Optimal Designs For the Restricted Maximum Likelihood Estimators in a Random Split-Plot Model

The design effect for the restricted maximum likelihood estimators of variance components in acompletely randomized split-plot model is studied. The model was used to represent the response generated froman experimental scenario where the whole-plot and split-plot factors are random. The work generated groups ofbalanced designs from same number of experimental runs and compared them for optimality using the derived Fisher Information matrix of the restricted maximum likelihood (REML) estimators. The measure for optimalityis the D-optimality criterion; the resulting optimal designs depend on the relative magnitudes of the true values of the variance components. The results show that when the factor variances are larger than the error variances, designs where the absolute difference between the number of whole-plots and the number of levels of the splitplot factor is relatively small show substantial gain in statistical efficiency over other designs.