The Design of Experiments to Discriminate Between Two Rival Generalized Linear Models

Abstract

The design of experiments for discrimination among rival regression models, either linear or nonlinear in the parameters, depends on a variety of assumptions. The formulation should reflect the nature of the models involved, whether or not prior information is available to the experimenter, whether the method to be adopted is sequential or not, etc. For instance, Box and Hill (1967). suggested a sequential method based on the concept of entropy that assumes knowledge of prior probabilities for the truth of each model, although it makes no use of prior information about the linear predictor parameters. Another widely adopted approach is the T-optimality criterion, introduced by Atkinson {&} Fedorov (1975a) in the context of optimal design theory. More recently, Ponce de Leon {&} Atkinson (1991) extended this criterion to incorporate not only prior distributions for the truth of the models but also prior distributions for the linear predictor parameters of the models. An analogous procedure can be applied to discriminate between two binary data models (Ponce de Leon {&} Atkinson, 1992).