cmenet: A New Method for Bi-Level Variable Selection of Conditional Main Effects

ABSTRACT

This article introduces a novel method for selecting main effects and a set of reparameterized 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. Supplementary materials for this article are available online.

KEYWORDS:

• Conditional effects
• Coordinate descent
• Gene association
• Interaction analysis
• Variable selection

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Acknowledgments

The authors gratefully acknowledge helpful advice from two referees, particularly one referee who pointed out a minor mistake in Proposition 1, and whose comments led to the development of the CME screening rules in Section 4.3. The authors also thank Prof. Ben Haaland for his useful comments and suggestions. An efficient C++ implementation of cmenet and cv.cmenet is available in the R package cmenet in CRAN.

Additional information

Funding

This work is supported by the U. S. Army Research Office under grant number W911NF-17-1-0007.