Mixtures of regressions with predictor-dependent mixing proportions

This work extends the standard mixture of linear regressions model by allowing the mixing proportions to be modeled nonparametrically as a function of the predictors, and presents an EM-like algorithm for estimation of the new model.

Abstract

We extend the standard mixture of linear regressions model by allowing the mixing proportions to be modeled nonparametrically as a function of the predictors. This framework allows for more flexibility in the modeling of the mixing proportions than the fully parametric mixture of experts model, which we also discuss. We present an EM-like algorithm for estimation of the new model. We also provide simulations demonstrating that our nonparametric approach can provide a better fit than the parametric approach in some instances and can serve to validate and thus reinforce the parametric approach in others. We also analyze and interpret two real data sets using the new method.