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Intersection Crash Prediction Methods for the Highway Safety Manual (2021)

Chapter: Chapter 2. Literature Review and Survey of Practice

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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 2. Literature Review and Survey of Practice." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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26 Chapter 2. Literature Review and Survey of Practice This section summarizes literature relevant to the objectives of this research and results of a survey of transportation agencies intended to gain knowledge about their experience with the current HSM intersection predictive methods and assess their needs and priorities as they relate to additional (new) intersection models and/or expanded capabilities of existing models. Information is summarized according to the following topics: • Review of current HSM intersection crash prediction methods • Protocols, best practices, and emerging approaches for predictive model development • Current knowledge related to intersection safety • Survey of current practice and crash prediction needs • Summary of current knowledge related to intersection crash prediction modeling 2.1 Review of Current HSM Intersection Crash Prediction Methods The current HSM predictive models for intersections were developed in the following order: • HSM Chapter 10—intersections on rural two-lane, two-way roads • HSM Chapter 11—intersections on rural multilane highways • HSM Chapter 12—intersections on urban and suburban arterials • HSM Chapter 19—crossroad ramp terminals at interchanges HSM Chapters 10, 11, and 12 are included in the first edition of the HSM published in 2010. Chapter 19 was published as a 2014 Supplement to the HSM. Concepts Common Across HSM Intersection Predictive Methods At the most disaggregate level, the HSM predictive methods provide procedures to estimate the expected average crash frequency for individual sites, which are either homogenous roadway segments or intersections (see Figure 1). At-grade intersections are the specific focus of this research. Applying predictive methods for at-grade intersections results in estimates of the expected average crash frequency due to the presence of intersections. This includes crashes occurring within the limits of the intersection (Region A in Figure 1) as well as intersection- related crashes that occur on the intersection legs (Region B in Figure 1). The latter are crashes classified on the crash report as intersection-related or crashes having characteristics consistent with intersection-related crashes (e.g., rear-end collisions in queues). The HSM Appendix A recommends using the intersection-related designation on the crash report when such a field is available to identify the intersection-related crashes that have occurred on the intersection legs.

27 Figure 1. HSM definitions of segments and intersections (AASHTO, 2010) The basic components of the HSM intersection predictive methods used to estimate the expected average crash frequency are: • SPFs • crash severity and collision type distributions • CMFs • calibration procedures • Empirical Bayes (EB) estimation Combining SPFs, CMFs, and calibration factors without the EB procedure results in a predicted average crash frequency, Npredicted, based only on the characteristics of the roadway. Estimates of the expected average crash frequency, which incorporate information about the crash history at the site, are available only after applying the EB technique. The basic model structure to predict the average crash frequency at intersections (Npredicted int) is shown in Equation 1. With Equation 1 and additional equations throughout this report, existing notation and definitions in the first edition of the HSM are used as much as possible; however, some modifications to HSM notation and definitions were made for clarity and consistency as necessary. 𝑁 𝑁 𝐶𝑀𝐹 𝐶𝑀𝐹 … 𝐶𝑀𝐹 𝐶 (Eq. 1) Where: Npredicted int = predicted average crash frequency for an individual intersection for the selected year (crashes/year) Nspf int = predicted average crash frequency for an intersection with base conditions (crashes/year) CMFyi = crash modification factors specific to intersection type i and specific geometric design and traffic control features y Ci = calibration factor to adjust the SPF for intersection type i to local conditions

28 Intersection SPFs generally take one of the two forms shown in Equation 2 and Equation 3. 𝑁 𝑒𝑥𝑝 𝑎 𝑏 𝑙𝑛 𝐴𝐴𝐷𝑇 𝑐 𝑙𝑛 𝐴𝐴𝐷𝑇 (Eq. 2) 𝑁 𝑒𝑥𝑝 𝑎 𝑑 𝑙𝑛 𝐴𝐴𝐷𝑇 (Eq. 3) Where: AADTmaj = annual average daily traffic (AADT) on the major road (veh/day) AADTmin = AADT on the minor road (veh/day) AADTtotal = AADT on the major and minor roads combined (veh/day) a, b, c, and d = estimated regression coefficients If AADTs on the two major legs of an intersection differ, the larger of the two AADT values is used for AADTmaj. Similarly, if AADTs on the two minor legs of a four-leg intersection differ, the larger of the two AADT values is used for AADTmin. As needed, AADTtotal can be estimated as the sum of AADTmaj and AADTmin. If AADTs are not available for each evaluation year, interpolation and extrapolation are used. Each SPF also has an associated overdispersion parameter, k. This parameter provides insights into how average crash frequencies at the sites used to estimate the SPF vary compared to the SPF predictions. Larger values indicate larger site-to-site variation around the SPF prediction. HSM Chapter 10—Predictive Methods for Intersections on Rural Two-Lane, Two-Way Roads Chapter 10 of the HSM includes SPFs for the following intersection configurations and traffic control types on rural two-lane, two-way roads: • Three-leg intersections with minor road stop control (3ST) • Four-leg intersections with minor road stop control (4ST) • Four-leg intersections with signal control (4SG) The intersection SPFs for rural two-lane, two-way roads predict an average crash frequency for all crash severities and collision types combined. Default tabular distributions are provided for crash severity and collision type. Crash severities can be disaggregated into five levels: fatal (K), incapacitating injury (A), non-incapacitating injury (B), possible injury (C), and property- damage-only (O or PDO). The collision type distributions are provided for three levels of severity: total—all severities combined (KABCO), FI severities (KABC), and PDO.

29 HSM Chapter 11—Predictive Methods for Intersections on Rural Multilane Highways Chapter 11 of the HSM includes SPFs for the following intersection configurations and traffic control types on rural multilane highways: • Three-leg intersections with minor road stop control on rural, four-lane divided or undivided highways (3ST) • Four-leg intersections with minor road stop control on rural, four-lane divided or undivided highways (4ST) • Four-leg intersections with signal control on rural, four-lane divided or undivided highways (4SG) For all three intersection types, the intersecting minor roads may be two- or four-lane highways. The intersection SPFs for rural multilane highways predict average crash frequency for all crash severities and collision types combined (KABCO), FI crashes (KABC), and FI crashes with possible injuries excluded (KAB). Default tabular distributions are provided for crash severity and collision type for four levels of severity: total – all severities combined (KABCO), FI severities (KABC), FI severities with possible injuries excluded (KAB), and PDO. Alternative SPFs by collision type and severity level are also provided in Appendix 11B of the HSM for stop-controlled intersections on rural multilane highways. HSM Chapter 12—Predictive Methods for Intersections on Urban and Suburban Arterials Chapter 12 of the HSM includes SPFs for the following intersection configurations and traffic control types on urban and suburban arterials: • Three-leg intersections with minor road stop control (3ST) • Three-leg intersections with signal control (3SG) • Four-leg intersections with minor road stop control (4ST) • Four-leg intersections with signal control (4SG) The HSM intersection predictive methods for urban and suburban arterials separately predict vehicle-pedestrian and vehicle-bicycle crashes. This results in a different model structure for Npredicted int than shown in Equation 1 to calculate total crashes at an intersection, combining vehicle-only plus vehicle-pedestrian plus vehicle-bicycle crashes. This structure of the SPFs for intersections in urban and suburban areas is illustrated in Equation 4 and Equation 5, again using existing HSM notations and variable definitions as appropriate. 𝑁 𝑁 𝑁 𝑁 𝐶 (Eq. 4) 𝑁 𝑁 𝐶𝑀𝐹 𝐶𝑀𝐹 … 𝐶𝑀𝐹 (Eq. 5)

