Application of finite mixture of negative binomial regression models with varying weight parameters for vehicle crash data analysis.

Recently, a finite mixture of negative binomial (NB) regression models has been proposed to address the unobserved heterogeneity problem in vehicle crash data. This approach can provide useful information about features of the population under study. For a standard finite mixture of regression models, previous studies have used a fixed weight parameter that is applied to the entire dataset. However, various studies suggest modeling the weight parameter as a function of the explanatory variables in the data. The objective of this study is to investigate the differences on the modeling and fitting results between the two-component finite mixture of NB regression models with fixed weight parameters (FMNB-2) and the two-component finite mixture of NB regression models with varying weight parameters (GFMNB-2), and compare the group classification from both models. To accomplish the objective of this study, the FMNB-2 and GFMNB-2 models are applied to two crash datasets. The important findings can be summarized as follows: first, the GFMNB-2 models can provide more reasonable classification results, as well as better statistical fitting performance than the FMNB-2 models; second, the GFMNB-2 models can be used to better reveal the source of dispersion observed in the crash data than the FMNB-2 models. Therefore, it is concluded that in many cases the GFMNB-2 models may be a better alternative to the FMNB-2 models for explaining the heterogeneity and the nature of the dispersion in the crash data.