A mixed integer optimization approach for model selection in screening experiments

After completing the experimental runs of a screening design, the responses under study are analyzed by statistical methods to detect the active effects. To increase the chances of correctly identifying these effects, a good analysis method should provide alternative interpretations of the data, reveal the aliasing present in the design, and search only meaningful sets of effects as defined by user-specified restrictions such as effect heredity. This article presents a mixed integer optimization strategy to analyze data from screening designs that possesses all these properties. We illustrate our method by analyzing data from real and synthetic experiments, and using simulations.