A random thresholds random parameters hierarchical ordered probit analysis of highway accident injury-severities

•Single-vehicle accident injury-severities are modeled in an ordered probit setting.•We estimate a random thresholds random parameters hierarchical ordered probit model.•Unobserved and thresholds heterogeneity are addressed.•The proposed model is counter-imposed against its model counterparts.•The proposed model is statistically superior to its model counterparts.

This study uses highway accident data collected in the State of Washington, between 2011 and 2013, to study the factors that affect accident injury-severities. To account for the fixed thresholds limitation of the traditional ordered probability models - which typically leads to incorrect estimation of outcome probabilities for the intermediate categories - and for the possibility of unobserved factors systematically varying across the observations, a random thresholds hierarchical ordered probit model with random parameters is estimated. This approach simultaneously allows the explanatory parameters to vary across roadway segments, and the thresholds to vary both as a function of explanatory parameters and across the observations, thus accounting for unobserved and threshold heterogeneity, respectively. Using goodness-of-fit measures, likelihood ratio tests and forecasting accuracy measures, the model estimation results are compared with the hierarchical and fixed thresholds ordered probit model counterparts, with fixed and random parameters. The comparative assessment among the ordered probit modeling approaches reveals the relative benefits and the overall statistical superiority of the random thresholds random parameters hierarchical ordered probit model.