-lane freeway (R4F) 138 59.38 2.59 Urban four-lane freeway (U4F) 105 36.34 2.69 Urban six-lane freeway (U6F) 126 38.33 3.66
64ââ Calibration and Development of State-DOT-Specific Safety Performance Functions South Dakota Summary Calibrated SPFs? Design-level State-specific SPFs? Network-screening-level, design-level Qin et al. (2013) developed design-level SPFs for total crashes on rural local two-lane two-way highway segments using observed crash data from 657 segments comprising approximately 750 miles occurring between 2009 and 2011. Four new models were developed using NB regression and Poisson regression following different forms of AADT and segment length as an offset and were compared to the HSM default SPF and each other based on MAD, correlation coefficient, and the calculated calibration factor for the new SPF. Ultimately, the Poisson models were found to better fit the South Dakota data, having a calibration factor closer to 1 than the HSM SPF or the NB models, and correlation coefficients and MAD nearly identical to the HSM SPF. The HSM SPF calibration factor for South Dakota was found to be 1.5368 as presented in Table 56, but that model was not recommended for use. Two additional models were developed for seg- ments on tribal lands based on crash data from the same time period based on 56 segments (approximately 200 miles), and a model considering a logarithmic form of AADT was recom- mended for this purpose. Qin et al. (2016) developed calibration factors and state-specific design-level SPFs for total crashes on rural two-lane two-way highways, rural multi-lane undivided highways, and rural multi-lane undivided highways using observed crash data from 2008 to 2016. Calibration factors were calculated through the HSM methodology while SPFs were developed through NB regres- sion. Calibration factors for both the HSM SPFs and the newly developed SPFs are provided in Table 57. In addition to comparing calibration factors, each predictive method was evaluated based on the sum of absolute errors (SAE) and two forms of symmetric mean absolute percentage errors (SMAPE). The calibrated state-specific model was found to outperform the calibrated HSM model in all goodness-of-fit measures. Qin et al. (2019) developed network-screening-level SPFs for total crashes at three-leg stop- controlled intersections on rural two-lane roads (337 sites) and four-leg stop-controlled inter sections on rural two-lane roads (582 sites) in South Dakota using observed crash data from 2009 Table 56.ââ Calibration factor for South Dakota from Qin et al. (2013). Facility Type Calibration Factor Two-lane two-way rural roads (R2U) 1.5368* *Not recommended for use due to limited sample size. Table 57.ââ Calibration factors for South Dakota from Qin et al. (2016). HSM SPF State-Speciï¬c Sample Sample Facility Type Calibration SPF Calibration Size Length (Miles) Factor Factor Rural two-lane undivided 16,828 6,362 1.18 0.99 roadway segments (R2U) Rural four-lane undivided 1,210 152 1.14 1.01 roadway segments (R4U) Rural four-lane divided 1,619 634 1.57 1.03 roadway segments (R4D)
Literature Reviewââ 65to 2011. NB regression was employed to develop the SPFs considering AADT of minor- andmajor-road approaches, as well as regional differences between the Eastern South Dakota, Pierre,and Rapid City regions. A proportion function for fatal and injury crashes was also provided, allow-ing for the prediction of these crash types based on the newly developed SPFs.TennesseeSummary Calibrated SPFs? Network-screening-level, design-level State-specific SPFs? Network-screening-level, design-level Khattak et al. (2017a) used observed crash data from 2011 to 2015 to develop calibrationfactors and network-screening-level SPFs for intersections on two-lane, two-way rural roads inTennessee using data from 299 roadway segments. Calibration factors were developed using base(i.e., network-screening-level) SPFs and design-level SPFs that incorporated adjustment factors.Table 58 provides a summary of the calibration factors that were obtained, including both statewideand regionalized values. Khattak et al. (2017b) used observed crash data from 2011 to 2015 to develop calibration factorsand network-screening-level SPFs for intersections on two-lane, two-way rural roads in Tennessee.Table 59 provides a summary of the calibration factors that were obtained, including both statewideand regionalized values. Between 37 and 238 intersections were available for each site type/regioncombination for which a calibration factor was developed. Khattak et al. (2020) developed calibration factors and state-specific network-screening-levelSPFs for rural multi-lane and urbanâsuburban highway segments in Tennessee using observedcrash data from 2013 to 2017. Table 60 provides a summary of the estimated calibration factors Table 58.ââ Calibration factors for two-lane rural roadway segments in Tennessee from Khattak et al. (2017a). Sample TDOT TDOT TDOT TDOT Tennessee Facility Size Region Region Region Region Statewide (Segments) 1 2 3 4 Base calibration factors 299 2.980 3.532 2.696 3.313 2.311 (R2U) Calibration factors with adjustment factors included 299 2.489 2.584 2.444 2.776 2.023 (R2U) Table 59.ââ Calibration factors for Tennessee from Khattak et al. (2017b). TDOT TDOT TDOT TDOT Sample Size Tennessee Facility Region Region Region Region (Intersections) Statewide 1 2 3 4 Unsignalized three-leg (stop control on minor 287 0.633 0.542 0.654 0.773 0.646 approaches) (R2 3ST) Unsignalized four-leg (stop control on minor 196 0.980 0.961 1.073 0.967 0.955 approaches) (R2 4ST) Signalized four-leg (R2 4SG) 86 0.730 â â 0.768 â
66ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 60.ââ Calibration factors for Tennessee from Khattak et al. (2020). Calibration Location Facility Type Number of Sites Factor Two-lane two-way (R2U) n/a 2.49 Four-lane (multi-lane, divided) 296 (187 miles) 1.47 Rural (R4D) Four-lane (multi-lane, undivided) 81 (34 miles) 2.25 (R4U) Two-lane (U2U) 234 (125 miles) 4.71 Urban Three-lane (U3T) 80 (24 miles) 5.82 and Four-lane (U4D) 278 (101 miles) 4.46 Suburban Four-lane (U4U) 80 (20 miles) 7.63 Five-lane (U5T) 304 (103 miles) 3.57 and sample sizes considered. Adjustment factors for state-specific SPFs were considered for the following features: driveway density, median presence, and median shoulder width. Chimba (2020) developed calibration factors and state-specific network-screening-level SPFs for intersections of the same facility types in the previous report using observed crash data from 2011 to 2015. Sample sizes generally ranged from 36 to 165 intersections; however, 4ST inter- sections on multi-lane rural roads had a sample size of just 12 intersections. Calibration factors are summarized in Table 61. SPFs were developed for single-vehicle crashes and multi-vehicle crashes for urban intersections and total crashes for rural intersections; however, these included only traffic volumes as input variables and thus were network-screening-level SPFs. Khattak et al. (2022) developed calibration factors and state-specific design-level SPFs for freeway segments and interchanges in Tennessee using observed crash data from 2015 to 2019. Approximately 300 segments (totaling approximately 30 miles) from interstates and express- ways and 80 ramps (40 entrances and 40 exits) were used for SPF development. The calibration factors were developed using two methods: a single calibration factor for each freeway facility (first approach) and unique calibration factors for each component (e.g., freeway segment and speed-change lane) within a facility (second approach). The calibration factors are summarized in Table 62 and Table 63. Traditional negative binomial-based SPFs and localized models based on geographically and temporarily weighted regressions were developed. The localized models were found to better fit the observed data, which suggests that SPF model coefficients might change over time and space in Tennessee; however, these are more difficult to implement and not consistent with the SPFs in the HSM. Table 61.ââ Calibration factors for Tennessee from Chimba (2020). Urban Intersection Single-Vehicle Urban Intersection Multi-Vehicle Rural Multi-Lane Collisions Collisions Facility Type Calibration Sample Calibration Calibration Sample Size Sample Size Factor Size Factor Factor Unsignalized three-leg (stop control on 2.201 36 1.805 156 2.505 156 minor approaches) (3ST) Unsignalized four-leg (stop control on 1.959* 12 1.652 138 2.622 138 minor approaches) (4ST) Signalized three-leg (3SG) n/a n/a 0.819 131 2.000 131 Signalized four-leg (4SG) 0.526* 23 0.982 165 1.834 165 *Without applying CMFs.
Literature Reviewââ 67 Table 62.ââ Calibration factors for Tennessee interstates and expressways from Khattak et al. (2022). Calibration Factors Approach Crash Type Interstates Expressways (N=281) (N=133) Single Fatal and injury (FI) 0.67 0.67 calibration Property damage only (PDO) 1.00 1.11 factor per Total freeway 0.90 0.98 facility Non-ramp related (FI) 0.66 0.68 Unique Non-ramp related (PDO) 0.96 1.10 calibration Ramp entrance speed-change lanes (FI) 0.91 0.74 factor for Ramp entrance speed-change lanes (PDO) 2.40 1.73 each Ramp exit speed-change lanes (FI) 0.67 0.49 component Ramp exit speed-change lanes (PDO) 0.92 0.66 Table 63.ââ Ramp calibration factors for Tennessee from Khattak et al. (2022). Ramp Type Crash Type Calibration Factor Fatal and injury 1.19 Entrance ramp Property damage only 1.71 (N=40) Total 1.52 Fatal and injury 1.77 Exit ramp Property damage only 2.26 (N=40) Total 2.07TexasSummary Calibrated SPFs? Network-screening-level, design-level State-specific SPFs? Design-level Geedipally et al. (2022) calibrated design-level HSM SPFs and developed state-specific design-level SPFs for facilities in HSM Chapters 10, 11, 12, and the HSM freeways supplement usingobserved crash data from 2017 to 2020. Additionally, state-specific design-level SPFs were alsodeveloped for one-way and two-way frontage roads and ramp segments. Calibration factors were calculated state-wide and regionally using the HSM methodology,and in the case of rural freeways, in two stages: Stage 1, using 100 segments with data from a stateroad-log database; and Stage 2, using 30â50 segments with data from supplemental data sources.The segment sample sizes ranged from 166 to 262 randomly selected segments, intersection samplesizes ranged from 28 to 348 sites, and frontage road sample sizes ranged from 100 to 413 sites.Table 64 to Table 68 show the calibration factors calculated as part of this study. Calibration factors were assessed for reliability using the coefficient of variation; in caseswhere the factors were deemed unreliable, new SPFs were developed and recommended for use.The following final recommendations were made:⢠Rural two-lane undivided highways â Roadway segments (R2U) â state-specific SPF â 3ST intersections â state-specific SPF â 4ST intersections â state-specific SPF â 4SG intersections â calibrated HSM SPF
68ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 64.ââ Calibration factors for Texas roadway segments from Geedipally et al. (2022). Sample Size Calibration Facility Type Crash Type (Segments) Factor Two-lane two-way undivided rural roads (R2U) 220 All 0.82 Four-lane divided rural roads (R4D) 175 All 0.91 Four-lane undivided rural roads (R4U) 232 All 0.69 Two-lane two-way undivided urban roads 186 MV 0.94 (U2U) 186 SV 1.10 Two-lane two-way urban roads with TWLTL 262 MV 0.61 (U3T) 262 SV 1.48 202 MV 1.67 Four-lane divided urban roads (U4D) 202 SV 1.97 166 MV 1.34 Four-lane undivided urban roads (U4U) 166 SV 1.50 171 MV 0.50 Four-lane urban roads with TWLTL (U5T) 171 SV 0.74 MV â Multi-vehicle, SV â Single-vehicle. Table 65.ââ Calibration factors for Texas intersections from Geedipally et al. (2022). Sample Size Intersection Crash Calibration Segment Type (Sites) Type Factor Rural two-lane 337 3ST-All 0.62 highways 222 4ST-All 0.64 (R2U) 133 4SG-All 0.58 Rural multi-lane 348 3ST-All 0.71 highways 208 4ST-All 0.75 (RMU, RMD) 106 4SG-All 0.29 326 3ST-MV 0.45 326 3ST-SV 0.16 75 4ST-MV 0.47 Urban arterials 75 4ST-SV 0.23 (UA) 28 3SG-MV 1.03 28 3SG-SV 0.89 113 4SG-MV 1.18 113 4SG-SV 1.22 MV â Multi-vehicle, SV â Single-vehicle. Table 66.ââ Calibration factors for Texas rural freeways from Geedipally et al. (2022). Sample Size Crash Stage 1 Stage 2 Facility Type (Segments) Type Calibration Factor Calibration Factor Four-lane Stage 1: MV FI 0.90 0.67 rural 101 (57.6 miles) MV PDO 1.00 0.77 freeways Stage 2: SV FI 0.55 0.56 (R4F) 45 (25.4 miles) SV PDO 0.74 0.68 Six-lane Stage 1: MV FI 0.98 0.63 rural 86 (49.7 miles) MV PDO 0.95 0.60 freeways Stage 2: SV FI 0.68 0.71 (R6F) 27 (15.2 miles) SV PDO 0.92 0.81
Literature Reviewââ 69 Table 67.ââ Calibration factors (regionalized) for Texas non-freeway segments from Geedipally et al. (2022). Calibration Factors Facility Type North South East West Region Region Region Region Two- lane two-way undivided 1.1 0.60 1.20 0.94 rural roads (R2U) Four-lane divided rural roads 0.91 1.11 1.01 0.90 (R4D) Four-lane undivided rural 0.89 1.03 1.23 0.71 roads (R4U) Two-lane two-way undivided 0.91 1.05 0.82 1.19 urban roads (U2U) Two-lane urban roads with 1.02 0.83 1.46 1.00 TWLTL (U3T) Four-lane divided urban roads 0.82 0.91 1.42 1.41 (U4D) Four-lane undivided urban 0.80 0.86 0.85 1.59 roads (U4U) Four-lane urban roads with 0.68 0.80 1.63 1.00 TWLTL (U5T) Table 68.ââ Calibration factors (regionalized) for Texas freeways from Geedipally et al. (2022). Calibration Factors Collision Type/ Facility Type North South East West Severity Region Region Region Region SV FI 1.00 0.82 1.33 0.72 SV PDO 1.18 0.67 1.1 1.03 Freeways MV FI 0.83 0.82 1.57 1.08 MV PDO 1.07 0.62 1.84 1.68⢠Rural multi-lane highways â Undivided roadway segments (R4U) â calibrated HSM SPF â Divided roadway segments (R4D) â state-specific SPF â 3ST intersections â state-specific SPF â 4ST intersections â state-specific SPF â 4SG intersections â calibrated HSM SPF⢠Urban arterials â Two-lane undivided roadway segments (U2U)â state-specific SPFs â Two-lane roadway segments with TWLTL (U3T) â calibrated HSM SPFs â Four-lane undivided roadway segments (U4U) â calibrated HSM SPF for multi-vehicle crashes, state-specific SPF for single-vehicle crashes â Four-lane divided roadway segments (U4D) â state-specific SPFs â Four-lane roadway segments with TWLTL (U5T) â state-specific SPFs â 3ST intersections â state-specific SPF â 4ST intersections â state-specific SPF â 3SG intersections â calibrated HSM SPF â 4SG intersections â calibrated HSM SPF
70ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Additional SPFs were developed for one- and two-way frontage roads because the HSM does not provide SPFs for frontage roads, and SPFs were also developed for single- and multi-vehicle crashes on freeway ramps due to unique ramp configurations specific to Texas. Pratt et al. (2023) developed calibration factors for network-screening level SPFs predicting single- and multi-vehicle fatal and injury, and PDO crashes on urban freeway segments with 4, 6, 8, and 10 general-purpose lanes using observed crash data from 2015 to 2019. Calibration factors were calculated through three different methods: first, by using all available segments for each site type (i.e., lane count); second, by calibrating over a sample of up to 550 segments with adjustment factors applied based on readily available data (such as lane and shoulder width); and third, by calibrating over a