Macro-level collision prediction using geographically weighted negative binomial regression

Abstract

We developed and tested geographically weighted Poisson regression and geographically weighted negative binomial regression models using five year's collisions, traffic, socio-demographic, road inventory, and land use data for Regina, Saskatchewan, Canada. The need for geographically weighted models became clear when Moran's I local indicator showed that our study data contained statistically significant levels of spatial autocorrelation. Bandwidth is a required input for geographically weighted regression models. We tested fixed and adaptive bandwidths. We found that fixed bandwidth was more suitable than adaptive bandwidth in our study. Models that used fixed and adaptive bandwidth produced a wide range of parameters across zones. We think the wide range of parameters helped explain unobserved heterogeneity issues within the zones. To compare the geographically weighted Poisson and geographically weighted negative binomial models, we applied seven well-known goodness-of-fit tests. The results were inconsistent, but the cumulative residual plot developed for each model showed that the fixed bandwidth geographically weighted Poisson model and the geographically weighted negative binomial model were better at predicting collisions than were the adaptive bandwidth models. Based on the CURE plots obtained, we concluded that the geographically weighted negative binomial model with fixed bandwidth was the best model for our study data.