Estimation of safety performance functions for urban intersections using various functional forms of the negative binomial regression model and a generalized Poisson regression model

•Multiple safety performance functions (SPFs) are developed by crash severity for urban intersections.•Three functional forms of negative binomial (NB) models and a generalized Poisson (GP) model are used to develop the SPFs.•The developed SPFs are compared based on goodness of fit and predictive performance measures to choose a better model.•The NB-P model outperforms the competing models for signalized intersections.•The GP model outperforms the competing models for unsignalized intersections. Intersections are established dangerous entities of a highway system due to the challenging and unsafe roadway environment they are characterized for drivers and other road users. In efforts to improve safety, an enormous interest has been shown in developing statistical models for intersection crash prediction and explanation. The selection of an adequate form of the statistical model is of great importance for the accurate estimation of crash frequency and the correct identification of crash contributing factors. Using a six-year crash data, road infrastructure and geometric design data, and traffic flow data of urban intersections, we applied three different functional forms of negative binomial models (i.e., NB-1, NB-2, NB-P) and a generalized Poisson (GP) model to develop safety performance functions (SPF) by crash severity for signalized and unsignalized intersections. This paper presents the relationships found between the explanatory variables and the expected crash frequency. It reports the comparison of different models for total, injury & fatal, and property damage only crashes in order to obtain ones with the maximum estimation accuracy. The comparison of models was based on the goodness of fit and the prediction performance measures. The fitted models showed that the traffic flow and several variables related to road infrastructure and geometric design significantly influence the intersection crash frequency. Further, the goodness of fit and the prediction performance measures revealed that the NB-P model outperformed other models in most crash severity levels for signalized intersections. For the unsignalized intersections, the GP model was the best performing model. When only the NB models were compared, the functional form NB-P performed better than the traditional NB-1 and, more specifically, the NB-2 models. In conclusion, our findings suggest a potential improvement in the estimation accuracy of the SPFs for urban intersections by applying the NB