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Approximate Model Spaces for Model-Robust Experiment Design

Summary: 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. This article presents 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. The authors build their procedure on a restricted columnwise-pairwise algorithm, and explore its effectiveness for two model spaces in the literature. For smaller full model spaces, the authors 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. The authors 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.

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  • Topics: Statistics
  • Keywords: Design of experiments (DOE), D-optimality, Robust design, Optimal design
  • Author: Smucker, Byran J.; Drew, Nathan M.;
  • Journal: Technometrics