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Scalable Bayesian estimation in the multinomial probit model

Ruben Loaiza-Maya, Didier Nibbering

arXiv 26 Jul 2020 · Econometrics · publishedJournal of Business and Economic Statistics (2021) · 9 citations (OpenAlex)

arXiv:2007.13247 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

22
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Burgette, L. F. and Nordheim, E. V (2012) The trace restriction: An alternative identification strategy for the Bayesian multinomial probit model1.00084100%
2Burgette, L. F., Puelz, D., and Hahn, P. R (2021) A symmetric prior for multinomial probit models0.87452100%
3McCulloch, R. and Rossi, P. E (1994) An exact likelihood analysis of the multinomial probit model0.8435460%
4McCulloch, R. E., Polson, N. G., and Rossi, P. E (2000) A Bayesian analysis of the multinomial probit model with fully identified parameters0.84333100%
5Imai, K. and Van Dyk, D. A (2005) A Bayesian analysis of the multinomial probit model using marginal data augmentation0.81142100%
6Piatek, R. and Gensowski, M (2017) A multinomial probit model with latent factors: Identification and interpretation without a measurement system0.73732100%
7Bunch, D. S (1991) Estimability in the multinomial probit model0.64422100%
8Yeo, I.-K. and Johnson, R. A (2000) A new family of power transformations to improve normality or symmetry0.5112250%
9Allenby, G. M. and Rossi, P. E (1991) Quality perceptions and asymmetric switching between brands0.51121100%
10Cripps, E., Fiebig, D. G., and Kohn, R (2009) Parsimonious estimation of the covariance matrix in multinomial probit models0.51121100%

Showing the top 10 of 22 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Fast variational Bayes methods for multinomial probit models0.84353
2Bundle Choice Model with Endogenous Regressors: An Application to Soda Tax0.73732
3Hybrid unadjusted Langevin methods for high-dimensional latent variable models0.51121
4Bayesian Forecasting in Economics and Finance: A Modern Review0.40511
5Structured Probit Estimation with Expectation Propagation0.40511