Statistica Sinica 21 (2011), 1415-1430
doi:10.5705/ss.2009.115

OPTIMAL DESIGNS FOR GENERALIZED LINEAR MODELS

WITH MULTIPLE DESIGN VARIABLES

Min Yang, Bin Zhang and Shuguang Huang

University of Missouri, University of Alabama-Birmingham and

Precision Therapeutics, Inc.

Abstract: 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.

Key words and phrases: A-optimality, D-optimality, E-optimality, Loewner ordering, logistic model, probit model.