A random-effect model approach for group variable selection

We consider regression models with a group structure in explanatory variables. This structure is commonly seen in practice, but it is only recently realized that taking the information into account in the modeling process may improve both the interpretability and accuracy of the model. In this paper, we study a new approach to group variable selection using random-effect models. Specific distributional assumptions on random effects pertaining to a given structure lead to a new class of penalties that include some existing penalties. We also develop an efficient computational algorithm. Numerical studies are provided to demonstrate better sensitivity and specificity properties without sacrificing the prediction accuracy. Finally, we present some real-data applications of the proposed approach.