Construction, Properties, and Analysis of Group-Orthogonal Supersaturated Designs

In this article, we propose a new method for constructing supersaturated designs that is based on the Kronecker product of two carefully chosen matrices. The construction method leads to a partitioning of the factors of the design such that the factors within a group are correlated to the others within the same group, but are orthogonal to any factor in any other group. We refer to the resulting designs as <i>group-orthogonal supersaturated designs</i>. We leverage this group structure to obtain an unbiased estimate of the error variance, and to develop an effective, design-based model selection procedure. Simulation results show that the use of these designs, in conjunction with our model selection procedure enables the identification of larger numbers of active main effects than have previously been reported for supersaturated designs. The designs can also be used in group screening; however, unlike previous group-screening procedures, with our designs, main effects in a group are not confounded. Supplementary materials for this article are available online.

本文提出了一种基于两组精心选取矩阵的克罗内克积（Kronecker product）构造超饱和设计（supersaturated designs）的新方法。该构造方法可对设计中的因子进行分组，使得同组内的因子彼此相关，而与其他组内的任意因子均正交。我们将此类所得设计命名为组正交超饱和设计（group-orthogonal supersaturated designs）。我们借助该分组结构实现了误差方差的无偏估计，并开发了一种高效的、基于设计的模型选择流程。仿真结果表明，将此类设计与我们的模型选择流程相结合，可识别出比现有超饱和设计相关研究中报道的更多数量的活跃主效应。此类设计还可应用于分组筛选；不过与以往的分组筛选流程不同，本设计中的组内主效应不会发生混杂。本文的补充材料可在线获取。