A random parameters copula-based binary logit-generalized ordered logit model with parameterized dependency: Application to active traveler injury severity analysis

A copula-based dependence approach accommodates various facets of dependence structures in building multivariate stochastic models. In existing studies, applications of copula for ordinal random variables are predominantly modeled by employing traditional ordered models (ordered logit/probit) while assuming the effects of parameters to remain the same across all observations. The methodological contributions of this study are grounded in addressing the abovementioned significant methodological gaps in the application of copula formulation by proposing a copula-based random parameters nominal-ordinal joint model construct of correlated random variables. Specifically, we propose and develop a random parameters binary logit-generalized ordered logit copula formulation while also complementing the proposed approach by accommodating the effects of unobserved heterogeneity in parameter estimates. To the best of the authors' knowledge, this study is the first instance to incorporate generalized ordered formulation within copula in extant econometrics literature. Further, to obtain a direct effect of exogenous variables on dependence, we parameterize the copula dependence structure as a function of different covariates in six different copula structures including a wide range of dependency structures which represent radial symmetry and asymmetry, and asymptotic tail dependence. The empirical contributions of this study are grounded in the application of the proposed copula-based formulation by examining 'active traveler (pedestrian and bicyclist) crash type' and 'active traveler injury severity outcomes' as two dimensions of active travel injury severity mechanism. The model is estimated by using crash data for the years 2012 through 2018 from the state of Queensland, Australia, by employing a comprehensive set of exogenous variables. In addition, the analyses are further augmented by complementing the elasticity effects of exogenous variables.