Optimal designs for asymmetrical factorial paired comparison experiments |
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Authors: | Abdalla T. El-Helbawy Essam A. Ahmed Abdullah H. Alharbey |
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Affiliation: | Department of Statistics , King Abdulaziz University , P.0.Box 9028, Jeddah, Saudi Arabia |
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Abstract: | Three forms of a general null hypothesis Ho on the factorial parameters of a general asymmetrical factorial paired comparison experiment are considered. A class of partially balanced designscorresponding to each form of H0 is constructed and the A,D and ioptimal design, minimizing the trace, determinant and largest eigenvalue of a defined covariance matrix of related maximumlikelihoodestimators, in that class is determined. Moreover, the optimal design in each class maximizes the noncentrality parameter λ2 of the asymptotic noncentral chi-square distribution of the likelihood ratiostatistic -2 log λ for testing Ho under defined local alternatives. These results apply directly to symmetrical factorial paired comparison experiments as special casesExamples are given forillustrating applications of the developed results |
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Keywords: | Bradley-Terry model mixed factorial model hypotheses on factorial effects treatment contrasts noncentrality parameter A-D- and E-optimality |
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