OPTIMAL DESIGNS FOR ASYMMETRICAL FACTORIAL PAIRED-COMPARISON EXPERIMENTS

Three forms of a general null hypothesis H-0 on the factorial parameters of a general asymmetrical factorial paired comparison experiment are considered. A class of partially balanced designs corresponding to each form of H-0 is constructed and the A-, D- and E-optimal design, minimizing the trace, determinant and largest eigenvalue of a defined covariance matrix of related maximum likelihood estimators, in that class is determined. Moreover, the optimal design in each class maximizes the noncentrality parameter lambda2 of the asymptotic noncentral chi-square distribution of the likelihood ratio statistic -2 log lambda for testing H-0 under defined local alternatives. These results apply directly to symmetrical factorial paired comparison experiments as special cases. Examples are given for illustrating applications of the developed results.