Effective Design-Based Model Selection for Definitive Screening Designs

Since their introduction by Jones and Nachtsheim in 2011 Jones, B., and Nachtsheim, C. J. (2011), “A Class of Three-Level Designs for Definitive Screening in the Presence of Second-Order Effects,” Journal of Quality Technology, 43, 1–15.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar], definitive screening designs (DSDs) have seen application in fields as diverse as bio-manufacturing, green energy production, and laser etching. One barrier to their routine adoption for screening is due to the difficulties practitioners experience in model selection when both main effects and second-order effects are active. Jones and Nachtsheim showed that for six or more factors, DSDs project to designs in any three factors that can fit a full quadratic model. In addition, they showed that DSDs have high power for detecting all the main effects as well as one two-factor interaction or one quadratic effect as long as the true effects are much larger than the error standard deviation. However, simulation studies of model selection strategies applied to DSDs can disappoint by failing to identify the correct set of active second-order effects when there are more than a few such effects. Standard model selection strategies such as stepwise regression, all-subsets regression, and the Dantzig selector are general tools that do not make use of any structural information about the design. It seems reasonable that a modeling approach that makes use of the known structure of a designed experiment could perform better than more general purpose strategies. This article shows how to take advantage of the special structure of the DSD to obtain the most clear-cut analytical results possible.