Full Bayes Poisson gamma, Poisson lognormal, and zero inflated random effects models: Comparing the precision of crash frequency estimates.

In recent years, complex statistical modeling approaches have being proposed to handle the unobserved heterogeneity and the excess of zeros frequently found in crash data, including random effects and zero inflated models. This research compares random effects, zero inflated, and zero inflated random effects models using a full Bayes hierarchical approach. The models are compared not just in terms of goodness-of-fit measures but also in terms of precision of posterior crash frequency estimates since the precision of these estimates is vital for ranking of sites for engineering improvement. Fixed-over-time random effects models are also compared to independent-over-time random effects models. For the crash dataset being analyzed, it was found that once the random effects are included in the zero inflated models, the probability of being in the zero state is drastically reduced, and the zero inflated models degenerate to their non zero inflated counterparts. Also by fixing the random effects over time the fit of the models and the precision of the crash frequency estimates are significantly increased. It was found that the rankings of the fixed-over-time random effects models are very consistent among them. In addition, the results show that by fixing the random effects over time, the standard errors of the crash frequency estimates are significantly reduced for the majority of the segments on the top of the ranking.