A comparative study of some exact designs for estimating the variance components

This study aims to investigate and compare several experimental designs for the efficient estimation of variance components. Some N-observation discrete/exact designs are to be considered for random effects models. In these statistical models the parameters of the model are also assumed to be random variables. Thus, the variance of an observation on the response variable is decomposed into several components, in addition to the error variance. The simplest approach to estimate variance components is to use the analysis of variance (ANOVA) method. The analysis considers both single-factor and two- factor experiments, and different allocations of observations across experimental cells are examined. Also, these investigations are carried out on the basis of total or “average variance” of the estimators, using the A-optimality criterion. The results indicate that the configurations depend on the ratios of the variance components. For higher factor variance ratios, designs with more levels and fewer replicates are more efficient, whereas lower ratios favor more replicates. Balanced configurations are preferable when the variance ratios are equal, and each variance component ratio can affect the optimal design according to the experimental case considered. • A-optimality is used to estimate variance components in random effects models • The study compares single and two factor experimental designs • The most efficient designs depend on the ratios of variance components. • The results provide guidelines for identifying preferred designs