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

Chiong, Khai X. and Shum, Matthew (2016) Random Projection Estimation of Discrete-Choice Models With Large Choice Sets. Social Science Working Paper, 1416. California Institute of Technology , Pasadena, CA. (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20160329-095921634

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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, the 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 a computational simulation and in a application to a supermarket scanner dataset.


Item Type:Report or Paper (Working Paper)
Related URLs:
URLURL TypeDescription
http://resolver.caltech.edu/CaltechAUTHORS:20190307-100818948Related ItemJournal Article
ORCID:
AuthorORCID
Shum, Matthew0000-0002-6262-915X
Additional Information:March 2016. First draft: February 29, 2016. This draft: March 2016. We thank Hiroaki Kaido, Michael Leung, Sergio Montero, and participants at the DATALEAD conference (Paris, November 2015) for helpful comments.
Group:Social Science Working Papers
Subject Keywords:semiparametric multinomial choice models, random projection, large choice sets, cyclic monotonicity, Johnson-Lindenstrauss Lemma
Series Name:Social Science Working Paper
Issue or Number:1416
Classification Code:JEL: C14, C25, C55
Record Number:CaltechAUTHORS:20160329-095921634
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160329-095921634
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65735
Collection:CaltechAUTHORS
Deposited By: Susan Vite
Deposited On:30 Mar 2016 22:57
Last Modified:03 Oct 2019 09:50

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