A systematic approach to the analysis of complex interaction patterns in two-level factorial designs

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 but 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-domain analyses. The net result is that guided tree-structured paths are offered for visiting the source-of-interaction factors in sequence, which appropriately reflects their relative importance and mutual relationship. The final stage modeling is simpler (linear). The quality of the fit can be assessed separately in each region, and the analyst comes away with greater insight as to the sensitivity and robustness of the various factor effects over various regions. Applications in digital electronics testing are illustrated by analyzing a dataset collected for studying the conversion error of a digital-to-analog converter.