Chiong, Khai Xiang and Shum, Matthew (2019) Random Projection Estimation of Discrete-Choice Models with Large Choice Sets. Management Science, 65 (1). pp. 256-271. ISSN 0025-1909. doi:10.1287/mnsc.2017.2928. https://resolver.caltech.edu/CaltechAUTHORS:20190307-100818948
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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.
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| Additional Information: | © 2018 INFORMS. Received: August 19, 2016; Accepted: August 16, 2017; Published Online: April 06, 2018. This paper was accepted by Juanjuan Zhang, marketing. For helpful comments, the authors thank Serena Ng, Hiroaki Kaido, Michael Leung, Sergio Montero, Harry Paarsch, Alejandro Robinson, and Frank Wolak, as well as seminar participants at Stanford Graduate School of Business, Olin Business School at Washington University in St. Louis, the University of Texas at Austin, University of British Columbia, “Machine Learning: What’s in it for Economics?” (University of Chicago), the Econometric Society Australasian meetings (Sydney, July 2016), Optimal Transport and Economics (New York university, April 2016), and DATALEAD (Paris, November 2015). | |||||||||
| Subject Keywords: | discrete choice models; large choice sets; random projection; machine learning; semiparametric; cyclical monotonicity; Johnson–Lindenstrauss lemma | |||||||||
| Issue or Number: | 1 | |||||||||
| DOI: | 10.1287/mnsc.2017.2928 | |||||||||
| Record Number: | CaltechAUTHORS:20190307-100818948 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20190307-100818948 | |||||||||
| Official Citation: | Random Projection Estimation of Discrete-Choice Models with Large Choice Sets. Khai Xiang Chiong and Matthew Shum. Management Science 2019 65:1, 256-271; doi: 10.1287/mnsc.2017.2928 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 93626 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 07 Mar 2019 21:00 | |||||||||
| Last Modified: | 16 Nov 2021 16:59 |
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