A Criterion for Constructing Powerful Supersaturated Designs When Effect Directions Are Known

Abstract

As a criterion for selecting supersaturated designs, we suggest minimizing the variance of the pairwise inner products of the design-matrix columns, subject to a constraint on the E(s2)-efficiency as well as a requirement that the average correlation between the columns is positive. We call these designs constrained positive Var(s)-optimal and argue that, if the direction of the effects can be specified in advance, these designs are more powerful to detect active effects than other supersaturated designs while not substantially increasing Type I error rates. These designs are constructed algorithmically, using a coordinate-exchange algorithm that exploits the structure of the criterion to provide computational advantages. We also demonstrate that, for the simulation scenarios considered, misspecification of the effect directions will, at worst, result in power and Type I error rates in line with standard supersaturated designs.