Random Projection Estimation of Discrete-Choice Models with Large Choice Sets
This addresses computational challenges in econometrics for researchers and practitioners dealing with high-dimensional choice data, though it is incremental as it adapts existing machine learning tools.
The authors tackled the problem of estimating discrete-choice models with large choice sets by introducing sparse random projection for dimension reduction, showing that their estimator performs well in simulations and a supermarket scanner dataset application.
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, 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 simulations and in an application to a supermarket scanner dataset.