Multivariate random parameters collision count data models with spatial heterogeneity

• Incorporated spatial correlation in multivariate random parameters collision model.
• Developed multivariate models for severe and no-injury collisions.
• Used collision, traffic, and geometrical data from the city of Vancouver.
• Three different multivariate model formulations yielded comparable results.
• Multivariate random parameters spatial models outperformed their univariate counterpart.

This study investigated the effects of including spatial heterogeneity in multivariate random parameters models and their influence on different collision severity levels. The models were developed for severe (injury and fatal) and no-injury collisions using three years of collision data from the city of Vancouver. Three different modeling formulations were applied to measure the effects of spatial heterogeneity in a multivariate random parameters model. The proposed models were estimated in a Full Bayesian (FB) context using Markov Chain Monte Carlo (MCMC) simulation. The Deviance Information Criteria (DIC) values indicated that all the models were comparable to one another. Therefore, no particular model can be distinctly preferred over others. According to parameter estimates, a variety of traffic and road geometric covariates were found to significantly influence collision severities. The variance for spatial heterogeneity was higher than the variance for heterogeneous effects. The correlation between severe and no-injury collisions for the total random effects (heterogeneous and spatial) was significant and quite high, indicating that higher no-injury collisions are associated with higher severe collisions. These results support the incorporation of spatial heterogeneity in multivariate random parameters models. Furthermore, the multivariate random parameters spatial models were compared with two independent univariate random parameters spatial models with respect to model inference and goodness of fit. The multivariate spatial models outperformed the two univariate spatial models with a very significant drop in the DIC value.