A- and R-optimal Design for Hierarchical Linear Model with Two-Group Assignments

This paper discusses the optimal design problem for the hierarchical linear model with twogroup assignments. A-optimal and R-optimal designs are considered for the estimation of the fixed effects. We establish two equivalence theorems to determine the A-optimality and R-optimality of a given design, respectively, and provide an illustrative example to find A- and R-optimal designs for the straight line model with random intercept.