Jointly modeling area-level crash rates by severity: a Bayesian multivariate random-parameters spatio-temporal Tobit regression

This study investigates the inclusion of spatio-temporal correlation and interaction in a multivariate random-parameters Tobit model and their influence on fitting areal crash rates with different severity outcomes. The spatial correlation is specified via a multivariate conditional autoregressiv (MCAR) prior, whereas the temporal correlation is specified by a linear time trend. A spatio-temporal interaction is formulated as the product of a time trend and a spatial term with an MCAR prior. A multivariate random-parameters spatio-temporal Tobit model is developed for slight injury and killed or serious injury crash rates using one year of crash data from 131 traffic analysis zones in Hong Kong. The proposed model is estimated and assessed in the Bayesian context. The model estimation results show that spatial and temporal effects and their interactive effects are significant and that the spatial and interactive effects have strong correlations across injury severities. The proposed model outperforms a multivariate random-parameters Tobit model and a multivariate random-parameters spatial Tobit model in terms of model fit. These findings highlight the importance of appropriately accommodating spatio-temporal correlation and interaction for the joint analysis of areal crash rates by severity.