An Evaluation of Estimation Capacity Under the Conditional Main Effect Parameterization

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...

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Bibliographic Details
Published in:Journal of statistical theory and practice Vol. 13; no. 4
Main Author: Sabbaghi, Arman
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.12.2019
Subjects:
Algorithms
Analysis and Advanced Methodologies in the Design of Experiments
Mathematics and Statistics
Original Article
Probability Theory and Stochastic Processes
Statistical Theory and Methods
Statistics
Regular fractional factorial design
62K15
05B15
Experimental design
Complex aliasing
Partial aliasing
ISSN:1559-8608, 1559-8616
Online Access:Get full text
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Summary: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.
ISSN:1559-8608
1559-8616
DOI:10.1007/s42519-019-0061-8