30 Where: Npredicted int = predicted average crash frequency for an individual intersection for the selected year (crashes/year) Nbi = predicted average crash frequency of an intersection (excluding vehicle-pedestrian and vehicle-bicycle crashes) (crashes/year) Npedi = predicted average crash frequency of vehicle-pedestrian crashes of an intersection (crashes/year) Nbikei = predicted average crash frequency of vehicle-bicycle crashes of an intersection (crashes/year) Nspf int = predicted total average crash frequency of intersection-related crashes for base conditions (excluding vehicle-pedestrian and vehicle-bicycle collisions) (crashes/year) CMF1i…CMFyi = crash modification factors specific to intersection type i and specific geometric design and traffic control features y Ci = calibration factor for intersection type i to adjust prediction to local conditions The SPF portion of Nbi, Nspf int, is the sum of two disaggregate predictions by collision type, as shown in Equation 6. 𝑁 = 𝑁 + 𝑁 (Eq. 6) Where: Nbimv = predicted average crash frequency of MV crashes of an intersection for base conditions (crashes/year); and Nbisv = predicted average crash frequency of SV crashes of an intersection for base conditions (crashes/year). SPFs to estimate MV crashes are provided for three severity levels: total (KABCO), FI, and PDO. Because the SPFs for the different severity levels were developed independently, for any given collision type (e.g., MV) and site type (e.g., 3ST), the “total” crash prediction (i.e., all severities) may not equal the sum of the FI and PDO predictions. Preliminary values for FI and PDO crashes obtained directly from the SPFs may be adjusted using an approach illustrated by Equations 7 and 8, provided as an example for MV crashes. The same approach is also used to make these same types of adjustments to the SV crash predictions. 𝑁 ( ) = 𝑁 ( ) × ( )( ) ( ) (Eq. 7) 𝑁 ( ) = 𝑁 ( ) −𝑁 ( ) (Eq. 8)

31 Where: Nbimv(FI) = predicted average crash frequency of MV, FI crashes of an intersection for base conditions (crashes/year) Nbimv(total) = predicted average crash frequency of MV crashes (all severities) of an intersection for base conditions (crashes/year) Nbimv(PDO) = predicted average crash frequency of MV, PDO crashes of an intersection for base conditions (crashes/year) N’bimv(FI) = preliminary value for predicted average crash frequency of MV, FI crashes of an intersection for base conditions (crashes/year) N’bimv(PDO) = preliminary value for predicted average crash frequency of MV, PDO crashes of an intersection for base conditions (crashes/year) Separate collision type distributions for MV, FI; MV, PDO; SV, FI; and SV, PDO are provided for each of the four intersection types addressed by the predictive method. Separate model structures are used to estimate the yearly number of vehicle-pedestrian crashes, Npedi, at stop-controlled and signalized intersections on urban and suburban arterials. The average number of annual vehicle-pedestrian crashes for stop-controlled intersections is estimated with Equation 9. 𝑁 = 𝑁 × 𝑓 (Eq. 9) Where: fpedi = pedestrian crash adjustment factor for intersection type i The average number of annual vehicle-pedestrian crashes for signalized intersections is estimated with Equation 10. 𝑁 = 𝑁 × 𝐶𝑀𝐹 × 𝐶𝑀𝐹 × 𝐶𝑀𝐹 (Eq. 10) Where: Npedbase = predicted average crash frequency of vehicle-pedestrian crashes for base conditions at signalized intersections (crashes/year) CMF1p = crash modification factor for number of bus stops within 1,000 ft of the center of the intersection CMF2p = crash modification factor for presence of one or more schools within 1,000 ft of the center of the intersection CMF3p = crash modification factor for number of alcohol sales establishments within 1,000 ft of the center of the intersection The predicted number of vehicle-pedestrian crashes per year for base conditions at signalized intersections, Npedbase, is estimated using Equation 11.

32 𝑁 = 𝑒𝑥𝑝 𝑎 + 𝑏 × 𝑙𝑛(𝐴𝐴𝐷𝑇 ) + 𝑐 × 𝑙𝑛 + 𝑑 × 𝑙𝑛(𝑃𝑒𝑑𝑉𝑜𝑙) + 𝑒 × 𝑛 (Eq. 11) Where: PedVol = sum of daily pedestrian volumes crossing all intersection legs (pedestrians/day), only considering crossing maneuvers immediately adjacent to the intersection (e.g., along a marked crosswalk or the extended path of any approaching sidewalk) nlanesx = maximum number of traffic lanes crossed by a pedestrian, including through and turning lanes, in any crossing maneuver at the intersection considering the presence of refuge islands (only raised or depressed refuges are considered). Base conditions associated with Npedbase are absence of bus stops, schools, and alcohol sales establishments near the intersection. All of the vehicle-pedestrian crashes predicted with Equations 10 and 11 are assumed to be FI crashes (none as PDO). The average number of annual vehicle-bicycle crashes, Nbikei, at all intersection types are predicted using the same model structure as that used to predict Npedi at stop-controlled intersections (see Equation 12). 𝑁 = 𝑁 × 𝑓 (Eq. 12) Where: fbikei = bicycle crash adjustment factor for intersection type i All of the vehicle-bicycle crashes predicted with Equation 12 are assumed to be FI crashes (none as PDO). HSM Chapter 19—Predictive Method for Ramps Chapter 19 of the HSM includes SPFs for the following types of crossroad ramp terminals at service interchanges: • Three-leg terminals with diagonal exit ramp (D3ex) • Three-leg terminals with diagonal entrance ramp (D3en) • Four-leg terminals with diagonal ramps (D4) • Four-leg terminals at four-quadrant parclo A (A4) • Four-leg terminals at four-quadrant parclo B (B4) • Three-leg terminals at two-quadrant parclo A (A2) • Three-leg terminals at two-quadrant parclo B (B2) These ramp terminal types are illustrated in Figure 2. Predictive methods provided in Chapter 19 of the HSM capture both stop control (ST) and signal control (SG) for each of the terminal types

33 and cover crossroad ramp terminals with anywhere from two to six crossroad through lanes (total of both travel directions). Utilizing new notation introduced as part of the 2014 Supplement to the HSM (Chapter 19), signal-controlled crossroad ramp terminal SPFs generally take the form shown in Equation 13. 𝑁 , , , , = exp 𝑎 + 𝑏 × ln(𝑐 × 𝐴𝐴𝐷𝑇 ) + 𝑑 × ln(𝑐 × 𝐴𝐴𝐷𝑇 + 𝑐 × 𝐴𝐴𝐷𝑇 ) (Eq. 13) with 𝐴𝐴𝐷𝑇 = 0.5 × (𝐴𝐴𝐷𝑇 + 𝐴𝐴𝐷𝑇 ) (Eq. 14) Where: Nspf,w,SGn,at,z = predicted average crash frequency of a signal-controlled crossroad ramp terminal of site type w (w = D3ex, D3en, D4, A4, B4, A2, or B2) with base conditions, n crossroad lanes, all collision types (at), and severity z (z = FI, PDO) (crashes/year) AADTxrd = AADT on the crossroad (veh/day) AADTin = AADT on the crossroad leg between ramps (veh/day) AADTout = AADT on the crossroad leg outside of the interchange (veh/day) AADTex = AADT on the exit ramp (veh/day) AADTen = AADT on the entrance ramp (veh/day) The AADT of the loop exit ramp at a B4 terminal configuration is not included in AADTex, and the AADT of the loop entrance ramp at an A4 configuration is not included in AADTen. The intersection SPFs predict average crash frequency for all collision types. Default collision type distributions are provided for both FI and PDO crashes. Separate collision type distributions are provided for signalized ramp terminals in rural and urban areas.

