A Bayesian instrumental variable model for multinomial choice with correlated alternatives

Endogeneity and correlated alternatives are major concerns to be addressed in travel behavior analysis. However, these issues have rarely been dealt with simultaneously in advanced discrete choice models. This study proposes a multinomial probit model that incorporates the instrumental variable method, namely, a fully parametric instrumental variable model for a multinomial choice. The proposed model has the following three characteristics: (1) it allows binary and/or continuous endogenous variables; (2) it allows any number of instrumental variables in each alternative; and (3) it allows positive and/or negative correlations between any choice alternatives. For parameter estimation, we also propose a Bayesian Markov chain Monte Carlo algorithm that can be accommodated in more extended model structures. The simulation study demonstrates that the proposed model addresses endogeneity while allowing correlations between the choice alternatives. Meanwhile, the simulation also implies that the users need to pay attention to the setting of the prior distribution when an endogenous variable of interest is binary, even if the sample size is moderate. The proposed model will be a useful tool in disciplines in which both endogeneity and correlations between choice alternatives are major concerns.