Simultaneous equation penalized likelihood estimation of vehicle accident injury severity

A bivariate system of equations is developed to model ordinal polychotomous dependent variables within a simultaneous additive regression framework. The functional form of the covariate effects is assumed fairly flexible with appropriate smoothers used to account for non‐linearities and spatial variability in the data. Non‐Gaussian error dependence structures are dealt with by means of copulas whose association parameter is also specified in terms of a generic additive predictor. The framework is employed to study the effects of several risk factors on the levels of injury sustained by individuals in two‐vehicle accidents in France. The use of the methodology proposed is motivated by the presence of common unobservables that may affect the interrelationships between the parties involved in the same crash and by the possible heterogeneity in individuals’ characteristics and accident dynamics. Better calibrated estimates are obtained and misspecification reduced via an enhanced model specification.