OPTIMAL DESIGNS FOR GENERALIZED LINEAR MODELS WITH MULTIPLE DESIGN VARIABLES

Binary response experiments are common in scientific studies. However, the study of optimal designs in this area is in a very underdeveloped stage. Sitter and Torsney (1995a) studied optimal designs for binary response experiments with two design variables. In this paper, we consider a general situation with multiple design variables. A novel approach is proposed to identify optimal designs for the commonly used multi-factor logistic and probit models. We give explicit formulas for a large class of optimal designs, including D-, A-, and E-optimal designs. In addition, we identify the general structure of optimal designs, which has a relatively simple format. This property makes it feasible to solve seemingly intractable problems. This result can also be applied in a multi-stage approach.