Optimal designs for multi-group linear mixed models with intraclass covariance structure

The use of intraclass correlation to determine the strength of intrafamily resemblance is a typical practice in disciplines like psychology, epidemiology and genetics. In this paper we generalize the commonly used intraclass correlation models to the context of linear mixed models with multiple groups and investigate the $$\phi _k$$ -optimal design problem for such models. To be precise, we establish equivalence conditions to verify the optimality of a given design and provide various applications to exemplify the derived theoretical findings.