Effects of design consistency measures and roadside hazard types on run-off-road crash severity: Application of random parameters hierarchical ordered probit model

•Effects of design consistency measures are examined on run-off-road crash severity.•17 different functional forms of design consistency indices are developed.•Effects of roadside hazard types are considered in run-off-road severity model.•7 roadside hazard types are generated from roadside object and clear zone data.•A hybrid (Machine Learning and Econometrics) model is estimated. Run-off-road crashes are one of the most significant causes of road deaths worldwide. Given such significant safety concerns, a number of earlier studies examined the critical factors contributing towards run-off-road crash severity outcomes, mostly by using the information compiled in the official crash database. However, the official crash databases are less likely to have detailed information on driver behavior (errors/expectations) and roadway environment (roadway geometry and roadside attributes). This study aims to investigate the effects of design consistency measures on run-off-road crash severity mechanisms by applying a random parameters hierarchical ordered Probit model. This study contributes towards existing safety literature by demonstrating a complementary approach to capturing the effects of driver behavior and heterogeneity in roadway environment on run-off-road crash severity outcome through the composite measures of design consistency indices and cosmopolite measures of roadside hazard type variables. Specifically, 17 different functional forms of design consistency indices are developed to capture the behavioral factors from the road-geometric changes in developing run-off-road crash severity models. Further, in examining the effect of different types of the roadside environment on run-off-road crash severity outcomes, seven roadside hazard type variables are generated as a composite function of roadside object type and clear zone (lateral distance to roadside object). The empirical analysis of this study involves a two-step modelling approach - in the first step, the decision tree algorithm is applied to identify the higher-order interaction among independent variables, and in the second step, crash severity models are developed by employing several econometric approaches. The hybrid models are estimated by employing four econometric frameworks, which include Ordered Probit, Hierarchical Ordered Probit, Random Parameters Ordered Probit, and Random parameters Hierarchical Ordered Probit models. The run-off-road crash severity models are estimated by using cra