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A Bayesian mixed logit-probit model for multinomial choice

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Author Info

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

Abstract

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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Bibliographic Info

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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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Multinomial discrete choice model Dirichlet process prior Non-conjugate priors Hierarchical latent class models;

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References

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  1. 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.
  2. Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
  3. Susan Athey & Guido Imbens, 2006. "Discrete Choice Models with Multiple Unobserved Choice Characteristics," Levine's Bibliography 122247000000001040, UCLA Department of Economics.
  4. Markus Jochmann & Roberto León-González, 2004. "Estimating the demand for health care with panel data: a semiparametric Bayesian approach," Health Economics, John Wiley & Sons, Ltd., vol. 13(10), pages 1003-1014.
  5. Austan Goolsbee & Amil Petrin, 2004. "The Consumer Gains from Direct Broadcast Satellites and the Competition with Cable TV," Econometrica, Econometric Society, vol. 72(2), pages 351-381, 03.
  6. Matthew C. Harding & Jerry Hausman, 2006. "Using a Laplace approximation to estimate the random coefficients logit model by non-linear least squares," CeMMAP working papers CWP01/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. 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.
  8. 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.
  9. Keisuke Hirano, 2002. "Semiparametric Bayesian Inference in Autoregressive Panel Data Models," Econometrica, Econometric Society, vol. 70(2), pages 781-799, March.
  10. 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.
  11. Beggs, S. & Cardell, S. & Hausman, J., 1981. "Assessing the potential demand for electric cars," Journal of Econometrics, Elsevier, vol. 17(1), pages 1-19, September.
  12. 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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Citations

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Cited by:
  1. Karabatsos, George & Walker, Stephen G., 2012. "Bayesian nonparametric mixed random utility models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1714-1722.
  2. Wan, Alan T.K. & Zhang, Xinyu & Wang, Shouyang, 2014. "Frequentist model averaging for multinomial and ordered logit models," International Journal of Forecasting, Elsevier, vol. 30(1), pages 118-128.
  3. Michael Keane & Nada Wasi, 2013. "Comparing Alternative Models Of Heterogeneity In Consumer Choice Behavior," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(6), pages 1018-1045, 09.
  4. Steven T. Berry & Philip A. Haile, 2009. "Nonparametric Identification of Multinomial Choice Demand Models with Heterogeneous Consumers," NBER Working Papers 15276, National Bureau of Economic Research, Inc.
  5. Jensen, Mark J & Maheu, John M, 2013. "Risk, Return and Volatility Feedback: A Bayesian Nonparametric Analysis," MPRA Paper 52132, University Library of Munich, Germany.
  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. Martin Burda & Artem Prokhorov, 2013. "Copula Based Factorization in Bayesian Multivariate Infinite Mixture Models," Working Papers tecipa-473, University of Toronto, Department of Economics.
  8. Michael P. Keane & Nada Wasi, 2013. "The Structure of Consumer Taste Heterogeneity in Revealed vs. Stated Preference Data," Economics Papers 2013-W10, Economics Group, Nuffield College, University of Oxford.
  9. Griffith, Rachel & Miller, Helen & O'Connell, Martin, 2011. "Corporate taxes and the location of intellectual property," CEPR Discussion Papers 8424, C.E.P.R. Discussion Papers.
  10. Nada Wasi & Michael P. Keane, 2012. "Estimation of Discrete Choice Models with Many Alternatives Using Random Subsets of the Full Choice Set: With an Application to Demand for Frozen Pizza," Economics Papers 2012-W13, Economics Group, Nuffield College, University of Oxford.
  11. Michael P. Keane, 2013. "Panel data discrete choice models of consumer demand," Economics Papers 2013-W08, Economics Group, Nuffield College, University of Oxford.
  12. Burda, Martin & Harding, Matthew & Hausman, Jerry, 2012. "A Poisson mixture model of discrete choice," Journal of Econometrics, Elsevier, vol. 166(2), pages 184-203.
  13. Kenneth L. Judd & Ben Skrainka, 2011. "High performance quadrature rules: how numerical integration affects a popular model of product differentiation," CeMMAP working papers CWP03/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  14. Matthew Harding & Ephraim Leibtag & Michael F. Lovenheim, 2012. "The Heterogeneous Geographic and Socioeconomic Incidence of Cigarette Taxes: Evidence from Nielsen Homescan Data," American Economic Journal: Economic Policy, American Economic Association, vol. 4(4), pages 169-98, November.
  15. Patrick Bajari & Jeremy T. Fox & Kyoo il Kim & Stephen P. Ryan, 2009. "A Simple Nonparametric Estimator for the Distribution of Random Coefficients," NBER Working Papers 15210, National Bureau of Economic Research, Inc.
  16. Patricia Apps & Jan Kabátek & Ray Rees & Arthur van Soest, 2012. "Labor Supply Heterogeneity and Demand for Child Care of Mothers with Young Children," CEPR Discussion Papers 677, Centre for Economic Policy Research, Research School of Economics, Australian National University.
  17. Cohen, Michael, 2010. "A Structured Covariance Probit Demand Model," Research Reports 149970, University of Connecticut, Food Marketing Policy Center.
  18. Igor Prünster & Matteo Ruggiero, 2011. "A Bayesian nonparametric approach to modeling market share dynamics," Carlo Alberto Notebooks 217, Collegio Carlo Alberto.

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