A two-stage variable selection strategy for supersaturated designs with multiple responses

A supersaturated design (SSD), whose run size is not enough for estimating all the main effects, is commonly used in screening experiments. It offers a potential useful tool to investigate a large number of factors with only a few experimental runs. The associated analysis methods have been proposed by many authors to identify active effects in situations where only one response is considered. However, there are often situations where two or more responses are observed simultaneously in one screening experiment, and the analysis of SSDs with multiple responses is thus needed. In this paper, we propose a two-stage variable selection strategy, called the multivariate partial least squares-stepwise regression (MPLS-SR) method, which uses the multivariate partial least squares regression in conjunction with the stepwise regression procedure to select true active effects in SSDs with multiple responses. Simulation studies show that the MPLS-SR method performs pretty good and is easy to understand and implement.