Model-robust and model-sensitive designs.pdf

Model-robust and model-sensitive designs Peter Goos Katholieke Universiteit Leuven Andr´e Kobilinsky Institut National de la Recherche Agronomique France Timothy E. O’Brien Loyola University Chicago Martina Vandebroek Katholieke Universiteit Leuven Abstract The main drawback of the optimal design approach is that it assumes the statistical model is known. In this paper, a new approach to reduce the dependency on the assumed model is proposed. The approach takes into account the model uncertainty by incorporating the bias in the design criterion and the ability to test for lack-of-fit. Several new designs are derived in the paper and they are compared to the alternatives available from the literature. Keywords: precision, bias, lack-of-fit, model-robustness, model-sensitive, model-discrimination, D-optimality, A-optimality 1 Introduction The assumption that underlies most research work in optimal experimental design is that the proposed model adequately describes the response of interest. It is unlikely however that the experimenter is completely certain that any model will be correct and this should be reflected 1 in the experimental design. Instead of searching for the optimal design to estimate the stated model several approaches have been proposed to account for model uncertainty, ranging from model-robust to model-sensitive strategies. For a nice overview, see for example Steinberg and Hunter (1984). In a