Screening Active Effects in Supersaturated Designs with Binary Response via Control Charts

Supersaturated designs are designs in which the number of factors exceeds the run size; consequently, there are not enough degrees of freedom to estimate all the main effects. The goal here is to identify the dominant factors that constitute a small proportion of the overall set of factors, according to the assumption of effect sparsity. The analysis of such designs constitutes a challenging task and, even though many methods have been proposed in the literature assuming a normal response, only few works attempted to address the case of non-normal responses. In this paper, we propose a method for screening out the most important features in supersaturated designs assuming a Bernoulli distributed response. This new approach is based on an effective chart in Statistical Process Control, the cumulative sum control chart, combined with an information theoretic measure, and it is referred as the MIC algorithm. We judge the value of MIC through comparisons with three existing approaches suggested in the literature: the least absolute shrinkage and selection operator penalization method, and two feature selection algorithms, the Conditional Mutual Information Maximization and the minimal-redundancy-maximal-relevance. The simulation study reveals that the proposed method can be considered an advantageous method because of its extremely good performance in terms of statistical power. Copyright (c) 2017 John Wiley & Sons, Ltd.