Discrete Choice Models Based on the Scale Mixture of Multivariate Normal Distributions

A rich class of parametric models is proposed for discrete choice data based on the scale mixture of multivariate normal distributions. The multinomial probit model is a special case in the class. The new models can be implemented in a Bayesian framework without much difficulty because of their special connections to the multinomial probit model. A Gibbs sampler with data augmentation is used to generate a sample from the posterior distribution. The techniques are illustrated with travel mode choice data. The empirical results suggest that the multinomial probit model does not fit the data as well as the other models in the proposed class. In selecting models, we propose the use of the pseudo-Bayes factor criterion based on cross-validated predictive densities. The proposed class of models is extended to panel data by building random-coefficients Bayesian hierarchical models.