Application of different negative binomial parameterizations to develop safety performance functions for non-federal aid system roads

•The model outperforms the NB model., regardless of the variance/dispersion structure.•The dispersion and variance structures can significantly affect the model performance.•Each family of models developed in this study (NB-L and NB) favors a specific dispersion structure.•The choice of the variance structure does not only depend on the data, but also on the NB formulation.•A NB-L model with a reasonably chosen dispersion/variance structure yield better estimates. Safety performance functions (SPFs) are the main building blocks in understanding the relationships between crash risk factors and crash frequencies. Many research efforts have focused on high-volume roadways that typically experience more crashes. A few studies have documented SPFs for non-federal aid system (NFAS) roads including rural minor collectors, rural local roads, and urban local roads. NFAS roads are characterized by unique features such as lower speeds, and shorter segment lengths, and they usually experience fewer crashes given the low exposure of these roads. As a result, there is a clear need to investigate the associated safety issues of NFAS roadways and generate distinct SPFs for them. The main objective of this study is to bridge the gap in the literature and develop SPFs for NFAS roads. This study examined the application of traditional negative binomial and zero-favored negative binomial models (i.e., negative binomial-Lindley). Both groups of models were formulated by different variance and dispersion structures. Using crash, roadway inventory, and traffic volume data from 2014 to 2018 in Virginia, the results showed that the NB-L models perform better than the traditional NB models. Furthermore, an appropriate variance structure along with a reasonably chosen dispersion function can further improve the model performance.