Selection of Two-Level Supersaturated Designs for Main Effects Models

Abstract

An extensive literature is available on design selection criteria and analysis techniques for two-level supersaturated designs. The most notable design selection criteria are the popular $E(s^2)$-criterion, $UE(s^2)$-criterion, and more recently, the var($s+$)-criterion, while the most notable analysis technique is the Gauss-Dantzig Selector. It has been observed that while the Gauss-Dantzig Selector is often the preferred analysis technique, differences in the screening performance of different designs are not captured well by any of the common design selection criteria. In addition, none of the criteria have any direct connection to the Gauss-Dantzig Selector. We develop two new design selection criteria inspired by large sample desiderata of the Gauss-Dantzig Selector. Then, using a multi-objective Pareto-based coordinate exchange algorithm, we find Pareto efficient designs. The obtained Pareto efficient designs perform better in about 85% of the considered cases as screening designs than the var($s+$)-optimal designs, especially when the true signs of effects are known. For the remaining 15% of the cases as well as for the unknown effect signs, the Pareto efficient designs perform at par with the var($s+$)-optimal designs.

Keywords:

• Active factors
• Effect sparsity
• Dantzig Selector
• Screening designs

Acknowledgments

The authors are grateful to the Editor, an Associate Editor, and two referees for detailed comments that resulted in a significant improvement of the initial version of the article.

Disclosure Statement

The authors declare that they have no conflict of interest.

Additional information

Funding

JS gratefully acknowledge support through NSF grant DMS-1935729.