An Information Theoretical Method for Analyzing Unreplicated Designs with Binary Response

Abstract

The analysis of unreplicated factorial designs constitutes a challenging but difficult issue since there are no degrees of freedom so as to estimate the error variance. In the present paper we propose a method for screening active effects in such designs, assuming Bernoulli distributed data rather than linear; something that hasn’t received much attention yet. Specifically, we develop an innovating algorithm based on an information theoretical measure, the well-known symmetrical uncertainty, so that it can measure the relation between the response variable and each factor separately. The powerfulness of the proposed method is revealed via both, a thorough simulation study and a real data set analysis.