Minimax designs for 2k factorial experiments for generalized linear models

ABSTRACT

Formulas for A- and C-optimal allocations for binary factorial experiments in the context of generalized linear models are derived. Since the optimal allocations depend on GLM weights, which often are unknown, a minimax strategy is considered. This is shown to be simple to apply to factorial experiments. Efficiency is used to evaluate the resulting design. In some cases, the minimax design equals the optimal design. For other cases no general conclusion can be drawn. An example of a two-factor logit model suggests that the minimax design performs well, and often better than a uniform allocation.