This study intended to investigate the interactions between accident severity levels and traffic signs in state roads located in Croatia and explore the correlation between accident severity levels and heterogeneity attributed to unobserved factors. The data from 460 state roads between 2012 and 2016 were collected from Traffic Accident Database System maintained by the Republic of Croatia Ministry of the Interior. To address the correlation and heterogeneity, Bayesian bivariate Tobit quantile regression models were proposed, in which the bivariate framework addressed the correlation of residuals with Bayesian approach, while the Tobit quantile regression model accommodated the heterogeneity due to unobserved factors. By comparing the Bayesian bivariate Tobit quantile and mean regression models, the proposed quantile models showed priority to mean model. Results revealed that (1) low visibility and the number of invalid traffic signs per km increased the accident rate of material damage, death, or injury; (2) average speed limit exhibited a close relation with accident rate; and (3) the number of mandatory signs was more likely to reduce the accident rate of material damage, while the number of warning signs was significant for accident rate of death or injury.
Valid Post-Selection Inference in High-Dimensional Approximately Sparse Quantile Regression Models