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A Bayesian mixed logit-probit model for multinomial choice

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Author Info
Martin Burda
Matthew Harding (Institute for Fiscal Studies and Stanford University)
Jerry Hausman () (Institute for Fiscal Studies and Massachusetts Institute of Technology)
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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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP23/08.

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Date of creation: Aug 2008
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Handle: RePEc:ifs:cemmap:23/08

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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. [Downloadable!] (restricted)
  2. Mark J. Jensen & John M. Maheu, 2008. "Bayesian semiparametric stochastic volatility modeling," Working Paper 2008-15, Federal Reserve Bank of Atlanta. [Downloadable!]
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  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Keisuke Hirano, 2002. "Semiparametric Bayesian Inference in Autoregressive Panel Data Models," Econometrica, Econometric Society, vol. 70(2), pages 781-799, March. [Downloadable!] (restricted)
  6. 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. [Downloadable!]
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  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. [Downloadable!] (restricted)
  8. 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 and Swedish Statistical Association, vol. 28(2), pages 355-375. [Downloadable!] (restricted)
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