34 Figure 2. Ramp terminal configurations (AASHTO, 2014)

35 Figure 2. Ramp terminal configurations (AASHTO, 2014) (continued)

36 One-way, stop-controlled crossroad ramp terminal SPFs generally take the form shown in Equation 15. 𝑁 , , , , = exp 𝑎 + 𝑏 × ln(𝑐 × 𝐴𝐴𝐷𝑇 ) + 𝑑 × ln(𝑐 × 𝐴𝐴𝐷𝑇 + 𝑐 × 𝐴𝐴𝐷𝑇 ) (Eq. 15) Where: Nspf,w,ST,at,z = predicted average crash frequency of a one-way, stop-controlled crossroad ramp terminal of site type w (w = D3ex, D3en, D4, A4, B4, A2, B2) with base conditions, all collision types (at), and severity z (z = FI, PDO) All other terms have been previously defined. The intersection SPFs predict average crash frequency for all collision types. Default collision type distributions are provided for both FI and PDO crashes. Separate collision type distributions are provided for one-way, stop-controlled ramp terminals in rural and urban areas. The predictive methods for ramps in Chapter 19 of the 2014 Supplement to the HSM, including crossroad ramp terminals, utilize SDFs to disaggregate the predicted average frequency of FI crashes into an estimate of average crash frequency for the following severity levels: fatal (K), incapacitating injury (A), non-incapacitating injury (B), and possible injury (C). Adopting the SDF notation introduced as part of the 2014 Supplement to the HSM, the SDFs for crossroad ramp terminals are illustrated in Equations 16 through 19. 𝑃 , , , = ( )., , ( ) ( ) × 𝑃 | , , , (Eq. 16) 𝑃 , , , = ( )., , ( ) ( ) × 1 − 𝑃 | , , , (Eq. 17) 𝑃 , , , = ( )., , ( ) ( ) (Eq. 18) 𝑃 , , , = 1 − (𝑃 + 𝑃 + 𝑃 ) (Eq. 19) Where: PaS,x,at,K = probability of a fatal crash (given that a fatal or injury crash occurred) for all ramp terminal sites (aS) based on all collision types (at) and control type x (x = ST: one-way stop control; Sgn: signal control, n-lane crossroad)

37 PaS,x,at,A = probability of an incapacitating injury crash (given that a fatal or injury crash occurred) for all ramp terminal sites (aS) based on all collision types (at) and control type x (x = ST: one-way stop control; Sgn: signal control, n-lane crossroad) PaS,x,at,B = probability of a non-incapacitating injury crash (given that a fatal or injury crash occurred) for all ramp terminal sites (aS) based on all collision types (at) and control type x (x = ST: one-way stop control; Sgn: signal control, n-lane crossroad) PaS,x,at,C = probability of a possible injury crash (given that a fatal or injury crash occurred) for all ramp terminal sites (aS) based on all collision types (at) and control type x (x = ST: one-way stop control; Sgn: signal control, n-lane crossroad) Vj = systematic component of crash severity likelihood for severity j PK|K+A,aS,x,at = probability of a fatal crash given that the crash has a severity of either fatal or incapacitating injury for all ramp terminal sites (aS) based on all collision types (at) and control type x (x = ST: one-way stop control; Sgn: signal control, n-lane crossroad) Csdf,aS,x = calibration factor to adjust SDF for local conditions for all ramp terminal sites (aS) and control type x (x = ST: stop control, Sgn: signal control, n-lane crossroad) The basic model form for the systematic components of crash severity likelihood at crossroad ramp terminals is illustrated by Equation 20. 𝑉 = 𝑎 + 𝑏 × 𝐼 , + 𝑐 × 𝑛 + 𝑛 + 𝑑 × 𝐼 + (𝑒 × 𝐼 ) (Eq. 20) Where: Ip,lt = protected left-turn operation indicator variable for crossroad (= 1 if protected operation exists, 0 otherwise) ndw = number of unsignalized driveways on the crossroad leg outside of the interchange and within 250 ft of the ramp terminal nps = number of unsignalized public street approaches to the crossroad leg outside of the interchange and within 250 ft of the ramp terminal Ips = non-ramp public street leg indicator variable (= 1 if leg is present, 0 otherwise) a, b, c, d, and e = estimated SDF coefficients Chapter 19 of the HSM does not provide a predictive method for crossroad ramp terminals with all-way stop control, but it does include an interim method that utilizes the one-way stop control models.

38 HSM Predictive Method Calibration The intersection predictive methods in the HSM contain calibration factors to adjust predictions of the HSM models, developed with data from selected jurisdictions and for specific time periods, to be applicable to other jurisdictions and time periods. Equation 1, for example, presents the calibration factor in general form as Ci, with i representing a specific site type. The notation Ci is generally used to represent predictive model calibration factors when the site type of interest is an intersection. Calibration factors associated with the intersection predictive methods are calculated as the ratio of total observed crash frequencies for a selected set of sites to total predicted average crash frequencies for the same sites, during the same time period, determined using the applicable predictive method. This ratio is illustrated in Equation 21. 𝐶 = ∑ ∑ (Eq. 21) Calibration is to be performed separately for each specific facility and site type. The introduction of SDFs in the freeway and interchange chapters of the HSM resulted in the need for an SDF calibration method. The calibration method utilizes comparisons of observed versus predicted severe crashes (i.e., fatal, incapacitating injury, and non-incapacitating injury crashes). First, observed crash data from the calibration sites are used to calculate the observed probability of a severe crash, given that an FI crash has occurred, using Equation 22. 𝑃 , , , , = ∑ ∑ , ( ), ( ), , , , ( ), ( ), , , , ( ), ( ), , ,∑ ∑ , ( ), ( ), , , , ( ), ( ), , , , ( ), ( ), , , , ( ), ( ), , , (Eq. 22) Where: Po,aS,ac,at,KAB = observed probability of a severe crash (i.e., K, A, or B) for all collision types (at), all sites (aS), and all control types (ac) No,w(i),x(i),at,m,t = observed crash frequency for site i with site type w(i), year t, control type x(i), for all collision types (at), and severity m (m = K, A, B, C) nsites = number of sites nc = number of years in calibration period Next, the predicted average crash frequency is used to calculate the predicted probability of a severe crash, given that an FI crash has occurred, using Equation 23. 𝑃 , , , , = ∑ ∑ , ( ), ( ), , , , ( ), ( ), , , , ( ), ( ), , ,∑ ∑ , ( ), ( ), , , , ( ), ( ), , , , ( ), ( ), , , , ( ), ( ), , , (Eq. 23)

39 Where: Pp,aS,ac,at,KAB = predicted probability of a severe crash (i.e., K, A, or B) for all collision types (at) all sites (aS) and all control types (ac); Np,w(i),x(i),at,m,t = predicted crash frequency for site i with site type w(i), year t, control type x(i), for all collision types (at), and severity m (m = K, A, B, C); The final step involves computing the calibration factor using Equation 24. 𝐶 , = , , , ,. , , , , × . , , , ,, , , , (Eq. 24) Calibration is performed separately for each SDF. Empirical Bayes Estimation This section describes the EB estimation, as used in Step 15 of the HSM Predictive Method (presented in the Part C Introduction and Applications Guidance) when applicable. EB estimation combines a predicted average crash frequency for a site with an observed crash frequency for that site, resulting in an estimate of the expected average crash frequency. Combining the observed crash frequency for a specific site with the predicted crash frequency for other similar sites increases the accuracy of the expected crash frequency estimate. The EB method reduces regression-to-the-mean (RTM) bias in estimates obtained from observed crash frequency alone, where locations experiencing higher than average crash frequency over some time period will naturally see lower crash frequencies in a following time period and vice versa. Two or more years of crash data are desirable for applying the EB method. A more straightforward EB estimation can occur when crash data are assigned to each segment or intersection (i.e., a site-specific EB analysis). However, when crash data are not segment- or intersection-specific, the EB method can be applied across multiple, aggregated sites (i.e., project-level EB method). Only the site-specific EB method is discussed here. Applying the site-specific EB method results in an estimate of expected average crash frequency for a site (Nexpected), produced by combining predicted average crash frequency for the site (Npredicted) with the observed crash frequency for that same site (Nobserved). Nexpected for a site is calculated using Equations 25 and 26. 𝑁 = 𝑤 × 𝑁 + (1.00 − 𝑤) × 𝑁 (Eq. 25) 𝑤 = × ∑ (Eq. 26)

