A Bayesian semi-parametric model to estimate relationships between crash counts and roadway characteristics

This paper uses a semi-parametric Poisson-gamma model to estimate the relationships between crash counts and various roadway characteristics, including curvature, traffic levels, speed limit and surface width. A Bayesian nonparametric estimation procedure is employed for the model's link function, substantially reducing the risk of a mis-specified model. It is shown via simulation that little is lost in terms of estimation quality if the nonparametric estimation procedure is used when standard parametric assumptions (e.g., linear functional forms) are satisfied, but there is significant gain if the parametric assumptions are violated. It is also shown that imposing appropriate monotonicity constraints on the relationships provides better function estimates. Results suggest that key factors for explaining crash rate variability across roadways are the amount and density of traffic, presence and degree of a horizontal curve, and road classification. Issues related to count forecasting on individual roadway segments and out-of-sample validation measures also are discussed.