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Scalable Bayesian Estimation in the Multinomial Probit Model

Author

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  • Rubén Loaiza-Maya
  • Didier Nibbering

Abstract

The multinomial probit (MNP) model is a popular tool for analyzing choice behavior 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 article 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 reparameterization 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 MNP specifications. Applications to purchase data show the economic importance of including a large number of choice alternatives in consumer choice analysis.

Suggested Citation

  • Rubén Loaiza-Maya & Didier Nibbering, 2022. "Scalable Bayesian Estimation in the Multinomial Probit Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1678-1690, October.
    • Handle: RePEc:taf:jnlbes:v:40:y:2022:i:4:p:1678-1690
    DOI: 10.1080/07350015.2021.1961788
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    Citations

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    Cited by:

    1. Ruben Loaiza-Maya & Didier Nibbering & Dan Zhu, 2023. "Hybrid unadjusted Langevin methods for high-dimensional latent variable models," Papers 2306.14445, arXiv.org.
    2. Michelle Sovinsky & Liana Jacobi & Alessandra Allocca & Tao Sun, 2023. "More than Joints: Multi-Substance Use, Choice Limitations, and Policy Implications," Rationality and Competition Discussion Paper Series 487, CRC TRR 190 Rationality and Competition.
    3. Michelle Sovinsky & Liana Jacobi & Alessandra Allocca & Tao Sun, 2024. "More than Joints: Multi-Substance Use, Choice Limitations, and Policy Implications," CRC TR 224 Discussion Paper Series crctr224_2024_501, University of Bonn and University of Mannheim, Germany.
    4. Martin, Gael M. & Frazier, David T. & Maneesoonthorn, Worapree & Loaiza-Maya, Rubén & Huber, Florian & Koop, Gary & Maheu, John & Nibbering, Didier & Panagiotelis, Anastasios, 2024. "Bayesian forecasting in economics and finance: A modern review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 811-839.
    5. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.
    6. Riccardo Lucchetti & Luca Pedini, 2024. "The Spherical Parametrisation for Correlation Matrices and its Computational Advantages," Computational Economics, Springer;Society for Computational Economics, vol. 64(2), pages 1023-1046, August.

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