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

30 Pages Posted: 18 Apr 2016 Last revised: 20 Aug 2016

See all articles by Khai Chiong

Khai Chiong

University of Texas at Dallas - Naveen Jindal School of Management

Matthew Shum

California Institute of Technology

Multiple version iconThere are 2 versions of this paper

Date Written: August 19, 2016

Abstract

We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a lower-dimensional Euclidean space using random projections. Subsequently, estimation proceeds using cyclic monotonicity moment inequalities implied by the multinomial choice model; the estimation procedure is semi-parametric and does not require explicit distributional assumptions to be made regarding the random utility errors. The random projection procedure is justified via the Johnson-Lindenstrauss Lemma - the pairwise distances between data points are preserved during data compression, which we exploit to show convergence of our estimator. The estimator works well in simulations and in an application to a supermarket scanner dataset.

Keywords: semiparametric discrete choice models, random projection, machine learning, large choice sets, cyclic monotonicity, Johnson-Lindenstrauss Lemma

JEL Classification: C14, C25, C55

Suggested Citation

Chiong, Khai and Shum, Matthew, Random Projection Estimation of Discrete-Choice Models with Large Choice Sets (August 19, 2016). USC-INET Research Paper No. 16-14. Available at SSRN: https://ssrn.com/abstract=2764607 or http://dx.doi.org/10.2139/ssrn.2764607

Khai Chiong (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

P.O. Box 830688
Richardson, TX 75083-0688
United States

Matthew Shum

California Institute of Technology ( email )

Pasadena, CA 91125
United States

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