Crash Modification Factors in the Highway Safety Manual: A Review (2023)

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29   Calibration of Prediction Models for Inclusion in the HSM2 7.1 Background Before the prediction models were included in Part C of the HSM1, the models predicting intersection crashes were calibrated with HSIS data from California, and the models predict­ ing segment crashes were calibrated with data from Washington (R. Srinivasan, F. Council, and D. Harkey, “Calibration Factors for HSM Part C Predictive Models,” submitted to HSM Task Force 2008). It was argued that end users could utilize these recalibrated models to directly compare the expected safety performance of different facility types. NCHRP 17­72 was tasked with recalibrating models that would be included in the HSM2. This exercise is also referred to as “common state calibration” or “single state calibration.” The intent was to find states with data that could be used to calibrate prediction models that would be compared with each other. Discussions with the AASHTO and TRB committees revealed that rural and urban models could be calibrated with data from different states, but that all the rural segment models needed to be calibrated to the same state, and all the urban segment models needed to be calibrated to the same state. Similarly, all the rural intersection models needed to be calibrated to the same state, and all the urban intersection models needed to be calibrated to the same state. The resources for this activity were limited, and so the intent was to find states that would have readily available data or find other resources (apart from NCHRP 17­72) for collecting the necessary data. For example, the project team was able to use resources from an ongoing HSRC­led project for the North Carolina Department of Transportation (DOT) to calibrate the predictive models from the HSM (hereafter referred to as the “North Carolina DOT calibration project”). Compared with the HSM1, the number of prediction models to be included in the HSM2 is significantly higher. The project team investigated multiple states that could provide the neces­ sary data. Ohio was able to provide data that were used for the calibration of rural two­lane roads, rural multilane undivided roads, and rural multilane divided roads. For other facility types, the project team decided to use the data that were collected from North Carolina roads as part of the North Carolina DOT calibration project. The methodology for calculating the calibration factors was the same as in the HSM1; that is, the calibration factor was defined as the ratio of the observed crash frequency to the predicted crash frequency. Calibration factors have been estimated for prediction models estimated in NCHRP Proj­ ects 17­58, 17­62, 17­68, and 17­70, which included segments on rural two­lane roads, segments on urban and suburban roads, and intersections. On the basis of guidance from AASHTO, SPFs estimated for freeways were not included in the calibration. The project team also did not calibrate the prediction models from NCHRP Project 17­84, “Pedestrian and Bicycle Safety Performance Functions for the Highway Safety Manual.” C H A P T E R 7

30 Crash Modification Factors in the Highway Safety Manual: A Review 7.2 Segments on Rural Roads Appendix K provides the details of the calibration effort that used Ohio data from 2013 to 2017 for rural segments that included rural two­lane undivided roads, rural four­lane undivided roads, and rural four­lane divided roads. To develop calibration factors for the base models (developed from NCHRP 17­62), the data provided were reduced to include only segments that met the relevant base conditions, where possible. In some cases, the base condition criteria were relaxed to provide for a sufficient sample size. FHWA’s tool “The Calibrator” (https://safety.fhwa .dot.gov/rsdp/toolbox­content.aspx?toolid=150) was used to estimate calibration factors and goodness­of­fit measures. If the calibration was based on few crashes, the notes column in the tables in Appendix K indicate which calibration factor should be used. 7.3 Segments on Urban and Suburban Arterials Appendix L provides the details of the calibration effort that used North Carolina data from 2013 to 2019 for urban segment prediction models developed in NCHRP 17­62 and 17­58 (Lord et al. 2016). Data were obtained for the following facility types: • Urban two­lane undivided (U2U), • Urban two­lane with TWLTL (U3T), • Urban four­lane divided (U4D), • Urban four­lane undivided (U4U), • Urban four­lane with TWLTL (U5T), • Urban six­lane divided (U6D), • Urban six­lane undivided (U6U), • Urban six­lane with TWLTL (U7T), and • Urban eight­lane divided (U8D). Data were also collected for one­way streets, but the sample size was too small to use (only 0.1 mile of three­lane roadways and 0.4 mile of four­lane roadways). Because of the small sample sizes that would result by limiting the sites to only those that fit the base conditions, all segments were included and the appropriate CMFs applied. As was the case in the calibration of the SPFs for rural roads, The Calibrator tool was used to estimate the calibration factors. 7.4 Intersections Appendix M provides the details of the calibration effort that used North Carolina data from 2013 to 2019 for intersection crash prediction models developed in NCHRP 17­58, 17­62, 17­68, and 17­70. Data were obtained for the following intersection types: • Rural two­lane, three­leg stop­controlled intersections (Rur2L­3ST); • Rural two­lane, three­leg signalized intersections (Rur2L­3SG); • Rural two­lane, four­leg stop­controlled intersections (Rur2L­4ST); • Rural two­lane, four­leg signalized intersections (Rur2L­4SG); • Rural multilane, three­leg stop­controlled intersections (RurML­3ST); • Rural multilane, three­leg signalized intersections (RurML­3SG); • Rural multilane, four­leg stop­controlled intersections (RurML­4ST); • Rural multilane, four­leg signalized intersections (RurML­4SG); • Urban arterial, three­leg stop­controlled intersections (UrbArt­3ST); • Urban arterial, three­leg signalized intersections (UrbArt­3SG); • Urban arterial, four­leg stop­controlled intersections (UrbArt­4ST); • Urban arterial, four­leg signalized intersections (UrbArt­4SG);

