Rubén Loaiza-Maya, Didier Nibbering
arXiv 25 Feb 2022 · Econometrics · publishedJournal of Business and Economic Statistics (2022) · 11 citations (OpenAlex)
arXiv:2202.12495 · PDF · DOI · OpenAlex · Extracted main text
The multinomial probit model is often used to analyze choice behaviour. However, estimation with existing Markov chain Monte Carlo (MCMC) methods is computationally costly, which limits its applicability to large choice data sets. This paper proposes a variational Bayes method that is accurate and fast, even when a large number of choice alternatives and observations are considered. Variational methods usually require an analytical expression for the unnormalized posterior density and an adequate choice of variational family. Both are challenging to specify in a multinomial probit, which has a posterior that requires identifying restrictions and is augmented with a large set of latent utilities. We employ a spherical transformation on the covariance matrix of the latent utilities to construct an unnormalized augmented posterior that identifies the parameters, and use the conditional posterior of the latent utilities as part of the variational family. The proposed method is faster than MCMC, and can be made scalable to both a large number of choice alternatives and a large number of observations. The accuracy and scalability of our method is illustrated in numerical experiments and real purchase data with one million observations.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Loaiza-Maya, R. and Nibbering, D (2021) Scalable Bayesian estimation in the multinomial probit model self | 0.843 | 5 | 3 | 60% |
| 2 | Burgette, L. F. and Nordheim, E. V (2012) The trace restriction: An alternative identification strategy for the Bayesian multinomial probit model | 0.737 | 3 | 2 | 100% |
| 3 | Loaiza-Maya, R., Smith, M. S., Nott, D. J., and Danaher, P. J (2021) Fast and accurate variational inference for models with many latent variables self | 0.737 | 3 | 2 | 100% |
| 4 | Bunch, D. S (1991) Estimability in the multinomial probit model | 0.644 | 2 | 2 | 100% |
| 5 | McCulloch, R. and Rossi, P. E (1994) An exact likelihood analysis of the multinomial probit model | 0.644 | 2 | 2 | 100% |
| 6 | Westling, T. and McCormick, T (2019) Beyond prediction: A framework for inference with variational approximations in mixture models | 0.644 | 2 | 2 | 100% |
| 7 | Zhang, X., Boscardin, W. J., and Belin, T. R (2008) Bayesian analysis of multivariate nominal measures using multivariate multinomial probit models | 0.511 | 2 | 2 | 50% |
| 8 | Burgette, L. F., Puelz, D., and Hahn, P. R (2021) A symmetric prior for multinomial probit models | 0.511 | 2 | 1 | 100% |
| 9 | Ong, V. M.-H., Nott, D. J., and Smith, M. S (2018) Gaussian variational approximation with a factor covariance structure | 0.511 | 2 | 1 | 100% |
| 10 | Albert, J. H. and Chib, S (1993) Bayesian analysis of binary and polychotomous response data | 0.405 | 1 | 1 | 100% |
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