Sure independence screening for analyzing supersaturated designs

ABSTRACT

Supersaturated designs (SSDs) constitute a large class of fractional factorial designs which can be used for screening out the important factors from a large set of potentially active ones. A major advantage of these designs is that they reduce the experimental cost dramatically, but their crucial disadvantage is the confounding involved in the statistical analysis. Identification of active effects in SSDs has been the subject of much recent study. In this article we present a two-stage procedure for analyzing two-level SSDs assuming a main-effect only model, without including any interaction terms. This method combines sure independence screening (SIS) with different penalty functions; such as Smoothly Clipped Absolute Deviation (SCAD), Lasso and MC penalty achieving both the down-selection and the estimation of the significant effects, simultaneously. Insights on using the proposed methodology are provided through various simulation scenarios and several comparisons with existing approaches, such as stepwise in combination with SCAD and Dantzig Selector (DS) are presented as well. Results of the numerical study and real data analysis reveal that the proposed procedure can be considered as an advantageous tool due to its extremely good performance for identifying active factors.

KEYWORDS:

• Main effects model
• Penalty functions
• Screening designs

MATHEMATICS SUBJECT CLASSIFICATION:

• 62K15
• 62K05

Acknowledgements

We are grateful to the editor, the associate editor, and the referees for their constructive comments, which have led to major improvements in the presentation.

Additional information

Funding

The research of the first author (K.D.) was financially supported by a scholarship awarded by the Secretariat of the Research Committee of National Technical University of Athens.