An algorithmic framework for generating optimal two-stratum experimental designs

Two-stratum experiments are widely used in case a complete randomization is not possible. In some experimental scenarios, there are constraints that limit the number of observations that can be made under homogeneous conditions. In other scenarios, there are factors whose levels are hard or expensive to change. In both of these scenarios, it is necessary to arrange the observations in different groups. Moreover, it is important that the analysis performed accounts for the variation in the response variable due to the differences between the groups. The most common strategy for the design of these kinds of experiments is to consider groups of equal size. The number of groups and the number of observations per group are usually defined by the constraints that limit the experimental scenario. We argue, however, that these constraints do not de ne the design itself, but should be considered only as upper bounds. The number of groups and the number of observations per group should be chosen not only to satisfy the experimental constraints, but also to maximize the quality of the experiment. In this paper, we propose an algorithmic framework to generate optimal designs for two-stratum experiments in which the number of groups and the number of observations per group are limited only by upper bounds. The results of an extensive set of computational simulations show that this additional exibility in the design generation process can significantly improve the quality of the experiments. Moreover, the results show that the grouping configuration of an optimal design depends on the characteristics of the two-stratum experiment, namely, the type of experiment, the model to be estimated and the optimality criterion considered. This is certainly a strong argument in favour of using algorithmic techniques that are able to identify not only the best factor-level con guration for each experimental run, but also the best grouping configuration.