Bayesian nonparametric modeling in transportation safety studies: Applications in univariate and multivariate settings

In transportation safety studies, it is often necessary to account for unobserved heterogeneity and multimodality in data. The commonly used standard or over-dispersed generalized linear models (e.g., negative binomial models) do not fully address unobserved heterogeneity, assuming that crash frequencies follow unimodal exponential families of distributions. This paper employs Bayesian nonparametric Dirichlet process mixture models demonstrating some of their major advantages in transportation safety studies. We examine the performance of the proposed approach using both simulated and real data. We compare the proposed model with other models commonly used in road safety literature including the Poisson-Gamma, random effects, and conventional latent class models. We use pseudo Bayes factors as the goodness-of-fit measure, and also examine the performance of the proposed model in terms of replicating datasets with high proportions of zero crashes. In a multivariate setting, we extend the standard multivariate Poisson-lognormal model to a more flexible Dirichlet process mixture multivariate model. We allow for interdependence between outcomes through a nonparametric random effects density. Finally, we demonstrate how the robustness to parametric distributional assumptions (usually the multivariate normal density) can be examined using a mixture of points model when different (multivariate) outcomes are modeled jointly.