An Evaluation of Estimation Capacity Under the Conditional Main Effect Parameterization
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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.
KeywordsComplex aliasing Experimental design Partial aliasing Regular fractional factorial design
Mathematics Subject Classification62K15 05B15
We are grateful to two reviewers for many valuable comments that improved this paper. We also thank the participants of the 2018 International Conference on Advances in Interdisciplinary Statistics and Combinatorics (AISC 2018), especially Robert Mee, J.P. Morgan, and Min Yang, for their insightful discussions that motivated the investigation in this paper.
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Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
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