Application of a nested trivariate copula structure in a competing duration hazard-based vehicle transaction decision model

Vehicle ownership has been the subject of numerous transportation studies, which typically have adopted a variety of econometric frameworks at both aggregate and disaggregate choice modeling levels. These models have covered various aspects of vehicle ownership, including vehicle transaction behavior, number of vehicles held, vehicle type choice, and vehicle use. Vehicle transaction models have been developed in both static and dynamic paradigms. However, traditionally transaction timing has been overlooked in static vehicle ownership models despite the significant role that it plays in explaining vehicle ownership behavior. The decision about transaction type is typically assumed to be independently made; therefore, independent timing models are developed for each transaction type. This study aims to introduce a joint transaction type and timing model at the disaggregate level of individuals using a discrete competing proportional hazard model. The inter-correlation among multiple transaction types is modeled in this study by utilizing a set of multivariate Archimedean copula density functions to approximate the multivariate probability density function for the error terms of transaction types in a fully nested structure.