A multivariate heterogeneous-dispersion count model for asymmetric interdependent freeway crash types

A multivariate count model is developed by introducing a simple and practical formula. The formulation begins with a modification of the standard ordered response model to adopt the count outcomes nature. This modification is accomplished by introducing a non-linear asymmetric interdependence structure among the error terms using the copula-based model. To avoid simulation maximum-likelihood for evaluating the multi-outcome density, we utilize the composite marginal likelihood (CML) approach. The proposed copula-based model with the CML approach allows for asymmetric (tail) dependency without a need for a simulation mechanism. Non-parametric graphical techniques with the empirical copula as well as conventional goodness-of-fit statistics are utilized to guide copula selection. In addition, unobserved heterogeneity across observations is also addressed through a heterogeneous dispersion parameter in the proposed model. The heterogeneous dispersion parameter model is a suitable alternative to random parameter count models in that captures heterogeneity in variance, while allowing for closed form while the latter needs numerical integration or simulation.