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  \textbf{\Large{\textsc{STANFORD UNIVERSITY}}}\\[5pt]
  \textbf{\Large{\textsc{DEPARTMENT OF STATISTICS}}}\\[5pt]
  \Large{\textsc{DEPARTMENTAL SEMINAR}}
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  4:15 p.m., Tuesday, May 20, 2008\\
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  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
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  \textsl{Matthew Harding} \\
  Department of Economics\\
  Stanford University
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  \subsection*{A Bayesian Mixed Logit-Probit Model for Multinomial Choice}
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\noindent

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 assumptionfree
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 bypass a problem of prior non-conjugacy by employing a
”latent class” sampling algorithm for the DP prior. 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, calculated using GPS software. Supermarket indicator variables form the
parametric part of our model.


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