Empirical Bayes estimates of finite mixture of negative binomial regression models and its application to highway safety

ABSTRACT

The empirical Bayes (EB) method is commonly used by transportation safety analysts for conducting different types of safety analyses, such as before–after studies and hotspot analyses. To date, most implementations of the EB method have been applied using a negative binomial (NB) model, as it can easily accommodate the overdispersion commonly observed in crash data. Recent studies have shown that a generalized finite mixture of NB models with K mixture components (GFMNB-K) can also be used to model crash data subjected to overdispersion and generally offers better statistical performance than the traditional NB model. So far, nobody has developed how the EB method could be used with finite mixtures of NB models. The main objective of this study is therefore to use a GFMNB-K model in the calculation of EB estimates. Specifically, GFMNB-K models with varying weight parameters are developed to analyze crash data from Indiana and Texas. The main finding shows that the rankings produced by the NB and GFMNB-2 models for hotspot identification are often quite different, and this was especially noticeable with the Texas dataset. Finally, a simulation study designed to examine which model formulation can better identify the hotspot is recommended as our future research.

KEYWORDS:

• Finite mixture model
• varying weight parameters
• empirical Bayes method
• negative binomial
• vehicle crash data
• hotspot identification

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is sponsored jointly by the National Natural Science Foundation of China (grant number 51608386) and Shanghai Sailing Program (grant number 16YF1411900). The paper benefitted from the input of reviewers and their comments are greatly appreciated.