A caution about using deviance information criterion while modeling traffic crashes

• Our study recommends not considering the DIC as the sole model selection criterion.
• Comparison should be done between the models that have similar parameterization.
• The study also recommends considering other alternatives in addition to the DIC.

The Poisson-Gamma (PG) or negative binomial (NB) model still remains the most popular method used for analyzing count data. In the software WinBUGS (or any other software used for Bayesian analyses), there are different ways to parameterize the NB model. In general, either a PG (based on the Poisson-mixture) or a NB (based on the Pascal distribution) modeling framework can be used to relate traffic crashes to the explanatory variables. However, it is important to note that the way the model is parameterized will influence the output of the Deviance Information Criterion (DIC) values. The objective of this short study is to document the difference between the PG and NB models in the estimation of the DIC. This is especially important given that the NB/PG model is still the most frequently used model in highway safety research and applications. To accomplish the study objective, PG and NB models were developed using the crash data collected at 4-legged signalized intersections in Toronto, Ont. The study results showed that there is a considerable difference in the estimation of the DIC values between the two models. It is thus recommended not to consider the DIC as the sole model selection criterion and the comparison should be done only between the models that have similar parameterization. Other alternatives such as Bayes Factors, Posterior predictive performance criterion, Bayesian Information Criterion (BIC), among others need to be considered in addition to the DIC in the model selection.