Scalable Bayesian estimation in the multinomial probit model

TL;DR

This paper introduces a scalable Bayesian estimation method for the multinomial probit model by employing a factor structure on the covariance matrix, enabling analysis of large choice sets with improved computational efficiency.

Contribution

It proposes a novel factor-structured covariance matrix with trace-restriction identification and develops an MCMC sampler, enhancing scalability for large choice sets.

Findings

Significantly improves performance in large choice sets

Demonstrates economic importance of large choice sets in consumer analysis

Provides an interpretable Bayesian estimation framework

Abstract

The multinomial probit model is a popular tool for analyzing choice behaviour as it allows for correlation between choice alternatives. Because current model specifications employ a full covariance matrix of the latent utilities for the choice alternatives, they are not scalable to a large number of choice alternatives. This paper proposes a factor structure on the covariance matrix, which makes the model scalable to large choice sets. The main challenge in estimating this structure is that the model parameters require identifying restrictions. We identify the parameters by a trace-restriction on the covariance matrix, which is imposed through a reparametrization of the factor structure. We specify interpretable prior distributions on the model parameters and develop an MCMC sampler for parameter estimation. The proposed approach significantly improves performance in large choice sets relative to existing multinomial probit specifications. Applications to purchase data show the economic importance of including a large number of choice alternatives in consumer choice analysis.