Development of Crash Prediction Models for Urban Road Segments Using Poisson Inverse Gaussian Regression

Transportation safety researchers utilize crash prediction models (CPMs) to examine the safety performance of roadway facilities. Using statistical modeling, the CPMs associate traffic and roadway design elements to crash frequency. Many studies in recent years have applied relatively advanced techniques to model crash data. Regardless of this, the traditional negative binomial (NB) model remains highly popular, probably because of the ease of estimation and the ability to accommodate overdispersion. Though the NB model performs well for data with moderate to low overdispersion, its performance is compromised in the case of highly overdispersed data. Analysts need alternative approaches to model such data sets. The Poissoninverse Gaussian (PIG) regression modeling framework has shown the potential to model highly dispersed data more effectively due to the flexible nature of the inverse Gaussian distribution. This study applied the PIG regression framework to model a six-year crash data for urban road segments, taking the traffic volume and roadway geometric design attributes as predictor variables. We compared the PIG models with the traditional NB models for goodness-of-fit and predictive performance. Moreover, we computed the prediction intervals (PIs) for the predicted responses at new sites to examine the level of uncertainty beyond the point estimates for the two modeling frameworks. The PIG and NB models revealed a significant association between the predictor variables (i.e., traffic volume and roadway design attributes) and crash frequency. In terms of performance (i.e., goodness-of-fit, predictive performance, and prediction intervals), the PIG models performed either better or equally well for the models developed in this study. In conclusion, the PIG models could be adopted as a potential alternative to the NB models, given the convenience in their estimation and the ability to accommodate overdispersion.