Spatial Correlation in Multilevel Crash Frequency Models

Abstract

Recent research has shown the importance of spatial correlation in road crash models. Because many different spatial correlation structures are possible, however, this study tested several segment neighboring structures to establish the most promising one to model crash frequency in road networks. A multilevel approach was also used to account for the spatial correlation between road segments of different functional types, which are usually analyzed separately. The study employed a full Bayes hierarchical approach with conditional autoregressive effects for the spatial correlation terms. Analyses of crash, traffic, and roadway inventory data from rural engineering districts in Pennsylvania and Washington affirmed the importance of spatial correlation in road crash models. Pure distance-based neighboring models (i.e., exponential decay) performed poorly compared with adjacency-based or distance order models. The results also suggest that spatial correlation is more important in distances of 1 mi or less. The inclusion of spatially correlated random effects significantly improved the precision of the estimates of the expected crash frequency for all segments by pooling strength from their neighbors and thus reducing their standard deviation. Results from Pennsylvania and Washington showed that spatial correlation substantially increased the random effects. There was a consistent indication that 70% to 90% of the variation explained by the random effects resulted from spatial correlation. This suggests that spatial models offer a significant advantage, since poor estimates that result from small sample sizes and low sample means are a frequent issue in highway safety analysis. Application of spatial correlation to the identification of sites with promise indicated that more sites were identified because of a reduction in the variance of the estimates, which would allow for greater confidence in the selection of sites for treatment.