Best practices for multi- and mixed-level supersaturated designs

AbstractSupersaturated designs offer cost-effective efficacy in discerning significant factors among a vast array of potential factors, thereby rendering them valuable. The current literature studies several design selection criteria and analysis methods for such designs. For two-level designs, the screening performance of optimal designs constructed under different optimality criteria remains similar, especially when the effect directions are not known in advance. The Gauss-Dantzig Selector (GDS) is the preferred analysis method for two-level designs. For the multi- and mixed-level supersaturated designs, despite the existence of multiple design optimality criteria and design construction methods, the literature lacks guidance for both the design selection and the choice of analysis method. Through extensive simulation studies, we show that the multi- and mixed-level designs constructed using different optimality criteria have equivalent screening performance for the unknown effect directions. For known effect directions, generalized minimum aberration-optimal designs have slightly better screening performance. On the analysis front, however, the story differs from two-level designs. While LASSO and GDS show superior performance among the analysis methods compared, they depend on the parameterization or the coding of factors. Since no single choice of parameterization is best across sparsity levels, scenarios, and designs, we propose using group LASSO, which is invariant to parameterizations. Finally, we characterize the settings in terms of the number of runs, factors, and the effect sparsity, which are too complex to get meaningful results from group LASSO.Keywords: group LASSOmain effectsmixed-levelscreening experimentsthree-level supersaturated design Disclosure statementNo potential conflict of interest was reported by the authors.Data availability statementData availability is not applicable to this article as no new data were created or analyzed in this study.Additional informationNotes on contributorsRakhi SinghDr. Rakhi Singh is an Assistant Professor in the Department of Mathematics and Statistics at Binghamton University in New York, USA. She did her PhD in Mathematics (with specialization in Statistics) under a joint PhD program between Indian Institute of Technology Bombay and Monash University, Australia. She also did a postdoc for a couple of years at TU Dortmund and UNC Greensboro. Her primary research areas are design and analysis of experiments and subdata selection for high-dimensional data.