sample of 50 segments with all available adjustment factors applied, including those with requirements for data from supplementary sources. The results of all three methods are presented in Table 69. Calibration factors were evaluated based on CURE plots, MAD, MSPE, the dispersion parameter, and the coefficient of variation. Results from the calcula- tions suggested that there was not much difference between the first and second methods, but the third method showed marked improvement. Additional calibration was performed for 12-lane freeways using the second method while applying the 10-lane SPF to 12-lane facilities. In addition to calibration, the study developed screening-level SPFs for single- and multi- vehicle crashes considering AADT and segment length for reversible and non-reversible managed- lane freeway facilities, and CMFs to account for design-level variables such as (a) access weaving section density, (b) access ramp density, (c) shoulder widths, and (d) variation in lane buffers (barrier, pylon, or striped). Table 69.ââ Freeway segment calibration factors for Texas from Pratt et al. (2023). Local Calibration Factor Crash Type and Facility Type Method Method Method Severity 1 2 3 SV - FI 0.80 0.73 0.77 Urban freeway with four SV - PDO 0.94 0.84 0.68 general-purpose lanes MV - FI 1.04 0.94 0.65 MV - PDO 1.05 0.99 0.57 SV - FI 0.86 0.90 0.70 Urban freeway with ï¬ve SV - PDO 0.85 0.80 0.56 to six general-purpose lanes MV - FI 1.21 1.19 0.95 MV - PDO 1.12 1.06 0.71 SV - FI 1.00 1.05 1.25 Urban freeway with SV - PDO 1.00 0.94 1.04 seven to eight general- MV - FI 1.44 1.37 1.27 purpose lanes MV - PDO 1.20 1.14 1.20 SV - FI 0.98 0.97 1.02 Urban freeway with nine SV - PDO 1.18 1.17 0.95 to ten general-purpose MV - FI 2.18 2.24 1.41 lanes MV - PDO 2.14 2.19 1.30 SV - FI â 1.01 â Urban freeway with 12 SV - PDO â 0.77 â general-purpose lanes MV - FI â 1.13 â MV - PDO â 1.04 â Values in italics were recommended for use.
Literature Reviewââ 71UtahSummary Calibrated SPFs? Design-level State-specific SPFs? None Wall (2023) developed calibration factors for design-level HSM SPFs for varying crash typesand severities on rural two-lane two-way roads, rural divided and undivided multi-lane high-ways, urban arterials, rural and urban freeways, and associated intersections. Calibration factorswere determined for segments using observed crash data from 2017 to 2021, while intersectionswere calibrated using observations from 2016 to 2020. Sample sizes for segments ranged from21.8 to 3,886 miles, while intersections ranged from 35 to 110 sites. A few facility types hadnotably small sample sizes, including (a) eight-lane urban arterials (3.1 miles), (b) other arterials(2.7 miles), (c) urban 10-lane freeways (7 miles), (d) other freeways (3.8 miles), (e) 4SG inter-sections on rural two-lane two-way roads (three sites), (f) 3ST intersections on rural multi-lanehighways (nine sites), and (g) 4SG intersections on rural multi-lane highways (13 sites). In addi-tion to calibration factors, Utah-specific crash proportions for multi-vehicle crash types such asrear-end, angle, sideswipe, head-on, parked vehicle, and other crashes, were provided, allowingfor predictions of these crash types. A summary of the calibration factors published in the UtahCPM is presented in Table 70 and Table 71.VermontSummary Calibrated SPFs? Design-level State-specific SPFs? None Sullivan (2019) developed calibration factors for design-level HSM SPFs for total crashes onrural two-lane two-way roadway segments, as well as three- and four-leg intersections on thesesegments, using observed crash data from 2014 to 2016. State-specific network-screening-levelSPFs were also developed. A total of 3,801 miles of roadways were segmented into 9,664 hom*o-geneous segments, while 9, 99, and 977 sites were available for 4SG, 4ST, and 3ST intersections,respectively. SPFs were developed using statewide data and regional calibration factors werecalculated for the Northern, Central, and Southern geographic regions, and the Western, VermontPiedmont, and Green Mountain geological regions. A summary of the statewide calibration factorsis presented in Table 72. The study recommended using the state-specific SPFs for the R2U, 3ST,and 4ST facility types, and calibration factors applied to the HSM SPF for the 4SG facility type.VirginiaSummary Calibrated SPFs? Network-screening-level State-specific SPFs? Network-screening-level Garber et al. (2010) developed screening-level SPFs for total and fatal and injury crasheson urban and rural two-lane roads using observed crash data from 2003 to 2007. SPFs weredeveloped both statewide and regionally for north, east, and west regions of Virginia using NBregression over 70% of available data (82,030 rural sites and 57,605 urban sites, totaling about69,660 miles), while the remaining 30% of observations were held out for validation purposes.Comparison to SafetyAnalyst default SPFs using MSPE, R2, and Freeman-Tukey R2 suggestedthat the state-specific SPFs developed for Virginia were a better fit, and the authors recom-mended the adoption of the newly developed SPFs in addition to applying an Empirical Bayesadjustment.
72ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 70.ââ Segment calibration factors for Utah from Wall (2023). Sample Calibration Facility Type Size Crash Type Factor (Miles) 3,886 Fatal and injury 1.30 Rural two-lane two-way roads Total single-vehicle 1.63 (R2U) Total 1.53 Rural undivided multi-lane 72.8 Fatal and injury 0.41 highways PDO 1.50 (RMU) Total 0.99 24.2 Fatal and injury 0.90 Rural divided multi-lane highways PDO 2.20 (RMD) Total 1.66 268.6 Multi-vehicle fatal and injury 1.64 Single-vehicle fatal and injury Urban two-lane undivided arterials Multi-vehicle PDO (U2U) 1.55 Single-vehicle PDO Total 1.58 67.2 Multi-vehicle fatal and injury 1.92 Single-vehicle fatal and injury Urban two-lane arterial with Multi-vehicle PDO TWLTL (U3T) 1.49 Single-vehicle PDO Total 1.60 113.1 Multi-vehicle fatal and injury 1.33 Single-vehicle fatal and injury Urban four-lane divided arterial Multi-vehicle PDO (U4D) 1.21 Single-vehicle PDO Total 1.24 195.3 Multi-vehicle fatal and injury 1.33 Single-vehicle fatal and injury Urban four-lane undivided arterial Multi-vehicle PDO (U4U) 1.44 Single-vehicle PDO Total 1.41 189.8 Multi-vehicle fatal and injury 0.84 Single-vehicle fatal and injury Urban four-lane arterial with Multi-vehicle PDO TWLTL (U5T) 0.74 Single-vehicle PDO Total 0.77 27.6 Multi-vehicle fatal and injury 0.86 Single-vehicle fatal and injury Urban six-lane divided arterial Multi-vehicle PDO (U6D) 1.37 Single-vehicle PDO Total 1.17 85.4 Multi-vehicle fatal and injury 0.72 Single-vehicle fatal and injury Urban six-lane undivided arterial Multi-vehicle PDO (U6U) 1.17 Single-vehicle PDO Total 1.00 21.8 Multi-vehicle fatal and injury 0.84 Single-vehicle fatal and injury Urban six-lane arterial with TWLTL Multi-vehicle PDO (U7T) 1.29 Single-vehicle PDO Total 1.10
Literature Reviewââ 73Table 70.ââ(Continued). Sample Calibration Facility Type Size Crash Type Factor (Miles) 1,308.8 Multi-vehicle fatal and injury 0.81 Single-vehicle fatal and injury Rural four-lane freeways Multi-vehicle PDO (R4F) 1.32 Single-vehicle PDO Total 1.13 71.8 Multi-vehicle fatal and injury 1.23 Single-vehicle fatal and injury Rural six-lane freeways Multi-vehicle PDO (R6F) 1.88 Single-vehicle PDO Total 1.67 225.5 Multi-vehicle fatal and injury 0.85 Single-vehicle fatal and injury Urban four-lane freeways Multi-vehicle PDO (U4F) 1.25 Single-vehicle PDO Total 1.12 125.0 Multi-vehicle fatal and injury 1.02 Single-vehicle fatal and injury Urban six-lane freeways Multi-vehicle PDO (U6F) 1.33 Single-vehicle PDO Total 1.23 26.4 Multi-vehicle fatal and injury 1.43 Single-vehicle fatal and injury Urban six-lane + HOV freeway Multi-vehicle PDO 1.24 Single-vehicle PDO Total 1.29 34.0 Multi-vehicle fatal and injury 1.25 Single-vehicle fatal and injury Urban eight-lane freeway Multi-vehicle PDO (U8F) 1.59 Single-vehicle PDO Total 1.49 57.1 Multi-vehicle fatal and injury 1.09 Single-vehicle fatal and injury Urban eight-lane + HOV freeway Multi-vehicle PDO 1.05 Single-vehicle PDO Total 1.06 7.0 Multi-vehicle fatal and injury 1.08 Single-vehicle fatal and injury Urban 10-lane freeway Multi-vehicle PDO (U10F) 1.36 Single-vehicle PDO Total 1.27 61.7 Multi-vehicle fatal and injury 1.61 Single-vehicle fatal and injury Urban 10-lane + HOV freeway Multi-vehicle PDO 1.42 Single-vehicle PDO Total 1.47
Table 71.ââ Intersection crash calibration factors for Utah from Wall (2023). Sample Size Calibration Facility Type Crash Type (Sites) Factor Rural two-lane two-way roads Three-leg stop controlled (R3ST) 55 0.78 Four-leg stop controlled (R4ST) 50 Total 0.61 Four-leg signal controlled (R4SG) 3 0.45 Rural multi-lane highways Three-leg stop controlled (R3ST) 9 1.57 Four-leg stop controlled (R4ST) 35 Total 0.71 Four-leg signal controlled (R4SG) 13 0.25 Urban arterials 80 Multiple vehicle Three-leg stop controlled (U3ST) 1.08 80 Single vehicle 100 Multiple vehicle Four-leg stop controlled (U4ST) 1.17 100 Single vehicle 37 Multiple vehicle Three-leg signal controlled (U3SG) 1.81 37 Single vehicle 110 Multiple vehicle Four-leg signal controlled (U4SG) 2.47 110 Single vehicle VehicleâPedestrian Three-leg stop controlled (U3ST) 80 n/a 1.01 Four-leg stop controlled 100 n/a 0.97 Three-leg signal controlled (U4ST) 37 n/a 1.51 Four-leg signal controlled (U4SG) 110 n/a 2.14 VehicleâBicycle Three-leg stop controlled (U3ST) 80 n/a 0.67 Four-leg stop controlled 100 n/a 1.18 Four-leg stop controlled (U4ST) 37 n/a 0.82 Four-leg signal controlled (U4SG) 110 n/a 2.24Table 72.