A random parameters regional quantile analysis for the varying effect of road-level risk factors on crash rates

Abstract

Many studies have been devoted to investigate the spatial variations (heterogeneities) in the effects of risk factors on crash likelihood. However, investigations mainly target the safety effects on the mean of the crash data (distribution). Less attention was paid to investigate the spatial nonstationary effects on the different quantiles of the crash data distribution. In this study, a conditional quantile-based Bayesian hierarchical random parameter Tobit model is proposed to investigate the regional varying effects of road-related factors on crash rate at different quantiles of the crash rate distribution. A specific roadway facility type, urban two-lane two-way roadway segments in Florida, with crash and road related data for a three-year period is used for a case study. The results show that: 1) the regression coefficients of all of the selected risk factors vary over a wide range among 34 counties on every investigated quantiles of crash rate distribution; 2) in each county, the regression coefficients of all of the factors vary over investigated quantiles of the crash rate distribution, and for the same factor, the coefficients present different ranges of the variation in different counties; 3) the 50th-quantile conditional quantile-based Bayesian hierarchical random parameter Tobit model outperforms the conditional mean-based Bayesian hierarchical random parameter Tobit model, Bayesian quantile Tobit model and Bayesian Tobit model in terms of the prediction accuracy measured by the MAE, and 75th-quantile conditional quantile-based Bayesian hierarchical random parameter Tobit model is outstanding in terms of the goodness-of-fit measured by the DIC. These findings suggest the importance of investigating the regional nonstationary effects of risk factors for different quantiles of the crash rate distribution. The practical implications of the proposed conditional quantile-based Bayesian hierarchical random parameter Tobit model in terms of data prediction, parameters interpretation and safety effects explanation are highlighted at the end of this paper.