An empirical evaluation of multivariate spatial crash frequency models

Abstract Many studies have employed spatial, temporal, or a combination of both specifications for analysis of roadway crashes at different spatial levels. However, there is lack of a comprehensive study which compares the crash estimation performance of different spatial weight matrices and their combination with various temporal treatments. The current study fills the research gap by comparing different Full Bayesian (FB) multivariate spatiotemporal crash models. The pedestrian and bicyclist crash data across an eight-year period for 58 counties in California were used as a case study. Three groups of models were developed based on temporal treatment, where each group comprised of 17 models differing on the basis of different adjacency- and distance-based spatial weight matrices. The first group of multivariate models incorporated only unstructured random error term and spatially structured conditional autoregressive (CAR) term. The second group built upon the former and introduced a linear time trend to develop a spatiotemporal model, while the third group allowed the interaction of space and time. The predictive performance of the alternate models across and within groups was assessed by employing several evaluation criteria. The modeling results demonstrated the robustness of models based on the similar signs and closeness of coefficients for the posterior estimates of parameters. For overall model comparison, the pure-distance model D0.5 demonstrated the best performance for different evaluation criteria based on training and test errors across three groups. The variability in performance of other distance models suggested that caution must be exercised for the choice of exponents. The correlation analysis revealed the presence of positive correlations among the criteria based on training errors, as well as with cross-validation. However, a very strong positive correlation was observed between the criteria based on effective number of parameters and posterior deviance, indicating that an increased number of parameters may not lead to improved model fit. This finding reinforced the importance of selecting the optimum weight matrix for spatial correlation as a more complex structure may not lead to expected advantages at model performance. For comparison among three groups of different temporal treatments, the third group demonstrated the best performance and conveyed the benefits of incorporating the spatial and temporal interaction. The results from ANOVA (analysis of variance) and HSD (Honest Significant Differences) tests also established the existence of statistical differences for the superiority of space-time interactions models. However, the box and whisker plots demonstrated high variability among the models of the third group, suggesting that some models may not benefit from interaction term. For comparison among adjacency- and distance-based models, the distance-based models were mostly observed to be superior. However, the greater variability of model performance associated with distance-based models suggested for careful consideration during their selection. Additionally, it is important to note that the results observed in this study are specific to the county-level crash data of California. As such, the study does not recommend generalization of the results for extension to other spatial levels of roadway network, and readers and future research studies are advised to exercise caution before implementing the models.