Do safety performance functions used for predicting crash frequency vary across space? Applying geographically weighted regressions to account for spatial heterogeneity.

Safety Performance Functions (SPFs) provide a basis for identifying locations where countermeasures can be effective. While SPFs in the Highway Safety Manual (HSM) were calibrated based on data from select states, calibration factors can be developed to localize SPFs to other states. Calibration factors typically provide a coarse adjustment-time and space stationarity of associations between crash frequencies and various factors is still assumed, implying that the SPF functional form is transferable. However, with increasing availability of statewide geo-referenced safety data, new spatial analysis methods, and increasing computational power, it is possible to relax the stationarity assumption. Specifically, to address spatial heterogeneity in SPFs, this study proposes relaxing SPFs (referring to them as Localized SPFs (L-SPFs)) that can be developed by using sophisticated geo-spatial modeling techniques that allow correlates of crash frequencies to vary in space. For demonstration, a 2013 geo-referenced freeway crash and traffic database from Virginia is used. As a potential methodological alternative, crash frequencies are predicted by estimating Geographically Weighted Negative Binomial Regressions. This model significantly outperforms the traditional negative binomial model in terms of model goodness-of-fit, providing a better and fuller understanding of spatial variations in modeled relationships. Our study results uncover significant spatial variations in parameter estimates for Annual Average Daily Traffic (AADT) and segment length. Ignoring such variations can result in prediction errors. The results indicate low transferability of a single statewide SPF highlighting the importance of developing L-SPFs. From a practical standpoint, L-SPFs can better predict crash frequencies and support prioritizing safety improvements in specific locations.