Analysis Methods for Supersaturated Design: Some Comparisons

Runze Li,Dennis K J Lin

doi:10.6339/jds.2003.01(3).134

Abstract

Supersaturated designs are very cost-effective with respect to the number of runs and as such are highly desirable in many preliminary studies in industrial experimentation. Variable selection plays an important role in analyzing data from the supersaturated designs. Traditional approaches, such as the best subset variable selection and stepwise regression, may not be appropriate in this sit- uation. In this paper, we introduce a variable selection procedure to screen active effects in the SSDs via nonconvex penalized least squares approach. Empirical comparison with Bayesian variable se- lection approaches is conducted. Our simulation shows that the non- convex penalized least squares method compares very favorably with the Bayesian variable selection approach proposed in Beattie, Fong and Lin (2001).

Highlights

Supersaturated designs (SSD) are useful in many preliminary studies in industry in the presence of a large number of potentially relevant factors, of which actual active effects are believed to be sparse
Fan and Li (2001) suggested using a = 3.7 from a Bayesian point of view. They found via Monte Carlo simulation that the performance of smoothly clipped absolute deviation (SCAD) is not sensitive to the choice of a provided that a ∈ (2, 10)
The goal of this section is to compare the performance of the penalized least squares approach with the SCAD penalty and the two Bayesian variable selection procedures, stochastic search variable selection (SSVS), proposed by George and McMulloch (1993) and extended for SSD by Chipman, Hamada and Wu (1993), denoted by CHW for short, and the two stage procedure (SSVS/intrinsic Bayesian factor (IBF)) by Beattie, Fong and Lin (2001), denoted by BFL

Summary

Introduction

Supersaturated designs (SSD) are useful in many preliminary studies in industry in the presence of a large number of potentially relevant factors, of which actual active effects are believed to be sparse. Fan and Li (2001) proposed a class of variable selection procedures by nonconcave penalized likelihood approaches. Extending the idea of the nonconcave penalized likelihood, Li and Lin (2002) suggested the use of nonconvex penalized least squares to screen active effects for supersaturated design. From their comparison, the penalized least squares performs much better than than the stepwise procedures using various variable selection criteria. The performance of the penalized least squares is compared with that of Bayesian variable selection procedures.

Nonconvex penalized least squares

The proposed procedure

Numerical comparison and example

Findings

Conclusion