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

• 成果类型: Article
• 署名作者: Chiong, Khai Xiang; Shum, Matthew
• 署名单位: University of Texas System; University of Texas Dallas; California Institute of Technology
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2017.2928
• 发表日期: 2019
• 页码: 256-271
• 关键词: Discrete choice models; large choice sets; random projection; Machine Learning; semiparametric; Cyclical monotonicity; Johnson-Lindenstrauss lemma

摘要

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.