A-optimal designs for generalized linear models with two parameters

An algebraic method for constructing A-optimal designs for two parameter generalized linear models is presented. It gives sufficient conditions to identify the A-optimal design. When the conditions are satisfied, the A-optimal design has exactly two points, which are symmetric but not weight symmetric. The methodology is illustrated by means of selected examples. This result proves the conjecture of Mathew and Sinha [2001. Optimal designs for binary data under logistic regression. J. Statist. Plann. Inference 93, 295-307] for a logistic model, and shows that the conjecture is also true for probit models and some cases of double exponential and double reciprocal models. (C) 2007 Elsevier B.V. All rights reserved.