We construct c and D A -optimal approximate designs for linear mixed models with group-specific treatment for estimating parameters or contrasts in the population parameters. We establish equivalence theorems to confirm optimality of these designs under a linear mixed model and provide illustrative application to find D, D A and c-optimal designs for polynomial and fractional polynomial models with multitreatment group assignments. For more complex models, we briefly review metaheuristics and their potential applications to find various optimal designs, including optimal designs for problems considered here and their extensions.
K E Y W O R D Sequivalence theorem, linear mixed model, optimal design
INTRODUCTIONLinear mixed models are very flexible models and are widely used to model outcomes across a variety of practical settings in many disciplines, such as in the physical, biological, and social and behavioral sciences. Depending on the context and disciplines, they are variously called multilevel models or hierarchical models for data analysis in many practical situations, especially in experiments where repeated measurements are taken on several individuals. There is a huge