Unobserved heterogeneity across space, time, and crash type is often non-negligible in crash frequency modeling. When multiple crash types with spatial and temporal features are analyzed, multivariate spatiotemporal models should be considered. For this study, we analyzed the yearly county-level fatal, major injury, and minor injury crashes in Iowa from 2006 to 2015 using a multivariate spatio-temporal Bayesian model. The model adopted a multivariate spatial structure, a multivariate temporal structure, and a multivariate spatiotemporal interaction structure to account for possible correlations across injury severities over space, time, and spatio-temporal interaction, respectively. Income and weather indicators were found to have no significant effects on crash frequencies in the presence of vehicle miles traveled and unemployment rate. Both spatial and temporal effects were found to be important, and they played nearly the same roles for all three crash types in the studied dataset. Counties located in north and southwest Iowa were found to tend to have fewer crashes than the remaining counties. All three crash types generally showed descending trends from 2006 to 2015. They also had significantly positive correlations between each other in space but not in time. The crude crash rates and predicted crash rates were generally consistent for major injury and minor injury crashes but not for low-count fatal crashes. High-risk counties were identified using the posterior expected rank by the predicted crash cost rate, which was more able to truly represent the underlying traffic safety status than the rank by the crude crash cost rate.

This supplementary document shows detailed proofs of the theoretical results in the main paper and the implementation of the bivariate spline smoothing over the triangulation. In Section B.1, we investigate the asymptotic properties of the oracle estimator, the first stage penalized spline pilot estimators, and the spline-backfitted local polynomial estimator. Section B.2 describes the implementation of bivariate spline. Section B.3 provides more simulation results from Examples 1

Urban midblock crashes are influenced mainly by traffic operation and roadway geometric features. In this paper, 10-year crash data from 1,506 directional urban midblock segments in Nebraska were analyzed using the multivariate random parameters zero-inflated negative binomial model to account for unobserved heterogeneity produced by correlations across segments, correlations across crash collision types, excessive zero crashes, and over dispersion. The multivariate random parameters zero-inflated negative binomial model was superior to many common crash frequency models in terms of both goodness of fit and prediction accuracy. Compared with the multivariate fixed parameters zero-inflated negative binomial model, the multivariate random parameters zero-inflated negative binomial model identified fewer key influencing factors and revealed segment-specific effects of these factors on different crash types. It showed that the number of lanes, annual average daily traffic per lane, and segment length might have non-positive effects on crash frequencies. Segments with a speed limit of 45 mph had fewer crashes than did those with lower speed limits, and there were fewer crashes on the segments in Omaha than on those in Lincoln. It was also found that neither the presence of a shoulder, on-street parking, or one-way traffic, nor lane width had significant influences on crash frequencies. These findings are informative for transportation agencies to take correct and efficient measures to accommodate diverse transportation demands without reducing traffic safety. By contrast, the fixed parameters model produced results consistent with intuition, but the results were insufficient to provide actionable recommendations.

Unobserved heterogeneity produced by spatial and temporal correlations of crashes often needs to be captured in crash frequency modeling. Although many studies have included either spatial or temporal effects in crash frequency modeling, only a limited number of studies have considered both. This study addresses the limitations of existing studies by exploring multiple models that best fit the spatial and temporal correlations. In this study, we used Bayesian spatio-temporal models to investigate regional crash frequency trends, and explored the effects of omitting spatial or temporal trends in spatio-temporal correlated data. The fast Bayesian inference approach, integrated nested Laplace approximation, was used to estimate parameters. It was found that fatal crashes showed decreasing trends in all Iowa counties from 2006 to 2015, but the decreasing rates varied by counties. Among all the covariates investigated, only vehicle miles traveled (VMT) was significant. None of the socioeconomic or weather indicators were found to be significant in the presence of VMT. Both spatial and temporal effects were found to be important, and they were responsible for both over dispersion and zero inflation in the crash data. In addition, spatial effects played a more important role than did temporal effects in the studied dataset, but temporal component selection was still important in spatio-temporal modeling.