A hierarchical Bayesian logistic regression with a finite mixture for identifying higher-than-expected crash proportions at intersections

The identification of high proportion of crashes at intersections is important in traffic safety management. Most statistical methods for that purpose have utilized greater-than-expected crash frequencies. However, methods utilizing higher-than-expected proportions of target crashes can also be used. One such method is included in the Highway Safety Manual (HSM). The HSM identifies crash patterns by making inferences from a Bayesian posterior beta-binomial probability distribution of the crash proportion at each location. For this research, another Bayesian method, hierarchical Bayesian logistic regression (HB), is applied and compared with the HSM. For this method, a mixture of three normal distributions was used to estimate location effects and handle an asymmetrical long-tailed crash frequency distribution. The methods are empirically tested and compared using signalized intersection crash data from Minnesota from 2003 to 2007. The proposed method demonstrated that the HB model is a robust alternative to identify crash patterns, particularly for multimodal or sparsely distributed data. The HB method is aligned theoretically with location ranking and inference strategies. It is shown to more efficiently identify crash patterns than the HSM method although the HB method is more computationally complex and demanding.