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

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.