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MCMC Methods for Fitting and Comparing Multinomial Response Models

Author

Listed:
  • Siddhartha Chib

    (Washington University)

  • Edward Greenberg

    (Washington University)

  • Yuxin Chen

    (Washington University)

Abstract

This paper is concerned with statistical inference in multinomial probit, multinomial-$t$ and multinomial logit models. New Markov chain Monte Carlo (MCMC) algorithms for fitting these models are introduced and compared with existing MCMC methods. The question of parameter identification in the multinomial probit model is readdressed. Model comparison issues are also discussed and the method of Chib (1995) is utilized to find Bayes factors for competing multinomial probit and multinomial logit models. The methods and ideas are illustrated in detail with an example.

Suggested Citation

  • Siddhartha Chib & Edward Greenberg & Yuxin Chen, 1998. "MCMC Methods for Fitting and Comparing Multinomial Response Models," Econometrics 9802001, University Library of Munich, Germany, revised 06 May 1998.
    • Handle: RePEc:wpa:wuwpem:9802001
    Note: Type of Document - ps; prepared on TeX; pages: 29 ; figures: included
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    References listed on IDEAS

    as
    1. Hausman, Jerry A & Wise, David A, 1978. "A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Econometrica, Econometric Society, vol. 46(2), pages 403-426, March.
    2. Keane, Michael P, 1994. "A Computationally Practical Simulation Estimator for Panel Data," Econometrica, Econometric Society, vol. 62(1), pages 95-116, January.
    3. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(3), pages 409-431, August.
    4. Geweke, John & Keane, Michael P & Runkle, David, 1994. "Alternative Computational Approaches to Inference in the Multinomial Probit Model," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 609-632, November.
    5. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    6. Keane, Michael P, 1992. "A Note on Identification in the Multinomial Probit Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 193-200, April.
    7. McCulloch, Robert & Rossi, Peter E., 1994. "An exact likelihood analysis of the multinomial probit model," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 207-240.
    8. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Rub'en Loaiza-Maya & Didier Nibbering, 2022. "Fast variational Bayes methods for multinomial probit models," Papers 2202.12495, arXiv.org, revised Oct 2022.
    2. Duncan Fong & Sunghoon Kim & Zhe Chen & Wayne DeSarbo, 2016. "A Bayesian Multinomial Probit MODEL FOR THE ANALYSIS OF PANEL CHOICE DATA," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 161-183, March.
    3. Luiz Moutinho & Graeme D. Hutcheson, 2006. "Store Patronage: The Utility Of A Multi-Method, Multi-Nomial Logistic Regression Model For Predicting Store Choice," Portuguese Journal of Management Studies, ISEG, Universidade de Lisboa, vol. 0(1), pages 5-25.
    4. Hoshino, Takahiro, 2008. "A Bayesian propensity score adjustment for latent variable modeling and MCMC algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1413-1429, January.
    5. Lahiri, Kajal & Gao, Jian, 2002. "Bayesian analysis of nested logit model by Markov chain Monte Carlo," Journal of Econometrics, Elsevier, vol. 111(1), pages 103-133, November.
    6. Daziano, Ricardo A., 2013. "Conditional-logit Bayes estimators for consumer valuation of electric vehicle driving range," Resource and Energy Economics, Elsevier, vol. 35(3), pages 429-450.
    7. Minjung Kyung & Jeff Gill & George Casella, 2011. "Sampling schemes for generalized linear Dirichlet process random effects models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(3), pages 259-290, August.
    8. McCulloch, Robert E. & Polson, Nicholas G. & Rossi, Peter E., 2000. "A Bayesian analysis of the multinomial probit model with fully identified parameters," Journal of Econometrics, Elsevier, vol. 99(1), pages 173-193, November.
    9. Patil, Priyadarshan N. & Dubey, Subodh K. & Pinjari, Abdul R. & Cherchi, Elisabetta & Daziano, Ricardo & Bhat, Chandra R., 2017. "Simulation evaluation of emerging estimation techniques for multinomial probit models," Journal of choice modelling, Elsevier, vol. 23(C), pages 9-20.
    10. Zhehan Jiang & Jonathan Templin, 2019. "Gibbs Samplers for Logistic Item Response Models via the Pólya–Gamma Distribution: A Computationally Efficient Data-Augmentation Strategy," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 358-374, June.

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    More about this item

    Keywords

    Bayes factor; Gibbs sampling; Monte Carlo EM algorithm; Marginal likelihood; Metropolis-Hastings algorithm; Multinomial logit; Multinomial probit; Multinomial-t; Model comparison.;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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