Analysis of Factors Influencing Road Crashes in the Urban Areas: The Application of Generalized Poisson Model vs Negative Binomial Model

Abstract

Transportation safety researchers extensively apply the negative binomial (NB) modeling framework to analyze crash data and identify factors influencing road crashes due to its ability to accommodate overdispersion. However, a few studies have informed that crash data can sometimes exhibit under-dispersion, meaning smaller data variance than its mean. The NB model cannot accommodate under-dispersion. In statistics and econometrics, generalized Poisson (GP) regression is applied to address over- and/or underdispersion, but its application in transportation safety is scarce. Another issue that is often highlighted in safety literature is the complex and somewhat contradictory understanding of the relationship between crash frequency and other covariates in urban areas. In this study, we applied the GP modeling framework to examine the impact of various geometric design factors and traffic volume on the frequency of different crash types in an urban context. We also applied the NB model to the same data and compared its results with the GP models using goodness-of-fit and predictive performance measures. The analysis showed that roadway design characteristics, including lane width, number of lanes, road separation, on-street parking, posted speed limit, and traffic volume, contribute to urban road crashes. Besides, it was revealed that the GP models outperformed the NB models for some crash types and demonstrated almost similar performance for the remaining ones. Given the predictive performance, ease of estimation, and ability to model under- and over-dispersion, our study proposes that the GP model could be a potential alternative to the NB model in crash data analysis.