Optimal design and refinement of the linera model with applications to repeated measurements designs

The information matrices of one design in a finer and a simpler linear model are compared to each other. The orthogonality condition ensuring that both matrices are equal is examined in the model for repeated measurements designs which was considered e.g. by Cheng and Wu (1980). Examples of unbalanced designs fulfilling the orthogonality condition are shown to be optimum. Moreover, nearly strongly balanced generalized latin squares are introduced and their universal optimality is proved, if the numbers of units and periods are sufficiently large.