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A Bayesian mixed logit-probit model for multinomial choice

  • Burda, Martin
  • Harding, Matthew
  • Hausman, Jerry

In this paper, we introduce a new flexible mixed model for multinomial discrete choice where the key individual- and alternative-specific parameters of interest are allowed to follow an assumption-free nonparametric density specification, while other alternative-specific coefficients are assumed to be drawn from a multivariate Normal distribution, which eliminates the independence of irrelevant alternatives assumption at the individual level. A hierarchical specification of our model allows us to break down a complex data structure into a set of submodels with the desired features that are naturally assembled in the original system. We estimate the model, using a Bayesian Markov Chain Monte Carlo technique with a multivariate Dirichlet Process (DP) prior on the coefficients with nonparametrically estimated density. We employ a "latent class" sampling algorithm, which is applicable to a general class of models, including non-conjugate DP base priors. The model is applied to supermarket choices of a panel of Houston households whose shopping behavior was observed over a 24-month period in years 2004-2005. We estimate the nonparametric density of two key variables of interest: the price of a basket of goods based on scanner data, and driving distance to the supermarket based on their respective locations. Our semi-parametric approach allows us to identify a complex multi-modal preference distribution, which distinguishes between inframarginal consumers and consumers who strongly value either lower prices or shopping convenience.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 147 (2008)
Issue (Month): 2 (December)
Pages: 232-246

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Handle: RePEc:eee:econom:v:147:y:2008:i:2:p:232-246
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  1. Dunson, David B., 2005. "Bayesian Semiparametric Isotonic Regression for Count Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 618-627, June.
  2. Mark J Jensen & John M Maheu, 2008. "Bayesian semiparametric stochastic volatility modeling," Working Papers tecipa-314, University of Toronto, Department of Economics.
  3. Susan Athey & Guido Imbens, 2006. "Discrete Choice Models with Multiple Unobserved Choice Characteristics," Levine's Bibliography 122247000000001040, UCLA Department of Economics.
  4. Matthew C. Harding & Jerry Hausman, 2007. "Using A Laplace Approximation To Estimate The Random Coefficients Logit Model By Nonlinear Least Squares," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1311-1328, November.
  5. Peter J. Green, 2001. "Modelling Heterogeneity With and Without the Dirichlet Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(2), pages 355-375.
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  7. Kenneth Train, 2003. "Discrete Choice Methods with Simulation," Online economics textbooks, SUNY-Oswego, Department of Economics, number emetr2, March.
  8. Imai, Kosuke & van Dyk, David A., 2005. "A Bayesian analysis of the multinomial probit model using marginal data augmentation," Journal of Econometrics, Elsevier, vol. 124(2), pages 311-334, February.
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  10. Conley, Timothy G. & Hansen, Christian B. & McCulloch, Robert E. & Rossi, Peter E., 2008. "A semi-parametric Bayesian approach to the instrumental variable problem," Journal of Econometrics, Elsevier, vol. 144(1), pages 276-305, May.
  11. Chib, Siddhartha & Hamilton, Barton H., 2002. "Semiparametric Bayes analysis of longitudinal data treatment models," Journal of Econometrics, Elsevier, vol. 110(1), pages 67-89, September.
  12. Keisuke Hirano, 2002. "Semiparametric Bayesian Inference in Autoregressive Panel Data Models," Econometrica, Econometric Society, vol. 70(2), pages 781-799, March.
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