An Evaluation of Estimation Capacity Under the Conditional Main Effect Parameterization

Abstract

The conditional main effect (CME) parameterization system can enable more informative analyses of regular two-level fractional factorial designs compared to the traditional orthogonal components system. However, formal evaluations of estimation capacities for designs under CME models have yet to be performed. We establish a necessary and sufficient condition for a model consisting of all of the main effects and a selection of CMEs to be estimable in a regular two-level design of resolution at least III. Our condition illuminates the implications of the maximum estimation capacity criterion for analyses of such traditional and conditional effects. A novel aspect of our evaluations is the direct derivation of D-efficiencies for regular designs of resolution at least III with respect to CME models in which the selected CMEs are not siblings or family members, and their corresponding two-factor interactions are not completely aliased with a main effect.