Hierarchical Bayesian Estimation of Safety Performance Functions for Two-Lane Highways Using Markov Chain Monte Carlo Modeling

A critical part of any risk assessment is identifying how to represent exposure to the risk involved. Recent research shows that the relationship between crash count and traffic volume is nonlinear; consequently, a simple crash rate computed as the ratio of crash count to volume is not suitable for comparing the safety of sites with different traffic volumes. To solve this problem, we describe a new approach for relating traffic volume and crash incidence. Specifically, we disaggregate crashes into four types: (1) single-vehicle, (2) multivehicle same direction, (3) multivehicle opposite direction, and (4) multivehicle intersecting, and then define candidate exposure measures for each (as a function of site traffic volumes) that we hypothesize will be linear with respect to each crash type. This article describes investigation using crash and physical characteristics data for highway segments from Michigan, California, Washington, and Illinois obtained from the Highway Safety Information System. We have used a hierarchical Bayesian framework to fit zero-inflated-Poisson regression models for predicting counts for each of the above crash types as a function of the daily volume, segment length, speed limit and lane/shoulder width using Markov Chain Monte Carlo methods. We found that the relationship between crashes and the daily volume is nonlinear and varies by crash type, and is significantly different from the relationship between crashes and segment length for all crash types. Significant differences in exposure functions by crash type are proven using analysis of variance and Tukey tests.