Computational aspects of experimental designs in multiple-group mixed models

We extend the equivariance and invariance conditions for construction of optimal designs to multiple-group mixed models and, hence, derive the support of optimal designs for first- and second-order models on a symmetric square. Moreover, we provide a tool for computation of D- and L-efficient exact designs in multiple-group mixed models by adapting the algorithm of Harman et al. (Appl Stoch Models Bus Ind, 32:3-17, 2016). We show that this algorithm can be used both for size-constrained problems and also in settings that require multiple resource constraints on the design, such as cost constraints or marginal constraints.