40 where: Nexpected = expected average crash frequency obtained by combining the predicted average crash frequency (Npredicted) with the observed crash frequency (Nobserved) using the EB method Npredicted = predicted average crash frequency obtained using the appropriate predictive model Nobserved = observed crash frequency w = weighted adjustment to be placed on the HSM predictive model estimate k = overdispersion parameter associated with the SPF 2.2 Protocols, Best Practices, and Emerging Approaches for Predictive Model Development This section discusses formal protocols and guidance for predictive model development, as well as best practices for predictive model development identified from past experience and emerging approaches. This discussion focuses on issues applicable to modeling at-grade intersection safety performance and does not necessarily address issues relevant only to roadway segments or ramps. Development of SPFs SPFs for intersections are equations that relate the expected intersection crash frequency (possibly by type and/or severity) for some defined time period to characteristics of the intersection. In the context of the intersection predictive methods in the HSM, SPFs are used to estimate a predicted average intersection crash frequency (in units of crashes/year) for a given combination of major- and minor road traffic volumes. SPFs in the HSM are provided for different facility types, numbers of intersecting legs, and traffic control types. Intersection SPFs can also appear as “fuller models,” which include additional variables beyond only major- and minor road traffic volumes for crash prediction. A synthesis paper published in Transportation Research Part A (Lord and Mannering, 2010) contains descriptions of key issues and methodological approaches applicable to SPF-like models that have been used to understand how various factors influence the frequency of crashes. Data and methodological issues explored in the paper include overdispersion, underdispersion, time-varying explanatory variables, temporal and spatial correlation, low sample mean, small sample size, injury severity and collision type correlation, omitted variable bias, endogenous variables, functional form, and fixed parameters. The wide variety of methods that appear in the published literature to deal with these issues are then identified and described, including Poisson regression, negative binomial regression, Poisson-lognormal models, zero- inflated models, Conway-Maxwell-Poisson model, Gamma model, generalized estimating equation model, generalized additive models, random effects models, negative multinomial models, random-parameters models, bivariate/multivariate models, finite mixture/Markov switching models, duration models, hierarchical/multilevel models, neural and Bayesian network models, and support vector machine models. Finally, maximum likelihood and Bayesian estimation methods are briefly covered. Similar to the synthesis paper by Lord and Mannering

41 (2010), the Federal Highway Administration (FHWA) Safety Performance Function Development Guide: Developing Jurisdiction-Specific SPFs (Srinivasan and Bauer, 2013) provides guidance for states interested in developing their own SPFs and addresses a variety of issues which may be encountered when developing jurisdiction-specific SPFs. Recent advances in SPF development allow for the estimation of variance and 95% confidence intervals for the estimate of average crash frequency resulting from multiplying SPFs and CMFs. More advanced SPFs deal with temporal correlation, usually through aggregating multiple years of data for a particular set of sites, as well as spatial correlation by using more complex modeling techniques. Model forms other than negative binomial are sometimes used to handle excessive numbers of sites with no crashes (zero-inflated models), to achieve more flexible model forms (Poisson-lognormal), and to deal with both overdispersion and underdispersion (Conway- Maxwell-Poisson models). These model forms are discussed very briefly in the FHWA SPF Guide, but the guide provides additional references for more complex model forms. The progress made in methodological approaches used to understand how various factors influence the frequency of crashes has been substantial (Lord and Mannering, 2010). The most common method for developing intersection SPFs is to estimate a negative binomial (NB) regression model with number of intersection and intersection-related crashes as the dependent variable and traffic volumes, geometry, traffic control devices, and other factors characterizing an intersection as independent variables. NB regression requires the specification of the “additional dispersion” (additional when compared to a Poisson model) that is common to crash data. It is typical for this “additional dispersion” to be specified as a dispersion parameter multiplied by the expected number of crashes squared (NB-2 model). The dispersion parameter for intersections is usually treated as a fixed parameter. There are some variations to the standard NB-2 model that can still be integrated with existing HSM predictive methods while at the same time possibly improving the parameter estimates associated with traffic volumes, geometric features, traffic control, and other factors in the models in terms of “accuracy” and “precision.” Count regression models with identification variables for counties, districts, regions, or states treated as “fixed effects” (see Le and Porter, 2012) or “random effects” (see Shankar et al., 1998) are modeling alternatives that help to address crash- influencing factors that may be common to groups of intersections, but that are not captured by the models. The methods were successfully employed in NCHRP Project 17-45, Enhanced Safety Prediction Analysis Tool for Freeways and Interchanges (Bonneson et al., 2012). Random effects models were also used to estimate multi-state models in developing the HSM Chapter 12 SPFs. The negative multinomial modeling approach can also be used to address correlations in disturbance terms across observations, and is particularly useful when a single intersection appears in a database multiple times due to multiple observation years that are kept disaggregated. NB regression, count regression models with “fixed effects” and “random effects,” and negative multinomial modeling were considered most relevant for developing SPFs for this research. Development of Crash Modification Factors CMFs are multiplicative factors used to compute the expected number of crashes at a site with a certain set of characteristics. CMFs are multiplied by the expected number of crashes at that site

42 without those characteristics, commonly referred to as “base conditions” in the HSM predictive model context. For any given characteristic or treatment, CMF values greater than one indicate that the characteristic or treatment is expected to increase the number of crashes compared to the base conditions, while values lower than one indicate that the treatment is expected to decrease the number of crashes. FHWA’s A Guide to Developing Quality Crash Modification Factors (CMF Guide) (Gross et al., 2010) was published with a primary purpose of describing methods behind the development of CMFs and providing guidance for adequate application and reporting of CMFs, depending on the available data and treatments that CMFs need to address. Crash Modification Functions (CMFunctions) may also be used to compute CMFs for a specific site, and while they require more data than computing single CMF values, they allow the CMF values to vary as site characteristics change, which may make them preferable among practitioners. A variety of study approaches have been used to develop CMFs including EB before-after studies, before-after with comparison group studies, full Bayes studies, surrogate measure studies, cross-sectional studies, case-control studies, cohort studies, meta-analysis studies, and expert-panel studies. For all types of CMF studies, the number of treatment and non-treatment sites and duration of the before and after periods, as well as the size of treatment effect, impact the estimated CMFs and their associated standard errors. Before-after studies are considered the most dependable study design for CMF development, but in both national HSM discussions and the research literature, there is emerging interest in whether quality CMFs can be developed using the estimated parameters of regression models from cross-sectional studies. The current state of the research literature indicates that it is possible to estimate reliable CMFs from cross- sectional studies as long as care is taken in the data collection and modeling approaches used. Desirable characteristics of such studies include: • Carefully collected databases created using both traditional and non-traditional data sources to confirm and enhance the independent variable measurements • Logical variable specifications with appropriate boundary conditions • Repeated, consistent findings across studies and locations • Implementation of observational study design methods, such as the propensity scores- potential outcomes framework to significantly reduce selection bias Treatment of Crash Severity in Predictive Methods The way in which crash severity is addressed within the HSM intersection predictive methods has evolved over time as chapters were developed. In Chapter 10 (Rural Two-Lane, Two-Way Roads), SPFs predict average crash frequency for all crash severities. Using proportional distributions, crash severities can be disaggregated into five levels: fatal (K), incapacitating injury (A), non-incapacitating injury (B), possible injury (C), and property-damage-only (O or PDO). In Chapter 11 (Rural Multilane Highways), the intersection SPFs predict average crash frequency for all crash severities combined (KABCO), FI crashes (KABC), and FI crashes with possible injuries excluded (KAB). No additional levels of disaggregation by severity level are available. In Chapter 12 (Urban and Suburban Arterials), intersection SPFs predict average crash frequency for all crash severities combined (KABCO), FI crashes (KABC), and PDO crashes. No additional levels of disaggregation by severity level are available. The urban and suburban