ââ Calibration factors for Vermont from Sullivan (2019). Calibration Factors Southern Region Northern Region Central Region Mountains Statewide Piedmont Sample Size Vermont Western Facility Type Green (Sites)Rural two-lanetwo-way 9,664 0.298 0.318 0.285 0.367 0.214 0.363 0.316roadway (3,801 miles)segments (R2U)Three-legintersection withminor-road 977 0.448 0.432 0.449 0.463 0.375 0.419 0.526yield or stopcontrol (3ST)Four-legintersection withminor-road 99 0.488 0.322 0.411 0.597 0.616 0.343 0.645yield or stopcontrol (4ST)Four-legsignalized 9 0.568 0.456 0.695 0.771 0.277 0.306 0.924intersection(4SG)
Literature Reviewââ 75 Kweon et al. (2014) developed state-specific network-screening level SPFs for total crashesand fatal and injury crashes on rural four-lane divided highways and four-leg signalizedintersections on this roadway type using observed crash data from 2004 to 2008. Calibrationfactors were also developed for roadway segments. Data included 1,401 segments at an averagelength of 0.613 miles and 127 signalized intersections. SPFs were developed using the sameform as HSM SPFs with model coefficients determined through NB regression. Calibrationfactors were determined through the HSM methodology and were calculated on a yearly basis,and by district. The product of the two calibration factors allowed for calibration by year anddistrict simultaneously. The resulting calibration factors are presented in Table 73. Note thatcalibration factors were not developed for intersections due to a lack of sample size in individualdistricts and clear variations in safety performance across individual districts. In additionto the calibration factors, statewide crash proportions were given for crash types, such ashead-on, sideswipe, rear-end, angle, single, and other, as well as nighttime crash proportionsby district, allowing for prediction of these crash types based on the SPFs and calibrationfactors provided.Washington StateSummary Calibrated SPFs? None State-specific SPFs? Design-level The Washington State case example discussion in Chapter 4 suggests that Washington Statecurrently applies uncalibrated versions of the HSM SPFs. Shankar, Venkataraman et al. (2016) developed state-specific design-level SPFs for urbanâsuburban arterial roadway segments in Washington State using observed crash data from 2010to 2012 on 107,695 roadway segments amounting to 6,868 miles. SPFs were developed for totalcrashes, as well as various individual crash severity outcomes. Over 170 SPFs were developedconsidering over 20 input variables, including (a) number of lanes, (b) roadway width, (c) shoulderwidth, (d) horizontal curve maximum super-elevation, (e) curve central angle, (f) horizontalcurve radius, (g) degree of curve, (h) absolute vertical grade difference, and (i) rate of verticalcurvature. Both traditional NB regression and random parameters NB regression were used todevelop these SPFs. Shankar, Hong et al. (2016) developed state-specific design-level SPFs for two-lane, two-wayrural roadway segments in Washington State using observed crash data from 2002 to 2010,considering a database of nearly 500,000 observations on 0.01-mile segments. These SPFsconsidered features for roadway geometry and roadside characteristics. Like the previousreport, both traditional and random parameters models were considered. In addition, route-specific SPFs were developed to account for unobserved microscale features (i.e., for an indi-vidual roadway).West VirginiaSummary Calibrated SPFs? None State-specific SPFs? None The authors did not find any documentation of state customization of HSM tools or SPFs forWest Virginia.
76ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 73.ââ Calibration factors for Virginia districts from Kweon et al. (2014). District- and District-Speciï¬c Year-Speciï¬c Year-Speciï¬c Facility Type District Year Calibration Calibration Calibration Factor Factor Factor 2004 0.96 1.05 2005 1.03 1.12 Bristol 2006 1.09 1.03 1.12 2007 1.03 1.12 2008 0.95 1.04 2004 0.96 1.16 2005 1.03 1.25 Salem 2006 1.21 1.03 1.25 2007 1.03 1.25 2008 0.95 1.15 2004 0.96 0.94 2005 1.03 1.01 Lynchburg 2006 0.98 1.03 1.01 2007 1.03 1.01 2008 0.95 0.93 2004 0.96 0.79 2005 1.03 0.84 Richmond 2006 0.82 1.03 0.84 2007 1.03 0.84 2008 0.95 0.78 2004 0.96 0.89 Rural four-lane 2005 1.03 0.96 divided Hampton 2006 0.93 1.03 0.96 roadway Roads segments (R4D) 2007 1.03 0.96 2008 0.95 0.88 2004 0.96 0.82 2005 1.03 0.88 Fredericksburg 2006 0.85 1.03 0.88 2007 1.03 0.88 2008 0.95 0.81 2004 0.96 1.01 2005 1.03 1.08 Culpeper 2006 1.05 1.03 1.08 2007 1.03 1.08 2008 0.95 1.00 2004 0.96 1.05 2005 1.03 1.12 Staunton 2006 1.09 1.03 1.12 2007 1.03 1.12 2008 0.95 1.04 2004 0.96 1.20 2005 1.03 1.29 Northern 2006 1.25 1.03 1.29 Virginia 2007 1.03 1.29 2008 0.95 1.19
Literature Reviewââ 77WisconsinSummary Calibrated SPFs? Design-level State-specific SPFs? Network-screening-level MSA Professional Services, Inc., et al. (2023) developed calibration factors and functions forHSM design-level segment SPFs for two-lane rural roads, rural multi-lane segments, urban andsuburban arterials, and rural and urban freeways based on observed crash data from 2015 to 2019.Segment sample sizes ranged from 34 to 1,502 segments and 13.7 to 631 miles, with the notableexception of 10-lane divided freeways, which only had 11 segments totaling 5.2 miles. Calibra-tion was performed for fatal and injury crashes and PDO crashes for single- and multi-vehiclecrashes using the HSM methodology. A summary of the calibration factors calculated is presentedin Table 74. Calibration functions were estimated using NB regression; the parameter estimatesfor the calibration functions, as well as the overdispersion parameters from the NB regression, arepresented in Table 75 and Table 76. Network-screening-level SPFs were also developed for all thesame site types as were calibrated SPFs. SPFs were developed using NB regression for KABCO,KABC, and O crashes considering traffic volumes and segment length.WyomingSummary Calibrated SPFs? None State-specific SPFs? Design-level Responses received from Wyoming to the survey described in Chapter 3 reveal that Wyomingdevelops both calibration factors and state-specific SPFs. However, only state-specific SPF develop-ment was found in the literature. Gaweesh et al. (2018) developed design-level SPFs for total crashes, fatal and injury crashes,and truck crashes on a 402-mile stretch of Interstate Highway 80 (segmented into 1,628 and834 hom*ogeneous segments in the directions of increasing and decreasing mileposts, respec-tively) using NB regression, a spatial autoregressive (SAR) method, and multivariate adaptiveregression splines (MARS) method, using observed crash data from 2012 to 2016. The modelsconsidered (a) traffic volumes; (b) weather conditions; (c) variable speed limits; (d) cross-sectionalelements such as shoulders, median presence, and type; (e) number and width of lanes; and(f) regional terrain in the form of categorical variables for flat/rolling terrain and mountainousterrain. The authors concluded that the MARS model provided a better model fit than the SARor NB models based on a lower AIC value. The SAR outperformed the other models when con-sidering spatial dependency between neighboring segments; the NB model outperformed theSAR when spatial correlation was insignificant. Ultimately, the authors recommended using thethree models interchangeably based on modeling needs.
78ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 74.ââ Segment calibration factors for Wisconsin from MSA Professional Services, Inc., et al. (2023). Sample Size Calibration Facility Type Crash Severity (Sites) Factor KABCO 2.15 All rural two-lane undivided road segments 1,486 KABC 2.15 (R2U) O 2.15 KABCO 2.15 Straight rural two-lane undivided road 1,135 KABC 2.13 segments (R2U) O 2.15 KABCO 2.17 Curved rural two-lane undivided road 351 KABC 2.23 segments (R2U) O 2.16 KABCO 1.93 Rural multi-lane four-lane divided roadway 930 KABC 0.65 segments (R4D) O 3.24 KABCO 2.62 Rural multi-lane four-lane undivided 50 KABC 1.01 roadway segments (R4U) O 5.18 KABCO 1.21 Urbanâsuburban two-lane undivided 1,502 KABC 0.78 roadway segments (U2U) O 1.41 KABCO 1.22 Urbanâsuburban four-lane undivided 217 KABC 0.92 roadway segments (U4U) O 1.37 KABCO 1.52 Urbanâsuburban four-lane divided roadway 952 KABC 1.10 segments (U4D) O 1.71 KABCO 0.88 Urbanâsuburban four-lane roadway 160 KABC 0.67 segments with TWLTL (U5T) O 0.97 KABC, MV 1.084 Four-lane divided rural freeway segments O, MV 1.685 1,198 (R4D) KABC, SV 0.614 O, SV 2.305 KABC, MV 1.250 Six-lane divided rural freeway segments O, MV 1.502 41 (R6D) KABC, SV 0.643 O, SV 1.589 KABC, MV 1.373 Eight-lane divided rural freeway segments O, MV 1.908 34 (R8D) KABC, SV 0.536 O, SV 1.456 KABC, MV 0.879 Four-lane divided urban freeway segments O, MV 1.422 721 (U4D) KABC, SV 0.582 O, SV 2.181 KABC, MV 1.348 Six-lane divided urban freeway segments O, MV 1.875 215 (U6D) KABC, SV 0.849 O, SV 1.551
Literature Reviewââ 79Table 74.ââ(Continued). Sample Size Calibration Facility Type Crash Severity (Sites) Factor KABC, MV 1.148 Eight-lane divided urban freeway segments O, MV 1.964 76 (U8D) KABC, SV 0.576 O, SV 1.236 KABC, MV 1.895 Ten-lane divided urban freeway segments O, MV 2.870 11 (U10D) KABC, SV 1.099 O, SV 2.162MV â Multi-vehicle crash, SV â Single-vehicle crash. Table 75.ââ Segment calibration function parameters for Wisconsin from MSA Professional Services, Inc., et al. (2023). Total Crash Number Facility Type Observed A B K Severity of Sites Crashes Two-lane two-way KABCO 1,486 4,618 2.598 0.707 0.42 undivided rural KABC 1,486 870 1.644 0.737 0.60 roads (R2U) O 1,486 3,748 2.448 0.703 0.48 Two-lane two-way KABCO 1,135 3,858 2.678 0.699 0.45 undivided rural KABC 1,135 722 1.719 0.765 0.58 roads, straight (R2U) O 1,135 3,134 2.533 0.686 0.51 Two-lane two-way KABCO 351 762 2.316 0.671 0.29 undivided rural KABC 351 148 1.112 0.538 0.69 roads, curved (R2U) O 351 614 2.155 0.706 0.30 KABCO 930 11,197 3.895 0.647 0.24 Four-lane divided KABC 930 1,903 1.031 0.640 0.50 rural roads (R4D) O 930 9,294 5.218 0.634 0.24 KABCO 50 304 2.989 0.878 0.45 Four-lane undivided KABC 50 72 1.055 0.930 0.86 rural roads (R4U) O 50 232 5.306 0.821 0.41 Two-lane two-way KABCO 1,502 3,194 1.961 0.310 1.65 undivided urban KABC 1,502 654 0.561 0.288 2.08 roads (U2U) O 1,502 2,540 1.751 0.304 1.79 KABCO 217 936 2.564 0.472 1.79 Four-lane undivided KABC 217 231 1.055 0.556 3.68 urban roads (U4U) O 217 705 2.383 0.447 1.77 KABCO 952 5,537 4.354 0.280 1.39 Four-lane undivided KABC 952 1,215 1.338 0.368 2.16 urban roads (U4D) O 952 4,322 3.830 0.256 1.41 Four-lane urban KABCO 160 945 3.028 0.388 1.39 roads with TWLTL KABC 160 211 0.985 0.536 1.71 (U5T) O 160 734 2.855 0.348 1.53 KABC calibration functions for U4U and U5T were found to not be signiï¬cant due to limited sample size and are not recommended for use.
80ââ Calibration and Development of State-DOT-Specific Safety Performance Functions Table 76.ââ Freeway calibration function parameters for Wisconsin from MSA Professional Services, Inc., et al. (2023). Single (SV) or Total Crash Number Facility Type Multi-vehicle Observed A B K Severity of Sites (MV) Crashes Rural four-lane KABC MV 1,198 1,094 1.067 1.100 0.29 divided O MV 1,198 3,060 1.805 0.914 0.15 freeway KABC SV 1,198 1,649 0.604 1.017 0.19 (R4D) O SV 1,198 10,573 2.816 0.868 0.19 Rural six-lane KABC MV 41 120 0.639 1.649 0.01 divided O MV 41 313 0.888 1.294 0.05 freeway KABC SV 41 96 0.836 0.814 0.09 (R6D) O SV 41 455 1.409 1.057 0.11 Rural eight-lane KABC MV 34 173 1.482 0.946 0.01 divided O MV 34 547 1.656 1.063 0.09 freeway KABC SV 34 88 0.606 0.929 0.01 (R8D) O SV 34 424 1.959 0.871 0.19 Urban four-lane KABC MV 721 1,580 0.973 0.915 0.59 divided O MV 721 4,491 2.949 0.591 0.59 freeway KABC SV 721 1,521 0.771 0.795 0.31 (U4D) O SV 721 9,395 3.679 0.725 0.31 Urban six-lane KABC MV 215 2,467 2.731 0.693 0.83 divided O MV 215 7,971 5.729 0.651 0.91 freeway KABC SV 215 1,110 1.117 0.856 0.59 (U6D) O SV 215 4,180 3.068 0.741 0.61 Urban eight- KABC MV 76 741 2.810 0.598 0.81 lane divided O MV 76 2,632 6.918 0.578 1.05 freeway KABC SV 76 303 1.609 0.483 0.47 (U8D) O SV 76 1,160 3.601 0.585 0.47 Urban ten-lane KABC MV 11 135 42.600 -1.027 2.06 divided O MV 11 418 136.952 -0.704 2.56 freeway KABC SV 11 76 10.799 -0.286 3.04 (U10D) O SV 11 269 170.548 -0.950 2.04 Urban segments of 10-lanes (U10D) were found not signiï¬cant for all crash severity levels and are not recommended for use.
