Bernoulli

  • Bernoulli
  • Volume 16, Number 3 (2010), 679-704.

Bayesian nonparametric estimation and consistency of mixed multinomial logit choice models

Pierpaolo De Blasi, Lancelot F. James, and John W. Lau

Full-text: Open access

Abstract

This paper develops nonparametric estimation for discrete choice models based on the mixed multinomial logit (MMNL) model. It has been shown that MMNL models encompass all discrete choice models derived under the assumption of random utility maximization, subject to the identification of an unknown distribution $G$. Noting the mixture model description of the MMNL, we employ a Bayesian nonparametric approach, using nonparametric priors on the unknown mixing distribution $G$, to estimate choice probabilities. We provide an important theoretical support for the use of the proposed methodology by investigating consistency of the posterior distribution for a general nonparametric prior on the mixing distribution. Consistency is defined according to an $L_1$-type distance on the space of choice probabilities and is achieved by extending to a regression model framework a recent approach to strong consistency based on the summability of square roots of prior probabilities. Moving to estimation, slightly different techniques for non-panel and panel data models are discussed. For practical implementation, we describe efficient and relatively easy-to-use blocked Gibbs sampling procedures. These procedures are based on approximations of the random probability measure by classes of finite stick-breaking processes. A simulation study is also performed to investigate the performance of the proposed methods.

Article information

Source
Bernoulli, Volume 16, Number 3 (2010), 679-704.

Dates
First available in Project Euclid: 6 August 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1281099880

Digital Object Identifier
doi:10.3150/09-BEJ233

Mathematical Reviews number (MathSciNet)
MR2730644

Zentralblatt MATH identifier
1220.62036

Keywords
Bayesian consistency blocked Gibbs sampler discrete choice models mixed multinomial logit random probability measures stick-breaking priors

Citation

De Blasi, Pierpaolo; James, Lancelot F.; Lau, John W. Bayesian nonparametric estimation and consistency of mixed multinomial logit choice models. Bernoulli 16 (2010), no. 3, 679--704. doi:10.3150/09-BEJ233. https://projecteuclid.org/euclid.bj/1281099880


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