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Bayesian Nonparametric Estimation and Consistency of Mixed Multinomial Logit Choice Models

  • Pierpaolo De Blasi

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  • Lancelot F. James
  • John W. Lau
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    This paper develops nonparametric estimation for discrete choice models based on the Mixed Multinomial Logit (MMNL) model. It has been shown that MMNL models encompass all discrete choice models derived under the assumption of random utility maximization, subject to the identification of an unknown distribution G. Noting the mixture model description of the MMNL, we employ a Bayesian nonparametric approach, using nonparametric priors on the unknown mixing distribution G, to estimate the unknown choice probabilities. Theoretical support for the use of the proposed methodology is provided by establishing strong consistency of a general nonparametric prior on G under simple sufficient conditions. Consistency is defined according to a L1-type distance on the space of choice probabilities and is achieved by extending to a regression model framework a recent approach to strong consistency based on the summability of square roots of prior probabilities. Moving to estimation, slightly different techniques for non-panel and panel data models are discussed. For practical implementation, we describe efficient and relatively easy to use blocked Gibbs sampling procedures. A simulation study is also performed to illustrate the proposed methods and the exibility they achieve with respect to parametric Gaussian MMNL models.

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    File URL: http://servizi.sme.unito.it/icer_repec/RePEc/icr/wp2007/ICERwp15-07.pdf
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    Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 15-2007.

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    Length: 29 pages
    Date of creation: Mar 2007
    Date of revision:
    Handle: RePEc:icr:wpmath:15-2007
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    1. T├╝lin Erdem, 1996. "A Dynamic Analysis of Market Structure Based on Panel Data," Marketing Science, INFORMS, vol. 15(4), pages 359-378.
    2. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    3. Lijoi, Antonio & Prunster, Igor & Walker, Stephen G., 2005. "On Consistency of Nonparametric Normal Mixtures for Bayesian Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1292-1296, December.
    4. Choi, Taeryon & Schervish, Mark J., 2007. "On posterior consistency in nonparametric regression problems," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1969-1987, November.
    5. Joan L. Walker & Moshe Ben-Akiva & Denis Bolduc, 2007. "Identification of parameters in normal error component logit-mixture (NECLM) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(6), pages 1095-1125.
    6. Stephen G. Walker & Antonio Lijoi & Igor Prunster, 2005. "Data tracking and the understanding of Bayesian consistency," Biometrika, Biometrika Trust, vol. 92(4), pages 765-778, December.
    7. Stephen Walker, 2003. "On sufficient conditions for Bayesian consistency," Biometrika, Biometrika Trust, vol. 90(2), pages 482-488, June.
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