Optimal designs for the prediction of mixed effects in linear mixed models

This paper considers the optimal design problem for predicting a linear combination of fixed and random effects when the variance components in the linear mixed model are known or unknown. New design criteria based on the mean squared error of the predictor are proposed to obtain the exact or continuous optimal designs. For unknown variance components, the uncertainty of their estimators is incorporated into the design criteria. Numerical results indicate the importance of this consideration. Special attention is paid to obtaining optimal designs for predicting individual curves or future observations.