Approximate Model Spaces for Model-Robust Experiment Design

Abstract

Optimal designs depend upon a prespecified model form. A popular and effective model-robust alternative is to design with respect to a set of models instead of just one. However, model spaces associated with experiments of interest are often prohibitively large and so algorithmically generated designs are infeasible. Here, we present a simple method that largely eliminates this problem by choosing a small set of models that approximates the full set and finding designs that are explicitly robust for this small set. We build our procedure on a restricted columnwise-pairwise algorithm, and explore its effectiveness for two model spaces in the literature. For smaller full model spaces, we find that the designs constructed with the new method compare favorably with robust designs that use the full model space, with construction times reduced by orders of magnitude. We also construct designs that heretofore have been unobtainable due to the size of their model spaces. Supplementary material (available online) includes code, designs, and additional results.

• D-optimality
• Supersaturated
• Two-level designs

SUPPLEMENTARY MATERIALS

Supplementary material for “Approximate Model Spaces for Model-Robust Experiment Design” is included online and consists of the following:

• A_Additional_Design_Results A folder that includes RCP results with CIs, design results based upon coordinate exchange, and model discrimination results.

• B_Additional_Meta-Design_Results A folder containing a file comparing results using NBIBD for the approximate model space with a random selection of this set.

• C_Designs A folder containing a collection of text files providing the designs described in Tables 3 and 4, and Tables 1–5 in Supplement A.2.

• D_Code A folder containing several subfolders with SAS code (to generate NBIBDs) and Matlab code (to generate model-robust designs).

ACKNOWLEDGEMENTS

The authors express their thanks to John Bailer and Steve Wright who gave feedback on an earlier version of this article. They also thank Brad Jones, who suggested the BIBD analogy. Additionally, the reviewers, the Associate Editor, and the Editor made suggestions that positively shaped the article. Jens Mueller provided vital computing assistance, and he is gratefully acknowledged. The first author also recognizes the support of the Committee on Faculty Research at Miami University as well as a summer research grant for new tenure-track faculty from the College of Arts and Science. The work of the second author was conducted at Miami University.