Variable Selection for Screening Experiments

Abstract

The first step in many applications of response surface methodology is typically the screening process. Variable selection plays an important role in screening experiments when a large number of potential factors are introduced in a preliminary study. Traditional approaches, such as the best subset variable selection and stepwise deletion, may not be appropriate in this situation. In this paper we introduce a variable selection procedure via penalized least squares with the SCAD penalty. An algorithm to find the penalized least squares solution is suggested, and a standard error formula for the penalized least squares estimate is derived. With a proper choice of the regularization parameter, it is shown that the resulting estimate is root n consistent and possesses an oracle property; namely, it works as well as if the correct submodel were known. An automatic and data-driven approach was proposed to select the regularization parameter. Examples are used to illustrate the effectiveness of the newly proposed approach. The computer codes (written in MATLAB) to perform all calculation are available through the authors for an automatic data-driven variable selection procedure.

Optimization of cephalosporin C acylase immobilization using crosslinked enzyme aggregates technique

“…In the first step, factors affecting CLEAs-CCA immobilization were screened using the FFD experimental design. The factor screening plays an important role when many potential factors influence the response while the resource availability is limited 22 . FFD screened out the influencing factors based on their main effects and excluded their interaction 23 .…”

Screening Procedure for Supersaturated Designs Using a Bayesian Variable Selection Method

“…Beattie et al 7 combined the SSVS with the intrinsic Bayes factor (IBF) procedure to create a two-stage Bayesian model selection strategy. Li and Lin 8,9 used penalized least squares with the smoothly clipped absolute deviation (SCAD) penalty. A partial least-squares regression was employed by Zhang et al 10 Georgiou 11 proposed an SVD principal regression method for supersaturated designs.…”