A joint count-continuous model of travel behavior with selection based on a multinomial probit residential density choice model

This paper formulates a multidimensional choice model system that is capable of handling multiple nominal variables, multiple count dependent variables, and multiple continuous dependent variables. The system takes the form of a treatment-outcome selection system with multiple treatments and multiple outcome variables. The Maximum Approximate Composite Marginal Likelihood (MACML) approach is proposed in estimation, and a simulation experiment is undertaken to evaluate the ability of the MACML method to recover the model parameters in such integrated systems. These experiments show that our estimation approach recovers the underlying parameters very well and is efficient from an econometric perspective. The parametric model system proposed in the paper is applied to an analysis of household-level decisions on residential location, motorized vehicle ownership, the number of daily motorized tours, the number of daily non-motorized tours, and the average distance for the motorized tours. The empirical analysis uses the NHTS 2009 data from the San Francisco Bay area. Model estimation results show that the choice dimensions considered in this paper are inter-related, both through direct observed structural relationships and through correlations across unobserved factors (error terms) affecting multiple choice dimensions. The significant presence of self-selection effects (endogeneity) suggests that modeling the various choice processes in an independent sequence of models is not reflective of the true relationships that exist across these choice dimensions, as also reinforced through the computation of treatment effects in the paper.