A systematic review and evaluation of statistical methods for group variable selection

This review condenses the knowledge on variable selection methods implemented in R and appropriate for datasets with grouped features. The focus is on regularized regressions identified through a systematic review of the literature, following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines. A total of 14 methods are discussed, most of which use penalty terms to perform group variable selection. Depending on how the methods account for the group structure, they can be classified into knowledge and data-driven approaches. The first encompass group-level and bi-level selection methods, while two-step approaches and collinearity-tolerant methods constitute the second category. The identified methods are briefly explained and their performance compared in a simulation study. This comparison demonstrated that group-level selection methods, such as the group minimax concave penalty, are superior to other methods in selecting relevant variable groups but are inferior in identifying important individual variables in scenarios where not all variables in the groups are predictive. This can be better achieved by bi-level selection methods such as group bridge. Two-step and collinearity-tolerant approaches such as elastic net and ordered homogeneity pursuit least absolute shrinkage and selection operator are inferior to knowledge-driven methods but provide results without requiring prior knowledge. Possible applications in proteomics are considered, leading to suggestions on which method to use depending on existing prior knowledge and research question.