# A Bayesian mixed logit-probit model for multinomial choice

*Martin Burda* (),
*Matthew Harding* () and
*Jerry Hausman*

*Journal of Econometrics*, 2008, vol. 147, issue 2, 232-246

**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.

**Keywords:** Multinomial; discrete; choice; model; Dirichlet; process; prior; Non-conjugate; priors; Hierarchical; latent; class; models (search for similar items in EconPapers)

**Date:** 2008

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Working Paper: A Bayesian mixed logit-probit model for multinomial choice (2008)

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:econom:v:147:y:2008:i:2:p:232-246

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