AN ALGEBRA FOR THE CONDITIONAL MAIN EFFECT PARAMETERIZATION

摘要

The conditional main effect (CME) parameterization system resolves the long-standing aliasing dilemma associated with the traditional orthogonal components system for two-level regular fractional factorial designs. However, the algebra of the CME system is not yet fully understood, which impedes the development of general results on this system that possess a broad scope of application across designs. Therefore, we establish a comprehensive algebra for the CME system based on indicator functions. Our algebra facilitates derivations of general partial aliasing relations for a wide variety of two-level designs. Using the proposed algebra, we examine the implications for resolution IV designs of traditional design criteria under the CME system. A novel feature of our algebra is that it enables immediate and simple D-efficiency calculations for two-level regular designs and for models consisting of multiple conditional and traditional effects.