A Full Bayesian multivariate count data model of collision severity with spatial correlation

• Investigated the inclusion of spatial and heterogeneous effects in safety models.
• Developed multivariate models for severe and no-injury collisions.
• Used collision, traffic, and geometrical data from two cities in Canada.
• Model with both spatial and heterogeneous effects provided the best fit.
• Multivariate spatial models outperformed the univariate spatial models.

This study investigated the inclusion of spatial correlation in multivariate count data models of collision severity. The models were developed for severe (injury and fatal) and no-injury collisions using three years of collision data from the city of Richmond and the city of Vancouver. The proposed models were estimated in a Full Bayesian (FB) context via Markov Chain Monte Carlo (MCMC) simulation. The multivariate model with both heterogeneous effects and spatial correlation provided the best fit according to the Deviance Information Criteria (DIC). The results showed significant positive correlation between various road attributes and collision severities. For the Richmond dataset, the proportion of variance for spatial correlation was smaller than the proportion of variance for heterogeneous effects. Conversely, the spatial variance was greater than the heterogeneous variance for the Vancouver dataset. The correlation between severe and no-injury collisions for the total random effects (heterogeneous and spatial) was significant and quite high (0.905 for Richmond and 0.945 for Vancouver), indicating that a higher number of no-injury collisions is associated with a higher number of severe collisions. Furthermore, the multivariate spatial models were compared with two independent univariate Poisson lognormal (PLN) spatial models, with respect to model inference and goodness-of-fit. Multivariate spatial models provide a superior fit over the two univariate PLN spatial models with a significant drop in the DIC value (35.3 for Richmond and 116 for Vancouver). These results advocate the use of multivariate models with both heterogeneous effects and spatial correlation over univariate PLN spatial models.