Abstract
After completing the experimental runs of a screening design, the responses understudy are analyzed by statistical methods to detect the active effects. To increasethe chances of correctly identifying these effects, a good analysis method should: (1)provide alternative interpretations of the data, (2) reveal the aliasing present in thedesign, and (3) search only meaningful sets of effects as defined by user-specifiedrestrictions such as effect heredity or constraints that include all the contrasts of amulti-level factor in the model. Methods like forward selection, the Dantzig selectoror LASSO do not posses all these properties. Simulated annealing model searchcannot handle other constraints than effect heredity. This paper presents a novelstrategy to analyze data from screening designs that posses properties (1)–(3) infull. It uses modern mixed integer optimization methods that returns the results ina few minutes. We illustrate our method by analyzing data from real and syntheticexperiments involving two-level and mixed-level screening designs. Using simulations,we show the capability of our method to automatically select the set of active effectsand compare it to the benchmark methods.
Keywords: Dantzig selector, definitive screening design, LASSO, sparsity, two-factorinteraction.