43 intersection SPFs for different levels of severity were independently estimated. For any given collision type (e.g., MV) and site type (e.g., 3ST), it is likely that a “total” crash prediction (i.e., all severities) will not equal the sum of the FI and PDO predictions. Preliminary values for FI and PDO crashes obtained directly from the SPFs are therefore adjusted to make this summing process work. All vehicle-pedestrian and vehicle-bicycle crashes that are predicted as part of the urban and suburban intersection methods are treated as FI crashes (none as PDO). Finally, in Chapter 19 (Predictive Method for Ramps), intersection SPFs predict average crash frequency for FI crashes (KABC) and PDO crashes at crossroad ramp terminals of freeway interchanges. SDFs are then used to further disaggregate the SPF predicted average frequency of FI crashes into an estimate of average crash frequency for the following severity levels: fatal (K), incapacitating injury (A), non-incapacitating injury (B), and possible injury (C). Two SDFs are provided, one for one-way stop-control terminals and another for signalized terminals. These two SDFs are applicable to other subcategories of terminal types within these broader categories. The evolution in the way severity is addressed in HSM predictive methods explicitly recognizes that severity distributions may change with traffic volumes, design decisions, traffic control, and other characteristics. A synthesis paper by Savolainen et al. (2011) presents key issues and methodological approaches that have been used to understand how various factors influence the severity outcomes of crashes. While Savolainen et al. state that there has been substantial progress made in modeling crash severities, this progress has been made and tracked primarily by those making more theoretical advancements in methodological areas of crash severity modeling. Only more recently have these methods been incorporated into applied, product- oriented safety research, such as research aimed at developing predictive methods. For example, the research that resulted in the development of HSM Chapter 19 (Predictive Method for Ramps) utilized multinomial logit (MNL) models to develop the SDFs. Generally speaking, the databases used to estimate severity models and corresponding SDFs consist of the same crashes and intersections as the databases used to estimate the frequency models and corresponding SPFs, but the databases are restructured so that the basic observation unit (i.e., database row) is the crash instead of the intersection. To more seamlessly work together with existing HSM predictive methods, the multinomial logit (e.g., Shankar and Mannering, 1996), nested logit (e.g., Shankar et al., 1996), and the binary logit (e.g., Al-Ghamdi, A., 2002) are the most logical severity modeling alternatives. These three severity modeling alternatives begin with defining a set of linear functions (Sjr), shown in general form in Equation 27, that define how injury severity outcome j for crash r is determined. 𝑆 = 𝑋 β + 𝜖 (Eq. 27)

44 Where: Xjr = a row of observed characteristics (e.g., driver, vehicle, roadway, environment) associated with crash r that have an impact on injury severity outcome j βj = a vector of parameters to be estimated that quantify how the characteristics in Xjr impact injury severity outcome j εjr = a disturbance term that accounts for unobserved and unknown characteristics of crash r that impact injury severity outcome j There are as many such linear functions as there are possible injury severity outcomes. The probability of having injury severity outcome j for crash r is then the probability that the linear function for that severity outcome is larger than the functions for any other severity outcome, i.e.: 𝑃 (𝑗) = 𝑃 𝑆 ≥ 𝑆 ∀ 𝐽 ≠ 𝐽 (Eq. 28) or 𝑃 (𝑗) = 𝑃 𝑋 β + 𝜖 ≥ 𝑋 β + 𝜖 ∀ 𝐽 ≠ 𝐽 (Eq. 29) with J denoting all possible injury outcomes for crash r, and Pr(j) the probability of crash r having injury outcome j. Obviously, the injury severity outcome of a crash, given a set of observable characteristics, can never be predicted with certainty because the values of the disturbance terms for the different injury outcomes are never known with certainty. The severity models, ultimately leading to the SDFs, are developed by making assumptions about the properties of these disturbance terms. The multinomial logit model is commonly used to model crash severity in cases with three or more possible injury severity outcomes. In NCHRP Project 17-45, for example, FI outcomes were classified as either fatal and incapacitating injury (KA), non-incapacitating injury (B), or possible injury (C). If the disturbance terms of the linear functions referenced in Equations 27-29 are assumed to be identically and independently distributed as extreme value, the multinomial logit model, shown in Equation 30, results. 𝑃 (𝑗) = ( )∑ ( )∀ (Eq. 30) For model estimation, one of the injury outcome categories is arbitrarily selected as the “base injury severity outcome,” and all of its corresponding parameters (i.e., βj’s) are represented with zeroes. The remaining βj’s that are estimated represent the values for the βj’s relative to the βj’s for the selected “base injury severity outcome.” This results in the form seen in the HSM Chapter 19 SDFs and provided in more general form in Equation 31. 𝑃 (𝑗) = ( )∑ ( ) (Eq. 31)

45 Where j in this case represents all possible injury severity outcomes except for the base outcome. In NCHRP Project 17-45, for example, possible injury (C) was selected as the base outcome. Pr(KA) and Pr(B) were predicted using an equation similar to Equation 28; Pr(C) was then predicted as 1 - Pr(KA) - Pr(B). The MNL model provides a high level of flexibility in terms of model specification, allowing exploration of various possible severity-related relationships such as: • Certain roadway characteristics and traffic conditions impacting the probability of some severity outcomes relative to the base outcome, but not impacting others • Certain roadway characteristics and traffic conditions increasing (or decreasing) the probability of the higher severity outcomes relative to the base outcome, while also increasing (or decreasing) the probability of the lower severity outcomes The MNL assumption that the disturbance terms of the linear functions referenced in Equations 27-29 are identically and independently distributed as extreme value leads to a practical model form for interpretation and prediction. However, the main disadvantage of the MNL model is that it is characterized by the independence of irrelevant alternatives (IIA) assumption, meaning that it does not appropriately handle scenarios with two or more severity outcomes that are close substitutes with shared unobserved effects captured by their disturbance terms (i.e., violations of the IIA assumption). The nested logit model is a common modeling alternative for discrete outcome data when the IIA assumption is violated. In the case of crash injury severity outcomes, it might be expected that the linear functions, Sjr, for possible injury (C) and no injury (O) have some shared unobserved effects captured in the disturbance terms. This results in a nesting structure, similar to the example illustrated in Figure 3. Figure 3. Example of nested structure for crash injury severities (Savolainen et al., 2011) The nested logit model handles this nesting structure through making the assumption that the disturbance terms of the linear functions referenced in Equations 27-29 are generalized extreme

