Joint model of freight mode choice and shipment size: A copula-based random regret minimization framework

In our study, we examine the joint choice of freight transportation mode and shipment size. While shipment size could be considered as an explanatory variable in modeling mode choice (or vice-versa), it is more likely that the decision of mode and shipment choice is a simultaneous process. A joint model system is developed in the form of an unordered choice model for mode and an ordered choice model for shipment size. We adopt a closed form copula-based model structure for capturing the impact of common unobserved factors affecting these two choices. Further, we explore alternatives to the traditional random utility structure in modeling mode choice. Specifically, we explore both the random utility (RU) based multinomial logit and the random regret (RR) minimization based multinomial logit (MNL) within a copula-based model. The shipment size is analyzed using ordered logit (OL) model within the copula structure. The RU and RR MNL structures are explored for several copula-based structures including Gaussian, Farlie-Gumbel-Morgenstern (FGM), Clayton, Gumbel, Frank and Joe. The proposed approach considers copula models with multiple copula-based dependencies within a single model. The copula-based model dependency is also allowed to vary across the data by parameterizing the dependency as a function of observed attributes. The models are estimated based on the data from 2012 U.S. Commodity Flow Survey data. The copula RRM based MNL-OL copula with Frank and Joe copula dependencies offered the best data fit indicating the strong interconnectedness between shipment mode and shipment size choice decisions. A validation exercise provides further evidence of the joint model superiority for overall sample level and freight characteristics variables specific sub-samples.