Approximations for Standard Errors of Estimators of Fixed and Random Effects in Mixed Linear Models

Abstract Best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known. If the true values are replaced by estimated values, the mean squared errors of the estimators of the fixed and random effects increase in size. The magnitude of this increase is investigated, and a general approximation is proposed. The performance of this approximation is investigated in the context of (a) the estimation of the effects of the balanced one-way random model and (b) the estimation of treatment contrasts for balanced incomplete block designs.