Application of Finite Mixture Models for Vehicle Crash Data Analysis

Developing sound or reliable statistical models for analyzing vehicle crashes is veryimportant in highway safety studies. A difficulty arises when crash data exhibit overdispersion.Over-dispersion caused by unobserved heterogeneity is a serious problemand has been addressed in a variety ways within the negative binomial (NB) modelingframework. However, the true factors that affect heterogeneity are often unknown toresearchers, and failure to accommodate such heterogeneity in the model can underminethe validity of the empirical results.Given the limitations of the NB regression model for addressing over-dispersion of crashdata due to heterogeneity, this research examined an alternative model formulation thatcould be used for capturing heterogeneity through the use of finite mixture regressionmodels. A Finite mixture of Poisson or NB regression models is especially useful whenthe count data were generated from a heterogeneous population. To evaluate thesemodels, Poisson and NB mixture models were estimated using both simulated andempirical crash datasets, and the results were compared to those from a single NBregression model. For model parameter estimation, a Bayesian approach was adopted,since it provides much richer inference than the maximum likelihood approach.Using simulated datasets, it was shown that the single NB model is biased if theunderlying cause of heterogeneity is due to the existence of multiple counting processes.The implications could be poor prediction performance and poor interpretation. Using two empirical datasets, the results demonstrated that a two-component finite mixture ofNB regression models (FMNB-2) was quite enough to characterize the uncertainty aboutthe crash occurrence, and it provided more opportunities for interpretation of the datasetwhich are not available from the standard NB model. Based on the models from theempirical dataset (i.e., FMNB-2 and NB models), their relative performances were alsoexamined in terms of hotspot identification and accident modification factors. Finally,using a simulation study, bias properties of the posterior summary statistics fordispersion parameters in FMNB-2 model were characterized, and the guidelines on thechoice of priors and the summary statistics to use were presented for different samplesizes and sample-mean values.