Effects of Spatial Correlation in Collision Modelling

Abstract

Despite previous research advocating the inclusion of spatially correlated random effects in order to significantly improve the estimation of the expected collision frequency, limited research efforts have been devoted to incorporating spatial correlation in both multivariate and random parameters collision modelling. Therefore, this thesis attempts to investigate the effects of including spatial correlation in three different collision modelling formulations: i) multivariate models, ii) univariate random parameters models, and iii) multivariate random parameters models. The models were developed 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 Deviance Information Criteria (DIC) and chi-square statistics were used to compare models and assess their goodness-of-fit, respectively. Models with spatial correlation yielded the best inference in terms of unbiased parameter estimates, precision, and capturing the multivariate nature of the collision data. Results showed significant and positive correlation between various road attributes and collision occurrence. A high percentage of the total variability was explained by the spatial correlation in most cases. This finding indicates that ignoring spatial correlation in collision modelling may lead to biased parameter estimation. The results also exhibit high and significant posterior correlation between severe and non-injury collisions for the total random effects (heterogeneous and spatial), indicating that a higher number of non-injury collisions is associated with a higher number of severe collisions. Furthermore, both multivariate spatial models and multivariate random parameters spatial models were compared against their univariate counterpart with respect to model inference and goodness-of-fit. Multivariate spatial models provide a superior fit over the two univariate spatial models, as demonstrated by a very significant drop in the DIC value. Similarly, multivariate random parameters spatial models outperformed the univariate random parameters spatial models.