Bayesian analysis and follow-up experiments for supersaturated multistratum designs

Abstract

Abstract Supersaturated multistratum designs are applied for identifying important factors in experiments in which the run order cannot be completely randomized. Since supersaturated multistratum designs have small run sizes and large numbers of factors, there exist problems of model uncertainty. A drawback of the stepwise regression analysis commonly used in the literature is that it only produces a single model and, thus, is not suitable to deal with model uncertainty. In this paper, we propose a Bayesian approach for analyzing the data collected from supersaturated multistratum designs. Instead of producing a single model, the Bayesian analysis reports several competing models and, thus, provides an opportunity for the experimenters to explore potentially important factors. To further reduce uncertainty, we suggest conducting follow-up experiments and develop a generalized model-discrimination criterion for selecting follow-up supersaturated designs that are effective in reducing ambiguity in the analysis results.