Correlated Random-Effects Bivariate Poisson Lognormal Model to Study Single-Vehicle and Multivehicle Crashes

Developing crash-prediction models remains one of the primary approaches for studying traffic safety. Most of the current studies on single-vehicle (SV) and multivehicle (MV) crashes have only focused on the effects of exposure and geometric features of roadways and the effects of weather and traffic conditions are rarely incorporated. To provide more insightful observations, detailed weather and traffic data are adopted in this study. As a result of adopting detailed data, multiple daily observations are generated for SV and MV crashes on each roadway segment, forming a multivariate panel data set that poses some methodological challenges. A new approach to analyze SV and MV crashes is proposed by developing a bivariate Poisson lognormal model with correlated segment-specific random effects. The proposed model can characterize both the multivariate and panel nature of the data, and readily address the following three types of serial correlations within the multivariate panel data used in this study: (1) correlation between SV and MV; (2) temporal correlations across time within each segment for SV and MV, respectively; and (3) possible connection between temporal correlations for SV and MV crashes. It is found that the proposed model outperforms the two competing models by addressing as much unobserved heterogeneity as possible, dealing with excessive zeros in the observed data, and bearing the smallest deviance information criteria value. The proposed methodology is applied to a mountainous freeway section on I-70 in Colorado, where the climate is subjected to rapid change due to high elevation. Results show that weather- and traffic-related explanatory variables, especially surface conditions, play a significant role in affecting the occurrence of SV and MV crashes. Moreover, differences between contributing factors for SV and MV crashes are also investigated.