Two-level experiments for binary response data

Information in a statistical experiment is often measured through the determinant of its information matrix. Under first order normal linear models, the determinant of the information matrix of a two-level factorial experiment neither depends on where the experiment is centered, nor on how it is oriented, and balanced allocations are more informative than unbalanced ones with the same number of runs. In contrast, under binary response models, none of these properties hold. The performance of two-level experiments for binomial responses is explored by investigating the dependence of the determinant of their information matrix on their location, orientation, range, presence or absence of interactions and on the relative allocation of runs to support points, and in particular, on the type of fractionating involved. Conventional wisdom about two-level factorial experiments, which is deeply rooted on normal response models, does not apply to binomial models. In binary response settings, factorial experiments should not be used for screening or as building blocks for binary response surface exploration, and there is no alternative to the optimal design theory approach to planning experiments.