  This paper introduces a novel method for selecting main effects and a set of
reparametrized effects called conditional main effects (CMEs), which capture
the conditional effect of a factor at a fixed level of another factor. CMEs
represent interpretable, domain-specific phenomena for a wide range of
applications in engineering, social sciences and genomics. The key challenge is
in incorporating the implicit grouped structure of CMEs within the variable
selection procedure itself. We propose a new method, cmenet, which employs two
principles called CME coupling and CME reduction to effectively navigate the
selection algorithm. Simulation studies demonstrate the improved CME selection
performance of cmenet over more generic selection methods. Applied to a gene
association study on fly wing shape, cmenet not only yields more parsimonious
models and improved predictive performance over standard two-factor interaction
analysis methods, but also reveals important insights on gene activation
behavior, which can be used to guide further experiments. Efficient
implementations of our algorithms are available in the R package cmenet in
CRAN.
