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

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.