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
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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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 | Burgette, L. F. and Nordheim, E. V (2012) The trace restriction: An alternative identification strategy for the Bayesian multinomial probit model | 1.000 | 8 | 4 | 100% |
| 2 | Burgette, L. F., Puelz, D., and Hahn, P. R (2021) A symmetric prior for multinomial probit models | 0.874 | 5 | 2 | 100% |
| 3 | McCulloch, R. and Rossi, P. E (1994) An exact likelihood analysis of the multinomial probit model | 0.843 | 5 | 4 | 60% |
| 4 | McCulloch, R. E., Polson, N. G., and Rossi, P. E (2000) A Bayesian analysis of the multinomial probit model with fully identified parameters | 0.843 | 3 | 3 | 100% |
| 5 | Imai, K. and Van Dyk, D. A (2005) A Bayesian analysis of the multinomial probit model using marginal data augmentation | 0.811 | 4 | 2 | 100% |
| 6 | Piatek, R. and Gensowski, M (2017) A multinomial probit model with latent factors: Identification and interpretation without a measurement system | 0.737 | 3 | 2 | 100% |
| 7 | Bunch, D. S (1991) Estimability in the multinomial probit model | 0.644 | 2 | 2 | 100% |
| 8 | Yeo, I.-K. and Johnson, R. A (2000) A new family of power transformations to improve normality or symmetry | 0.511 | 2 | 2 | 50% |
| 9 | Allenby, G. M. and Rossi, P. E (1991) Quality perceptions and asymmetric switching between brands | 0.511 | 2 | 1 | 100% |
| 10 | Cripps, E., Fiebig, D. G., and Kohn, R (2009) Parsimonious estimation of the covariance matrix in multinomial probit models | 0.511 | 2 | 1 | 100% |
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