Screening main and interaction effects in a Plackett-Burman design

Abstract

In a supersaturated design, the number of factors is greater than the number of observations. A design that is not supersaturated but has more parameters to be estimated than observations results in a supersaturated model (SSM). An SSM may occur when two-factor interactions exist in addition to main effects. The goal is to find the few active effects from the many in the SSM. Several approaches may be used to find a set of potential models and then to select the best model using some criterion. This may be done in a single stage by considering all main effects and two-factor interactions simultaneously, or by screening main effects first, then identifying the active interactions. In this paper, we study a single-stage and multiple two-stage approaches as well as different algorithms and criteria for selecting the models. For the Plackett-Burman design we study, we find that the SCAD algorithm with the corrected Akaike Information criterion (cAIC) generally performs well, but the best procedure depends on the true, unknown, underlying model.

Keywords:

• Dantzig selector
• LASSO
• Plackett-Burman
• SCAD
• Supersaturated design

Disclosure statement

No potential conflict of interest was reported by the authors.