Regression analysis of experiments with complex confounding patterns guided by the alias matrix

Abstract

Resolution III experiments with complex confounding patterns, often called main effect plans. Their main effects are partially confounded with two-factor interactions rather than being either independent or completely aliased, as they are in regular designs that are constructed from a defining relation. It is possible to detect some two-factor interactions, from experiments with complex confounding patterns if only a few of the factors are active. The partial confounding of interactions with main effects in these experiments allows one to estimate interactions with regression analysis. Recent papers have shown how the interactions can be detected using repeated runs of stepwise regression, or computationally intensive Bayesian methods. This paper shows that, with a short list of candidate interactions, the important interactions can be detected efficiently by a single pass of all subsets regression. The short list of candidates interactions for the all subsets regression are selected with regard to their potential for contributing to the value of the large estimated effects calculated from the data. The potential is determined by summing coefficients in the alias matrix. This paper reviews the concept of the alias matrix, and defines the alias plot that can be obtained from the alias matrix. The alias plot provides simple graphic for viewing the potential contribution of interactions to large estimated effects. The interactions identified on the alias plot, along with main effects, are used as candidates in an all subsets regression analysis of data from partially confounded experiments. The resulting strategy allows exploration of a wide range of the potential model space, can reveal several plausible models for the data if they exist, and can be completed using standard statistical software. Examples are presented.