Supersaturated designs: Are our results significant?
AbstractTwo-level supersaturated designs (SSDs) are designs that examine more than n-1 factors in n runs. Although SSD literature for both construction and analysis is plentiful, the dearth of actual applications suggests that SSDs are still an unproven tool. Whether using forward selection or all-subsets regression, it is easy to select simple models from SSDs that explain a very large percentage of the total variation. Hence, naive p-values can persuade the user that included factors are indeed active. We propose the use of a global model randomization test in conjunction with all-subsets (or a shrinkage method) to more appropriately select candidate models of interest. For settings where the large number of factors makes repeated use of all-subsets expensive, we propose a short-cut approximation for the p-values. Two state-of-the-art model selection methods that have received considerable attention in recent years, Least Angle Regression and the Dantzig Selector, were likewise supplemented with the global randomization test. Finally, we propose a randomization test for reducing the number of terms in candidate models with small global p-values. Randomization tests effectively emphasize the limitations of SSDs, especially those with a large factor to run size ratio.
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Bibliographic InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 55 (2011)
Issue (Month): 9 (September)
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Web page: http://www.elsevier.com/locate/csda
Adjusted p-value All-subsets regression Effect sparsity Global model test Randomization test Shrinkage methods;
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- III, Harrison W. Kelly & Voelkel, Joseph O., 2000. "Asymptotic-power problems in the analysis of supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 47(4), pages 317-324, May.
- Marley, Christopher J. & Woods, David C., 2010. "A comparison of design and model selection methods for supersaturated experiments," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3158-3167, December.
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