Support Points of Locally Optimal Designs for Multinomial Logistic Regression Models

While multinomial logistic models have been widely applied in practice, the research on design selection has not kept pace. The complication in studying optimal/efficient designs for multinomial logistic models is the complicated structure of information matrices due to the model complexity and existence of many variants. A critical step in deriving optimal/efficient designs is to determine the number of support points needed. In this paper, we systematically characterize the optimal designs through the complete class framework. The results hold for any optimal designs, regardless of optimality criterion chosen, parameters of interest, one-stage or multi-stage designs. It provides insight in the structure of optimal designs for multinomial logistic models from theoretical perspective and makes the follow-up derivation much easier.