46 value distributed, resulting in the model structure shown in Equations 32-34 (as outlined in Washington et al., 2010 and Savolainen et al., 2011). 𝑃 (𝑗) = ( )∑ ( )∀ (Eq. 32) 𝑃 (𝑞|𝑗) = ( | )∑ ( | )∀ (Eq. 33) 𝐿𝑆 = 𝑙𝑛 ∑ 𝑒𝑥𝑝(𝑋 𝛽 | )∀ (Eq. 34) Where: Pr(j) = probability of crash r having injury outcome j, where j is an outcome in the “top level” of the nest (e.g., fatal injury, evident injury, or no evident injury) Xjr, Xqr = rows of observed characteristics (e.g., driver, vehicle, roadway, environment) associated with crash r that have an impact on injury severity outcome j (across the top level of the nests) and q (within the nests), respectively βj, βq|j = vectors of parameters to be estimated that quantify how the characteristics in Xjr and Xqr impact injury severity outcome j (across the top level of the nests) and q (within the nests), respectively Pr(q|j) = probability of crash r having injury outcome q, conditioned on the outcome being in category j (e.g., probability of either possible injury or no injury conditioned on a no evident injury crash) LSjr = “log-sum” or “inclusive value” for the nest (i.e., the expected value of the linear functions, such as those in Equation 27, for the outcomes within the nest) ϕj = “log-sum coefficient” to be estimated Within this framework, the probability of having one of the severity outcomes (q) within the nest, Pr(q), is given in Equation 35 (with all terms previously defined). Pr(q) = Pr(j) × Pr(q|j) (Eq. 35) For the nested logit to be considered an appropriate modeling alternative for a given context, the “log-sum coefficient” should fall between zero and one. If the parameter equals one, the model reduces to the MNL. A hypothesis test can be set up to determine whether the “log-sum coefficient” is different than one at some level of statistical significance. This approach was used in NCHRP Project 17-45 before selecting the MNL as an appropriate model form for estimating the HSM Chapter 19 SDFs. In cases where crash severity is assigned one of two possible outcomes [e.g., fatal and incapacitating injury (KA) or not (BCO)], there are only two such linear functions. With the disturbance terms of these two functions identically and independently distributed as extreme value, the binary logit model results, shown in Equation 36.

47 𝑃 (𝑗) = ( )( ) (Eq. 36) The outcome j in this case represents one of two possible injury severity outcomes. Continuing the example from the previous paragraph, an injury severity outcome can be classified as either fatal and incapacitating injury (KA) or not (BCO). If the BCO outcomes are set to the “base injury severity outcome,” the binary logit parameters could be estimated and the severity probabilities predicted using Equations 37 and 38. 𝑃 (𝐾𝐴) = ( )( ) (Eq. 37) 𝑃 (𝐵𝐶𝑂) = 1 − 𝑃 (𝐾𝐴) (Eq. 38) The binary logit is a key modeling alternative for multiple reasons, including: • Sample size challenges, particularly those associated with more severe injury outcomes, may limit the SDFs to being only “two-category SDFs” (an example of which is provided in Equations 37 and 38); • When injury severity outcomes are classified into more than two categories, estimating a series of binary logit models instead of an MNL model can “temper” estimation issues when IIA is violated. Anytime that more than one severity outcome has to be combined into one severity outcome category for SDF estimation (e.g., combining both “K” and “A” crashes into a “KA” category), the severity outcome proportions can later be disaggregated with a combination of the SDF probability prediction and default severity distributions for those categories. Treatment of Collision Type in Predictive Methods The way in which collision type is addressed within the HSM intersection predictive methods is also different from chapter to chapter, but not to the extent of severity differences. In Chapter 10 (Rural Two-Lane, Two-Way Roads), Chapter 11 (Rural Multilane Highways), and Chapter 19 (Ramps), intersection SPFs predict average crash frequency for all collision types combined. Default collision type distributions are then used to disaggregate the crash predictions by collision type. Different default collision type distributions are provided for different crash severities. An appendix to Chapter 11 also provides alternative SPFs by collision type for intersections along rural multilane highways. The HSM notes the advantage of this is that more accurate safety prediction for a specific collision type can be obtained using a model developed specifically for that collision type than from using a model for all collision types multiplied by a collision type proportion. The disadvantages include model availability for only selected collision types and the sum of predictions from a series of collision type models will not necessarily equal the prediction for a model with all those collision types combined. There were no base conditions or CMFs specific to the alternative SPFs. In Chapter 12 (Urban and Suburban Arterials), intersection SPFs and other predictive method components predict average crash frequency for the following collision types: MV (excluding crashes involving a pedestrian or bicyclist); SV (excluding crashes involving a pedestrian or bicyclist); vehicle-pedestrian; and

48 vehicle-bicycle. Handling collision types within HSM predictive methods remains a topic of ongoing research. Calibration Factors for Predictive Models The HSM calibration procedures for both predictive methods and SDFs are described in Section 2.1.6 of this report. In 2014, Bahar and Hauer (2014) prepared A User’s Guide to Develop Highway Safety Manual Safety Performance Function Calibration Factors to expand on calibration-related information provided to an HSM user (currently contained in the HSM’s Appendix A of Part C), covering four key aspects of predictive model calibration: • Why calibration is needed • How to implement the calibration process • How to assess the results of calibration • How to prepare for future calibration updates 2.3 Current Knowledge Related to Intersection Safety This section summarizes recent literature related to intersection safety, focusing on: • Predictive models developed for intersections configurations and traffic control types not currently addressed in the HSM; • Recently developed CMFs for intersections that could potentially be incorporated, or used in conjunction, with intersection predictive models. For this section, the research team reviewed literature published since 2008. Predictive Models for Intersection Configurations and Traffic Control Types Not Currently Addressed in the HSM Several predictive models have been developed for intersection configurations and traffic control types not currently addressed in the HSM, including three-leg intersections with signal control on rural highways and three- and four-leg intersections with all-way stop control on rural highways. Virginia Department of Transportation (DOT) developed SPFs using NB regression for several different intersection types, including three-leg intersections with signal control on rural highways (Garber and Rivera, 2010). SPFs were created for both total and FI severity levels. A total of 183 rural signalized three-leg intersections were used for model development. The models consisted of major- and minor road AADT. Safety Analyst contains SPFs developed for use in predicting the safety performance of specific site subtypes (Harwood et al., 2009). The SPFs developed for Safety Analyst predict crash frequency as a function of AADT only. NB regression was used to create the SPFs. Data from Minnesota were used to develop the intersection SPFs for Safety Analyst. Within Safety Analyst, SPFs to predict total and FI crash frequencies are available for the following intersection configurations and traffic control types not currently addressed in the HSM:

49 • Three-leg intersections with all-way stop control on rural highways - Software makes use of SPF for four-leg intersections with all-way stop control on rural highways for three-leg intersections with all-way stop control on rural highways • Three-leg intersections with signal control on rural highways - Software makes use of SPF for four-leg intersections with signal control on rural highways for three-leg intersections with signal control on rural highways • Four-leg intersections with all-way stop control on rural highways • Three-leg intersections with all-way stop control on urban streets - Software makes use of SPF for four-leg intersections with all-way stop control on rural highways for three-leg intersections with all-way stop control on urban streets • Four-leg intersections with all-way stop control on urban streets - Software makes use of SPF for four-leg intersections with all-way stop control on rural highways for four-leg intersections with all-way stop control on urban streets The Pennsylvania DOT developed SPFs (Donnell et al., 2014) for rural two-lane highway segments and intersections. Of the five types of intersections examined, two intersection types currently are not addressed in the HSM: three-leg intersections with signal control, and four-leg intersections with all-way stop control. The SPFs were created based on a NB distribution. Forty- five three-leg signalized intersections and thirty-three four-leg all-way stop-controlled intersections in Pennsylvania were used for model development. Several independent variables were used in the regression modeling for both three-leg intersections with signal control and four-leg intersections with all-way stop control. The independent variables used in the SPF for three-leg intersections with signal control on rural two-lane highways included major- and minor road AADTs, posted speed limit on the major road, and the presence/absence of marked crosswalks. For the four-leg intersection with all-way stop control SPF, significant predictor variables included major- and minor road AADTs and posted speed limit on the major road. Vehicle speed or posted speed limit is a variable that is not addressed in any fashion in the SPFs in the first edition of the HSM for any roadway segments or intersections. It is accounted for in some manner for ramps. Recently Developed CMFs for Intersection Predictive Models Not Currently Addressed in the HSM The following paragraphs summarize recently developed CMFs that are not addressed in the current HSM intersection predictive methodology and are not presented in HSM Part D, but could potentially be considered for use in a future edition of the HSM. The CMFs presented in this section address the following topics and countermeasures: • Intersection sight distance • Increase signal change interval • Change left-turn phasing from permissive to protected-permissive • Implement protected-permissive phasing with flashing yellow arrow for permissive phase

