A Systematic Approach to the Analysis of Complex Interaction Patterns in Two-Level Factorial Designs

Abstract

Analysis of data from two-level full factorial designs often ends up with a final prediction equation that gives only the significant main-effect and interaction terms. When the number of interactions is small, simple and useful interpretation of the equation can then be drawn immediately. This article addresses a different situation in which the number of significant interactions may be large so that additional efforts are needed to sort out the pattern and the relationship between them. In particular, we bring out a class of models in which most interactions can be attributed to just one or two (or very few) factors, and conditional on these factors, the models become essentially linear. We offer a strategy for uncovering this structure by linear domain splitting, whereby a complicated global model is replaced by a series of local domain-specific linear models. We present a recommended methodology (PHD—principal Hessian direction) for systematically proceeding from the global equation to local split-dom...