Scalable Bayesian estimation in the multinomial probit model

Ruben Loaiza-Maya; Didier Nibbering

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arXiv · 2007.13247

Scalable Bayesian estimation in the multinomial probit model

Ruben Loaiza-Maya·Didier Nibbering

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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.

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BibTeX RIS

Ruben Loaiza-Maya, Didier Nibbering. 2021-03-24. Scalable Bayesian estimation in the multinomial probit model. https://arxiv.org/abs/2007.13247

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