D-optimal designs for hierarchical linear models with intraclass covariance structure

Intraclass correlation, used for measuring the degree of intrafamily resemblance, arises typically in psychology, education and genetics. In this paper, we extend the popular intraclass correlation model to the framework of hierarchical linear mixed models and consider D-optimal designs for the estimation of the fixed effects as well as the prediction of random effects in such settings. Moreover, characterizations of optimal designs are derived for determining the optimality of designs, and several examples are presented for illustration.