A Novel Bagging Ensemble Approach for Variable Ranking and Selection for Linear Regression Models

Abstract

With respect to variable selection for linear regression models, a novel bagging ensemble method is developed in this paper based on a ranked list of variables. Specifically, a mixed importance measure is assigned to each variable according to the order that it is selected by stepwise search algorithm into the final model as well as the improvement resulted from its inclusion. Considering that small permutations in training data may lead to some changes in the order that the variables enter the final model, the above process is repeated for multiple times with each executed on a bootstrap sample. Finally, the importance measure of each variable is averaged across the bootstrapping trials. The experiments conducted with some simulated data demonstrate that the novel method compares favorably with some other variable selection techniques.