Investigating exposure measures and functional forms in urban and suburban intersection safety performance functions using generalized negative binomial - P model

Selecting an appropriate exposure measure and functional form for Safety Performance Functions (SPFs) is critical in precisely predicting crash counts by different crash types for intersections. This study proposes a new approach, namely Generalized Negative Binomial-P (GNB-P) model, to model the complex relationship between crashes and different exposure measures by crash type for intersections, which helps not only identify the most reliable exposure measure for intersection SPFs, but also explore the most appropriate functional form of the NB models. To this end, three types of SPF functional forms, namely Power function, Hoerl function 1 and Hoerl function 2 with different exposure measures including major road AADT, minor road AADT and total AADT were estimated by crash type for stop-controlled and two types of signalized intersections. The over-dispersion of the SPF models was estimated using the exposure measures to account for crash data variation across different intersections. The SPF estimation results highlighted that the mean-variance structure of NB models is not consistent and varies by crash data. The over-dispersion of SPFs by crash type is not constant and varies across different intersections. The minor road AADT is shown to be positively correlated with the over-dispersion of SPFs in estimating crash counts for Same-Direction Crashes (SDC), Intersecting-Direction Crashes (IDC) and Single-Vehicle Crashes (SVC). Estimating the over-dispersion using exposure measures results in more reliable SPF results. Furthermore, it is found that the Power function with major road and minor road AADT as the exposure measure performs the best in estimating SPFs for Opposite-Direction Crashes (ODC). The Hoerl function 2 with total AADT and the proportion of minor road AADT over the total as the exposure measure performs the best in estimating SVC SPFs for intersections. The Hoerl function 1 with major road and minor road AADT as the exposure measure is more accurate in estimating SPFs for both SDC and IDC.