A Fast Parsimonious Maximum Likelihood Approach for Predicting Outcome Variables from a Large Number of Predictors

A new model with K correlated components is presented for predicting outcome variables where the number of predictors G may exceed the total sample size N. A fast maximum likelihood algorithm provides closed-form expressions for the model parameters and statistical tests for determining the number of components. We also propose a way to reduce the number of predictors in a stepwise fashion, at each step eliminating the least important predictor based on a new measure of predictor importance. When at least one suppressor variable is included among the predictors, the new model predicts and validates better than traditional models, especially when G is large.