cc_byPrus, MarynaFilová, Lenka2025-12-082025-12-082023https://doi.org/10.1007/s00362-023-01416-1https://hohpublica.uni-hohenheim.de/handle/123456789/18583We 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.engOptimal designExact designRandom coefficient regressionEquivarianceInvarianceResource constraints510Article2025-12-04