50 • Install dynamic signal warning flashers • Discontinue late night flash operations at signalized intersections • Construct bypass lanes In NCHRP Project 17-59, researchers developed CMFs for intersection sight distance at unsignalized intersections (i.e., intersections with minor road stop control). CMFs are available for total target crashes (i.e., crashes involving a vehicle on the mainline and a vehicle on the minor road) and several subsets of target crashes including: injury crashes, right-angle crashes, angle crashes, left-turn crashes, and daytime crashes. CMFs vary by major route volume, minor route volume, and available intersection sight distance. Srinivasan et al. (2011) developed several CMFs based on increasing the yellow interval, all red interval, and both, as well as comparing the change interval to Institute of Transportation Engineers (ITE) recommendations. CMFs were developed for total and FI severity levels and angle and rear-end crashes at urban signalized intersections. The CMFs were developed based on a before-after EB analysis. The CMFs that were found statistically significant at the 0.05 confidence level were for: increase the all red interval (total crashes); increase the change interval while still below ITE recommendation (total crashes and FI crashes); and increase the change interval while greater than ITE recommendation (rear-end crashes). Srinivasan et al. (2011) conducted a before-after EB analysis that produced CMFs for changing the left-turn phasing from permissive to protected-permissive at urban signalized intersections. There are separate CMFs for treating a single approach and treating more than one approach, as well as CMFs for total crashes, FI crashes, left-turn-opposing-through crashes, and rear-end crashes. Srinivasan et al. (2011) conducted a before-after EB and comparison group analysis to create CMFs for using a flashing yellow arrow for the permissive phase on a protected- permissive left turn at urban signalized intersections. CMFs were broken down into several categories based on permissive and protected phasing, and each category has a CMF for total crashes and left-turn crashes. Simpson and Troy (2015) also studied the safety effectiveness of replacing protected only, protected-permissive, and permissive-only left turns with flashing yellow arrows using an EB before-after methodology to develop several CMFs. Srinivasan et al. (2011) developed CMFs for installing dynamic signal warning flashers using data from 30 signalized intersections and cross-sectional models. CMFs were developed for total crashes, rear-end crashes, angle crashes, FI crashes, and heavy-vehicle crashes. The CMFs are applicable to urban and rural sites as well as three-leg and four-leg intersections. Lan and Srinivasan (2013) used naïve before-after, EB before-after, and Full Bayesian (FB) before-after (univariate Poisson-gamma as well as multivariate Poisson-log normal models) analysis approaches to establish CMFs for removing late night flash operations at rural and urban signalized intersections. Signalized intersections in North Carolina were examined: 61 sites with the treatment and 395 reference sites. CMFs were developed for total nighttime crashes, nighttime FI crashes, and nighttime frontal impact crashes. Shams and Dissanayake (2014) quantified the safety benefits of constructing bypass lanes at rural unsignalized intersections. A case-control study was used to estimate the safety effectiveness of bypass lanes at both three- and four-leg unsignalized intersections. There were

51 382 treated sites (302 four-leg, 80 three-leg intersections) and 367 untreated sites (319 four-leg, 48 three-leg intersections) included in the study. CMFs were estimated for total crashes (i.e., all collision types and severity levels). 2.4 Survey of Current Practice and Crash Prediction Needs The research team conducted a survey of state and local highway agencies and HSM users to inquire about their use and experiences with the HSM. The survey was intended to: • Better understand users’ experiences with the first edition of the HSM • Identify and prioritize intersection configuration needs for future editions of the HSM • Identify and prioritize intersection design elements and traffic control features considered by engineers and planners during the project development process that should be addressed in the new models • Identify potential agencies (and contacts) to work with towards the completion of the research objectives The survey was conducted online using SurveyMonkey, a web-based survey package. Responses from 24 state highway agencies, eight county/city highway agencies, and one FHWA representative were received. The survey results are summarized below. Responses to categorical questions are summarized by showing both the percentage of the responses and the frequency/number of responses shown in parentheses. For questions inquiring about priorities, as appropriate, the responses are sorted in priority order. Survey Results: HSM Intersection Survey • What type of agency do you work for? State highway agency 73.5% (25) County agency 11.8% (4) Township agency 0% (0) City or other municipal agency 11.8% (4) Design consultant 0% (0) Federal agency 2.9% (1) • What is your role within your agency? Safety engineer 52.9% (18) Traffic engineer 29.4% (10) Design engineer 5.9% (2) Planner 2.9% (1) Other 8.8% (3) • Has your agency incorporated the HSM into your policies, practices, and procedures? Yes 63.6% (21) No 36.4% (12) • How frequently does your agency use HSM procedures?

52 Very often 11.8% (4) Regularly 26.5% (9) Occasionally 38.2% (13) Rarely 23.5% (8) Never 0% (0) • Please indicate which parts of the HSM your agency uses frequently (select all that apply). Part A—Introduction, Human Factors, and Fundamentals of Safety 21.2% (7) Part B—Roadway Safety Management Process 42.4% (14) Part C—Predictive Methods 60.6% (20) Part D—Crash Modification Factors 78.8% (26) We have never used the HSM 3.0% (1) • Has your agency implemented HSM Part C procedures (crash prediction methods) as part of the planning and/or design of at-grade intersection projects? Yes 38.2% (13) No 61.8% (21) • For which types of at-grade intersections has your agency used the HSM Part C procedures (check all that apply)? Intersections along rural two-lane highways 70.0% (14) Intersections along rural multilane highways 40.0% (8) Intersections along urban and suburban arterials 65.0% (13) • What improvements or enhancements would be desirable for the HSM at-grade intersection procedures (please describe)? • Responses included adding specific SPFs for different types of control, SPFs for urban and suburban arterial intersections with six and eight lanes. One respondent suggested adding a method to estimate AADT on minor road approaches when precise AADT is not available for the minor road approaches. • What tools has your agency used to implement the HSM Part C procedures for intersections (check all that apply)? Interactive Highway Safety Design Model (IHSDM) 29.2% (7) Spreadsheet-based tools 75.0% (18) Tools developed by your agency 45.8% (11) Other (please describe below) 16.7% (4) • Vision Zero Suite and ISATe were two tools mentioned by respondents that answered “Other” for this question.

