Functional forms of the negative binomial models in safety performance functions for rural two-lane intersections

Safety Performance Functions (SPFs) play a prominent role in estimating intersection crashes, and identifying the sites with the highest potential for safety improvement. To maximize the crash prediction accuracy, this paper describes the application of different functional forms of the Negative Binomial (NB) models (i.e. NB-1, NB-2 and NB-P) in estimating safety performance functions by crash type for three types of rural two-lane intersections, including three-leg stop-controlled (3ST) intersections, four-leg stop-controlled (4ST) intersections and four-leg signalized (4SG) intersections. Crash types were aggregated into same-direction, opposite-direction, intersecting-direction and single-vehicle crashes. Major and minor road Annual Average Daily Traffic (AADT) were used as predictors in the SPF estimation. In addition, major and minor road AADT were also used as predictors in the estimation of the over-dispersion parameter of the NB models to account for the crash data heterogeneity. In the end, all NB models were compared based on both the model estimation goodness-of-fit and the prediction performance. The model goodness-of-fit indicates that the NB-P model outperforms the NB-1 and NB-2 models for most crash types and intersection types, by providing a flexible variance structure to the NB approaches. The parameterization of the over-dispersion factor verifies that the over-dispersion parameter of the NB models highly depends on how the variance structure is defined in the model, and the over-dispersion parameter is shown to vary among different intersections for each crash type and can be estimated using both the major and minor road AADT at rural two-lane intersections. The NB-P model is found to more effectively capture the variation of over-dispersion among intersections in NB models, which benefits the accommodation of data heterogeneity in intersection SPF development. The prediction performance comparison illustrates that the NB-P model slightly improves the crash prediction accuracy compared with the other two models, especially for the 3ST and 4SG intersections. In conclusion, the NB-P model with parameterized over-dispersion factor is recommended to provide more unbiased parameter estimates when estimating SPFs by crash type for rural two-lane intersections.