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This paper introduces a novel method for selecting main effects and a set ofreparametrized effects called conditional main effects (CMEs), which capturethe conditional effect of a factor at a fixed level of another factor. CMEsrepresent interpretable, domain-specific phenomena for a wide range ofapplications in engineering, social sciences and genomics. The key challenge isin incorporating the implicit grouped structure of CMEs within the variableselection procedure itself. We propose a new method, cmenet, which employs twoprinciples called CME coupling and CME reduction to effectively navigate theselection algorithm. Simulation studies demonstrate the improved CME selectionperformance of cmenet over more generic selection methods. Applied to a geneassociation study on fly wing shape, cmenet not only yields more parsimoniousmodels and improved predictive performance over standard two-factor interactionanalysis methods, but also reveals important insights on gene activationbehavior, which can be used to guide further experiments. Efficientimplementations of our algorithms are available in the R package cmenet inCRAN.

cmenet: a new method for bi-level variable selection of conditional main effects