53 • Has your agency developed its own SPFs for use with HSM Part C? Yes 26.5% (9) We plan to develop our own SPFs 17.6% (6) No 55.9% (19) • If you answered “Yes” or “We plan to” to the previous question, what stage of the model development are you currently at for the following facility types? Plan to start development sometime in the future Plan to begin development within one month Have begun development Have completed initial development Model development is complete Intersections along rural two-lane highways 42.9% (6) 0% (0) 21.4% (3) 7.1% (1) 28.6% (4) Intersections along rural multilane highways 46.2% (6) 0% (0) 23.1% (3) 7.7% (1) 23.1% (3) Intersections along urban and suburban arterials 26.7% (4) 0% (0) 20.0% (3) 33.3% (5) 20.0% (3) • The following intersection types are not included in the current HSM Part C procedures. Please rate the priority for inclusion of each intersection type in HSM updates ( 1= lowest priority; 5 = highest priority). (NOTE: Roundabouts will not be addressed in this project, but will be addressed in NCHRP Project 17-70.) Lowest Priority Highest Priority Weighted Average 1 2 3 4 5 Intersections with all-way stop control 6.2% (2) 15.6% (5) 21.9% (7) 25.0% (8) 31.2% (10) 3.59 Three-leg signalized intersections on rural two-lane highways 9.4% (3) 12.5% (4) 25.0% (8) 25.0% (8) 28.1% (9) 3.50 Intersections on high-speed expressways 22.6% (7) 3.2% (1) 19.4% (6) 12.9% (4) 41.9% (13) 3.48 Three-leg signalized intersections on rural multilane highways 15.6% (5) 18.8% (6) 21.9% (7) 25.0% (8) 18.8% (6) 3.13 Three-leg intersections where the through movement makes a turning maneuver at the intersection 6.3% (2) 25.0% (8) 34.4% (11) 28.1% (9) 6.2% (2) 3.03 Three-leg intersections with a commercial driveway forming the fourth leg 9.4% (3) 15.6% (5) 50.0% (16) 15.6% (5) 9.4% (3) 3.00 Five-leg intersections 24.2% (8) 21.2% (7) 24.2% (8) 21.2% (7) 9.1% (3) 2.70 Single-point diamond ramp terminal at crossroad 25.8% (8) 19.4% (6) 25.8% (8) 25.8% (8) 3.2% (1) 2.61 Diverging-diamond ramp terminals at crossroad 19.4% (6) 25.8% (8) 35.5% (11) 12.9% (4) 6.4% (2) 2.61 Intersections with yield control on minor approaches 31.2% (10) 37.5% (12) 21.9% (7) 9.4% (3) 0.0% (0) 2.09 Six-or-more-leg intersections 45.2% (14) 22.6% (7) 22.6% (7) 3.2% (1) 6.4% (2) 2.03 Intersections with no control (typically very low traffic volumes) 60.6% (20) 18.2% (6) 12.1% (4) 6.1% (2) 3.0% (1) 1.73

54 • Are there any other intersection configurations not listed in the previous question that you believe should receive high priority for inclusion in the HSM? - U-turn intersections, also referred to as J-turn intersections, were mentioned the most by survey respondents. Continuous flow intersections and continuous green “T” intersections were also mentioned frequently. Roundabouts and one-way crossing two-way intersections were also suggested by respondents; however, these intersection types are being addressed in other NCHRP projects. • Current HSM procedures include the effects on safety of number of intersection legs, intersection traffic control, major- and minor road AADTs, intersection skew angle, left- and right-turn lanes, left-turn phasing, right-turn-on-red, lighting, and red light cameras. What additional intersection design elements should desirably have safety effects included in HSM predictive methods? (Please check all that apply.) Intersection sight distance 71.9% (23) Number of approach lanes 62.5% (20) Horizontal alignment on approaches 59.4% (19) Offset left-turn lane 59.4% (19) Median width 50.0% (16) Vertical alignment on approaches 50.0% (16) Sight distance to traffic control device 43.8% (14) Median type 43.8% (14) Curb return radius 25.0% (8) Transverse rumble strips 21.9% (7) Approach width 21.9% (7) Bulbout 21.9% (7) Raised intersection 3.1% (1) - Additional design elements suggested by survey respondents included lane width, presence of dual turn lanes (left and/or right), and right-turn channelization. • Which intersection traffic control features should desirably have safety effects included in HSM predictive methods? - Typical responses included advance warning flashers, attributes of signals (flashing yellow arrow, presence of coordinated/adaptive signal, signal head size, right-turn overlap and retroreflective signal backplates), and pedestrian countdown signals. • For development of the next edition of the HSM, please rate the priority that should be assigned to each of the following (1 = lowest priority, 5 = highest priority). Lowest Priority Highest Priority Weighted Average 1 2 3 4 5 Adding new at-grade intersection types to the HSM Part C procedures 6.3% (2) 15.6% (5) 18.8% (6) 31.2% (10) 28.1% (9) 3.59 Improving current HSM Part C procedures for existing intersection types (e.g., replacing crash severity distribution tables with crash SDFs) 6.1% (2) 18.2% (6) 24.2% (8) 24.2% (8) 27.3% (9) 3.48 Developing pedestrian crash prediction procedures for additional intersection types 9.1% (3) 12.1% (4) 33.3% (11) 21.2% (7) 24.2% (8) 3.39 Developing new bicycle crash prediction procedures 15.2% (5) 24.2% (8) 15.2% (5) 21.2% (7) 24.2% (8) 3.15

55 • What types of data does your agency have available for intersections that might be useful for development of intersection crash prediction models? (Please check all that apply.) Intersection characteristics (intersection inventory data) 54.6% (18) AADT data for major road legs of intersections 93.9% (31) AADT data for minor road legs of intersections 69.7% (23) Pedestrian volumes at intersections 3.0% (1) Bicycle volumes at intersections 3.0% (1) Crash data for intersections 97.0% (32) • For which of the following intersection types does your agency have sufficient locations for development of intersection crash prediction models (25 or more intersections are desirable)? (Please check all that apply.) Intersections with all-way stop control 70.4% (19) Intersections on high-speed expressways 48.2% (13) Three-leg intersections with a commercial driveway forming the fourth leg 37.0% (10) Intersections with no control (typically very low traffic volumes) 29.6% (8) Three-leg intersections where the through movement makes a turning maneuver at the intersection 18.5% (5) Single-point diamond ramp terminal at crossroad 18.5% (5) Intersections with yield control on minor approaches 14.8% (4) Five-leg intersections 14.8% (4) Diverging-diamond ramp terminals at crossroad 7.4% (2) Six-or-more-leg intersections 0.0% (0) • Would your agency be willing to supply data to the NCHRP Project 17-68 research team for developing intersection crash prediction models? Yes 21.9% (7) Possibly (after further discussion) 75.0% (24) No 3.1% (1) 2.5 Summary of Current Knowledge Related to Intersection Crash Prediction Modeling The existing HSM crash predictive methods all have a common structure to estimate the expected average crash frequency, which include: • SPFs; • Crash severity and collision type distributions; • CMFs; • Calibration procedures; • EB estimation. However, the sophistication of the predictive methods has evolved as the chapters have been developed. In particular, the science of crash severity prediction has evolved. Specifically, Chapter 10 uses SPFs for all crash severities combined, with tabulated severity distributions used to disaggregate the crash frequency predictions by individual crash severity levels. Chapters 11 and 12 use separate SPFs by crash severity level, while Chapter 19 uses a single SPF for all FI crash severity levels combined and a separate SPF for PDO crashes and then uses crash SDFs to disaggregate the overall crash frequency by severity level.

56 SPFs for intersections are equations that relate the expected intersection crash frequency (possibly by type and/or severity) for some defined time period to characteristics of the intersection. In the context of the HSM intersection predictive methods, SPFs are used to estimate a predicted average intersection crash frequency for a given combination of major- and minor road traffic volumes. The progress made in methodological approaches that have been used to develop SPFs and to understand how various factors influence the frequency of crashes has been substantial since the publication of the first edition of the HSM.

Next: Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control »
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The first edition of the Highway Safety Manual (HSM), in 2010, included Safety Performance Functions (SPFs) for roadway segments and intersections. However, not all intersection types are covered in the first edition of the HSM.

The TRB National Cooperative Highway Research Program's NCHRP Web-Only Document 297: Intersection Crash Prediction Methods for the Highway Safety Manual develops SPFs for new intersection configurations and traffic control types not covered in the first edition of the HSM, for consideration in the second edition of the HSM.

Supplemental to the Document is recommended draft text for the second edition if the HSM, a worksheet for Chapter 10, a worksheet for Chapter 11, a worksheet for Chapter 12, a worksheet for Chapter 19, and a presentation.

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