On locally optimal designs for generalized linear models with group effects

Generalized linear models with group effects are commonly used in scientific studies. However, there appear to be no results for selecting optimal designs. In this paper, we identify the structure of locally optimal designs, provide a general strategy to determine the design points and the corresponding weights for optimal designs, and present theoretical results for the special case of D-optimality. The results can be applied to many commonly studied models, including the logistic, probit, and loglinear models. The design region can be restricted or unrestricted, and the results can also be applied for a multi-stage approach.