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Random Projection Estimation of Discrete-Choice Models with Large Choice Sets

Khai Xiang Chiong () and Matthew Shum ()
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Khai Xiang Chiong: Naveen Jindal School of Management, University of Texas at Dallas, Richardson, Texas 75080
Matthew Shum: California Institute of Technology, Pasadena, California 91125

Management Science, 2019, vol. 65, issue 1, 256-271

Abstract: We introduce random projection , an important dimension-reduction tool from machine learning, for the estimation of aggregate discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are projected into a lower-dimensional Euclidean space using random projections. Subsequently, estimation proceeds using cyclical monotonicity moment inequalities implied by the multinomial choice model; the estimation procedure is semiparametric and does not require explicit distributional assumptions to be made regarding the random utility errors. Our procedure is justified via the Johnson–Lindenstrauss lemma—the pairwise distances between data points are preserved through random projections. The estimator works well in simulations and in an application to a supermarket scanner data set.

Keywords: discrete choice models; large choice sets; random projection; machine learning; semiparametric; cyclical monotonicity; Johnson–Lindenstrauss lemma (search for similar items in EconPapers)
Date: 2019
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