Optimum experimental design for model discrimination and generalized linear models
The main subject of this thesis concerns the optimum design of experiments for discriminating between two rival mathematical models. In addition, optimality of designs for parameter estimation is investigated although restricted to binary response models. Optimal design theory and generalized linear models form the background for this work. The former provides the tools for construction of the optimum designs whereas the latter provides the framework in which the methods are developed. For model discrimination the procedures which are proposed may not only be applied to compare two regression models but also to compare two generalized linear models as long as they belong to the same subclass. The principle of the so called T-optimality criterion, originally introduced for discriminating between two regression models, is extended to other classes such as generalized linear models. Within each context a theorem based on the General Equivalence Theorem from the optimal design theory is shown to hold thus allowing both constructing and checking optimum designs. Optimum experimental designs to estimate the parameters of a binary response model is the other subject of this thesis. Initially, well known link functions such as logit, probit and complementary log-log are considered. Later, this range is widened by introducing a family of link functions which includes the logit and the complementary log-log links as particular members. One common feature of these two problems is that classical optimal designs depend on the unknown values of the model parameters. Therefore, only locally optimal designs can be obtained unless observations may be taken sequentially, in which case several methods to search for the optimum are available in the literature. As an alternative to locally and sequentially optimal experiments, Bayesian designs are introduced for both model discrimination and parameter estimation.