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Scalable Bayesian estimation in the multinomial probit model

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  • Ruben Loaiza-Maya
  • Didier Nibbering

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.

Suggested Citation

  • Ruben Loaiza-Maya & Didier Nibbering, 2020. "Scalable Bayesian estimation in the multinomial probit model," Papers 2007.13247, arXiv.org, revised Mar 2021.
    • Handle: RePEc:arx:papers:2007.13247
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    Cited by:

    1. Patrick Ding & Guido Imbens & Zhaonan Qu & Yinyu Ye, 2024. "Computationally Efficient Estimation of Large Probit Models," Papers 2407.09371, arXiv.org, revised Sep 2024.
    2. Rub'en Loaiza-Maya & Didier Nibbering, 2022. "Fast variational Bayes methods for multinomial probit models," Papers 2202.12495, arXiv.org, revised Oct 2022.

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    More about this item

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis

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