Modeling endogeneity between motorcyclist injury severity and at-fault status by applying a Bayesian simultaneous random-parameters model with a recursive structure

Motorcyclists’ at-fault status is an important factor influencing crash injury severity in that intrinsically unsafe riders tend to be at fault and are the ones likely to be involved in severe crashes. However, this endogeneity issue and its influence on model estimations have seldom been investigated with regard to motorcyclist crash severity analysis. This study proposes a simultaneous model system to account for the endogenous effects of at-fault status in the motorcyclists’ injury severity analysis. Four Bayesian simultaneous models were developed using motorcyclist crash injury data from Queensland, Australia, from the year 2017 through 2018, including an independent binary and independent ordered Probit model, a simultaneous binary-ordered Probit model without recursive structure, a simultaneous binary-ordered Probit model with a recursive structure, and a simultaneous random-parameters binary-ordered Probit model with a recursive structure. The results of all simultaneous models indicate the existence of endogeneity associated with at-fault status in the injury outcome analysis. In particular, the endogenous relationship is detected by the significant cross-equation correlations in the simultaneous models. The model comparison by Deviance Information Criteria highlights the superiority of the simultaneous random-parameters model with a recursive structure. It was found that exogenous variables such as traffic sign-controlled measures, posted speed limits of 100–110 km/h, the presence of vertical grades, rider age 16–24 years, and unlicensed influenced injury severity indirectly through at-fault status, and ignoring these indirect influences could result in biased estimates. The presence of random parameters, such as collisions with heavy vehicles and riders over 59 years, highlights the importance of considering heterogeneity. The simultaneous random-parameters model with a recursive structure model revealed that the critical factors contributing to riders’ at-fault status included unlicensed riders and posted speed limits of 100–110 km/h, and the crucial factors influencing riders’ injury levels included head-on crashes, collisions with heavy vehicles, darkness-unlighted, and riders over 59 years old. The proposed model system demonstrates the importance of considering both endogeneity and heterogeneity for modeling the injury severity of motorcyclists.