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: (1) provide alternative interpretations of the data, (2) reveal the aliasing present in the design, and (3) search only meaningful sets of effects as defined by user-specified restrictions such as effect heredity or constraints that include all the contrasts of a multi-level factor in the model. Methods like forward selection, the Dantzig selector or LASSO do not posses all these properties. Simulated annealing model search cannot handle other constraints than effect heredity. This paper presents a novel strategy to analyze data from screening designs that posses properties (1)-(3) in full. It uses modern mixed integer optimization methods that returns the results in a few minutes. We illustrate our method by analyzing data from real and synthetic experiments involving two-level and mixed-level screening designs. Using simulations, we show the capability of our method to automatically select the set of active effects and compare it to the benchmark methods.