Supersaturated designs: Are our results significant?

Two-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.