Screening active factors in supersaturated designs

Identification of active factors in supersaturated designs (SSDs) has been the subject of much recent study. Although several methods have been previously proposed, a solution to the problem beyond one or two active factors still seems to be unsatisfactory. The smoothly clipped absolute deviation (SCAD) penalty function for variable selection has nice theoretical properties, but due to its nonconvex nature, it poses computational issues in model fitting. As a result, so far it has not shown much promise for SSDs. Another issue regarding its inefficiency, particularly for SSDs, has been the method used for choosing the SCAD sparsity tuning parameter. The selection of the SCAD sparsity tuning parameter using the AIC and BIC information criteria, generalized cross-validation, and a recently proposed method based on the norm of the error in the solution of systems of linear equations are investigated. This is performed in conjunction with a recently developed more efficient algorithm for implementing the SCAD penalty. The small sample bias-corrected cAIC is found to yield a model size closer to the true model size. Results of the numerical study and real data analyses reveal that the SCAD is a valuable tool for identifying active factors in SSDs.