Bayesian nonparametric estimation and consistency of mixed multinomial logit choice models

摘要

This paper develops nonparametric estimation for discrete choice models basedon the mixed multinomial logit (MMNL) model. It has been shown that MMNL modelsencompass all discrete choice models derived under the assumption of randomutility maximization, subject to the identification of an unknown distribution$G$. Noting the mixture model description of the MMNL, we employ a Bayesiannonparametric approach, using nonparametric priors on the unknown mixingdistribution $G$, to estimate choice probabilities. We provide an importanttheoretical support for the use of the proposed methodology by investigatingconsistency of the posterior distribution for a general nonparametric prior onthe mixing distribution. Consistency is defined according to an $L_1$-typedistance on the space of choice probabilities and is achieved by extending to aregression model framework a recent approach to strong consistency based on thesummability of square roots of prior probabilities. Moving to estimation,slightly different techniques for non-panel and panel data models arediscussed. For practical implementation, we describe efficient and relativelyeasy-to-use blocked Gibbs sampling procedures. These procedures are based onapproximations of the random probability measure by classes of finitestick-breaking processes. A simulation study is also performed to investigatethe performance of the proposed methods.