Calibration of Prediction Models for Inclusion in the HSM2 31 • Urban arterial (six or more lanes), three­leg stop­controlled intersections (UrbArt6+­3ST); • Urban arterial (six or more lanes), three­leg signalized intersections (UrbArt6+­3SG); • Urban arterial (six or more lanes), four­leg stop­controlled intersections (UrbArt6+­4ST); • Urban arterial (six or more lanes), four­leg signalized intersections (UrbArt6+­4SG); • Urban arterial, one­way, three­leg stop­controlled intersections (UrbArtOW­3ST); • Urban arterial, one­way, three­leg signalized intersections (UrbArtOW­3SG); • Urban arterial, one­way, four­leg stop­controlled intersections (UrbArtOW­4ST); • Urban arterial, one­way, four­leg signalized intersections (UrbArtOW­4SG); • Rural two­lane, four­leg all­way stop­controlled intersections (Rur4Leg­AWSC); • Urban arterial, three­leg all­way stop­controlled intersections (Urb3Leg­AWSC); • Urban arterial, four­leg all­way stop­controlled intersections (Urb4Leg­AWSC); • Rural roundabouts (Rur­RndAbt); • Urban, single­lane roundabouts (Urb­RndAbtSL); and • Urban, multilane roundabouts (Urb­RndAbtML). Sufficient data for the following facility types could not be obtained; therefore, they were not calibrated: • Urban five­leg signalized intersections (@ segments with two or more lanes), • Urban crossroad ramp terminals at single­point diamond interchanges, • Urban three­leg stop­controlled intersections (@ segments with two or more lanes—high speed), • Urban three­leg signalized intersections (@ segments with two or more lanes—high speed), • Urban four­leg stop­controlled intersections (@ segments with two or more lanes—high speed), and • Rural three­leg stop­controlled intersections (@ two­lane segments). Due to small sample sizes that would result from limiting the sites to those fitting the base conditions and the AADT ranges used for SPF estimation, all intersections were included (including those outside of the AADT ranges used in the SPF estimation) and the appropriate CMFs applied. For some urban arterial intersections, minor road AADT values were not available. Use of urban arterial intersections with the minor road AADT only would have substantially dimin­ ished the sample used for calibration for some intersection types. To include more intersections in the calibration procedure, the project team estimated the missing minor road AADT values as follows: 1. The minimum, maximum, average, and standard deviation of the available minor road values for AADT were calculated as a percentage of the major road AADT by intersection type. 2. Microsoft Excel’s uniform random number generator was used to randomly generate the missing minor road AADT values as a percentage of the major road AADT with upper and lower bounds defined as the average percentage of the available minor road AADT values ± 1 standard deviation. The project team conducted a sensitivity analysis to determine the effect of minor road AADT values on the calibration factors and found variations in calibration factors to be in the range of ±2% for the various randomly generated minor road AADT samples. On the basis of this minimal variation in the effects of minor road AADT on the calibration factors, the project team went ahead with including all urban arterial intersections with estimated minor road AADT values in cases where minor road AADT values were missing.