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Heydari, S., Fu, L., Joseph, L., Miranda-Moreno-L.F. (2016). Bayesian nonparametric modeling in transportation safety studies: Applications in univariate and multivariate settings. Analytic Methods in Accident Research, 12, 18-34.

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.

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