A mixed integer optimization approach for model selection in screening experiments

Abstract

After completing the experimental runs of a screening design, the responses under study are analyzed by statistical methods to detect the active effects. To increase the chances of correctly identifying these effects, a good analysis method should provide alternative interpretations of the data, reveal the aliasing present in the design, and search only meaningful sets of effects as defined by user-specified restrictions such as effect heredity. This article presents a mixed integer optimization strategy to analyze data from screening designs that possesses all these properties. We illustrate our method by analyzing data from real and synthetic experiments, and using simulations.

KEYWORDS:

• best-subset selection
• Dantzig selector
• definitive screening design
• sparsity
• two-factor interaction

Acknowledgments

Part of the simulation study was carried out at the HPC core facility CalcUA at the University of Antwerp. We are grateful to José Núñez Ares and Nha Vo-Thanh for drawing our attention to the work of Bertsimas, and to Robert Mee for suggesting us to include factor sparsity constraints. We also thank José Núñez Ares for his thoughtful comments on a preliminary version of this article.

Funding

The research of the first and second authors was financially supported by the Flemish Fund for Scientific Research FWO.

Additional information

Notes on contributors

Alan R. Vazquez

Dr. Vazquez is a Junior Postdoctoral Fellow of the Flemish Fund for Scientific Research FWO and a Postdoctoral Researcher at KU Leuven. His email address is [email protected]

Eric D. Schoen

Dr. Schoen is a Guest Professor at the Faculty of Bioscience Engineering of KU Leuven and a Senior Statistical Consultant at TNO. His email address is [email protected].

Peter Goos

Dr. Goos is a Full Professor at the Faculty of Bioscience Engineering of KU Leuven and at the Faculty of Business and Economics of the University of Antwerp. He is a Senior Member of the American Society for Quality. His email address is [email protected].