Assessing Heterogeneity in Discrete Choice Models Using a Dirichlet Process Prior

Kim Jin Gyo, Menzefricke Ulrich and Feinberg Fred M.
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Kim Jin Gyo: MIT Sloan School of Management, kimjg@mit.edu
Menzefricke Ulrich: Rotman School of Management, University of Toronto, menzefricke@rotman.utoronto.ca
Feinberg Fred M.: University of Michigan Business School, feinf@umich.edu

Review of Marketing Science, 2004, vol. 2, issue 1, 41

Abstract: The finite normal mixture model has emerged as a dominant methodology for assessing heterogeneity in choice models. Although it extends the classic mixture models by allowing within component variablility, it requires that a relatively large number of models be separately estimated and fairly difficult test procedures to determine the "correct" number of mixing components. We present a very general formulation, based on Dirichlet Process Piror, which yields the number and composition of mixing components a posteriori, obviating the need for post hoc test procedures and is capable of approximating any target heterogeneity distribution. Adapting Stephens' (2000) algorithm allows the determination of 'substantively' different clusters, as well as a way to sidestep problems arising from label-switching and overlapping mixtures. These methods are illustrated both on simulated data and A.C. Nielsen scanner panel data for liquid detergents. We find that the large number of mixing components required to adequately represent the heterogeneity distribution can be reduced in practice to a far smaller number of segments of managerial relevance.

Keywords: Choice Models; Heterogeneity; Dirichlet Process; Bayesian Methods; Markov chain Monte Carlo (search for similar items in EconPapers)
Date: 2004
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DOI: 10.2202/1546-5616.1003

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