Design selection criteria for discrimination between nested models for binomial data

The aim of an experiment is often to enable discrimination between competing forms for a response model. We consider this problem when there are two competing generalized linear models (GLMs) for a binomial response. These models are assumed to have a common link function with the linear predictor of one model nested within that of the other. We consider selection of a continuous design for use in a non-sequential strategy and investigate a new criterion, TE-optimality, based on the difference in the deviances from the two models. A comparison is made with three existing design selection criteria, namely T-, Ds- and D-optimality. Issues are raised through the study of two examples in which designs are assessed using simulation studies of the power to reject the null hypothesis of the simpler model being correct, when the data are generated from the larger model. Parameter estimation for these designs is also discussed and a simple method is investigated of combining designs to form a hybrid design to achieve both model discrimination and estimation. Such a method may offer a computational advantage over the use of a compound criterion and the similar performance of the resulting designs is illustrated in an example.