Selecting an Orthogonal or Nonorthogonal Two-Level Design for Screening

ABSTRACT

This article presents a comparison of criteria used to characterize two-level designs for screening purposes. To articulate the relationships among criteria, we focus on 7-factor designs with 16–32 runs and 11-factor designs with 20–48 runs. Screening based on selected designs for each of the run sizes considered is studied with simulation using a forward selection procedure and the Dantzig selector. This article compares Bayesian D-optimal designs, designs created algorithmically to optimize estimation capacity over various model spaces, and orthogonal designs by estimation-based criteria and simulation. In this way, we furnish both general insights regarding various design approaches, as well as a guide to make a choice among a few final candidate designs. Supplementary materials for this article are available online.

KEYWORDS:

• Estimation capacity
• False discovery rate
• G-aberration
• Orthogonal array
• Power
• Q_B

Supplementary Materials

Supplementary sections.pdf: Background on regular and nonorthogonal designs; Q_B under weak effect heredity; a study of all OA(40,11,3); selection of nonregular designs for the power simulations; and the simulated analysis methods.

Programs.zip: Matlab and R programs for power simulations.

Designs.zip: Text files with the selected designs.

Acknowledgments

The authors thank Byran Smucker for providing all the MEPI designs. The research of the second author was supported by a grant from the Research Foundation - Flanders (FWO). The third author gratefully acknowledges support from the Simons Foundation (award no. 244759).