Bayesian partial factor regression

A Bayesian linear regression model is developed that cleanly addresses a long-recognized and fundamental difficulty of factor analytic regression – the response variable could be closely associated with the least important principal component. The model possesses inherent robustness to the choice of the number of factors and provides a natural framework for variable selection of highly correlated predictors in high dimensional problems. In terms of out-of-sample prediction, the model is demonstrated to be competitive with partial least squares, ridge regression, and standard factor models under data regimes for which each of those methods excels; thus representing a promising default regression tool. By incorporating pointmass priors on key parameters this model permits variable selection in the presence of highly correlated predictors, as well as estimation of the sufficient dimension, in the p n setting. 1 The Predictor Distribution’s Role in Linear Regression 1.