Robust Variable Selection Methods for Grouped Data

Abstract

When predictor variables possess an underlying grouping structure in multiple regression, selecting important groups of variables is an essential component of building a meaningful regression model. Some methods exist to perform group selection, but do not perform well when the data include outliers. Four methods for robust variable selection of grouped data, based on the group LASSO, are presented: two regular methods and two adaptive methods. For each of the two methods in the regular and adaptive groups, one method works well for data with outliers in the y-direction, and the other method works well for data with outliers in both the x- and y- directions. The effectiveness of each of these methods is illustrated with an extensive simulation study and a real data example.