Two-stage designs robust to model uncertainty

D-optimal designs are known to depend quite critically on the particular model that is assumed. These designs tend to concentrate all the experimental runs on a small number of design points and are ideally suited for estimating the coefficients of the assumed model, but they provide little or no ability for model checking. To address this problem we use the notion of empirical models that have both important and potential terms. We propose within the Bayesian paradigm, a two-stage design strategy for planning experiments in the face of model uncertainty. In the first stage, the experimenter's prime interest is to highlight the uncertainties in the specification of the model in order to refine or modify the model(s) initially entertained. A design criterion is used that accounts for precision of the important terms but also facilitates the improvement of the proposed model(s) by detecting lack of fit. Data from the first stage provide model information enabling the second stage design to be chosen efficiently with reduced model uncertainty. The design in the second stage is obtained using a weighted criterion with weights being posterior model probabilities computed from first stage data. The criterion in the second stage also takes into account precise estimation of important terms as in the first stage but now attempts to minimize bias with respect to potential terms. Results from simulations show that the proposed two-stage strategy performs well. The combined first and second stage design has good properties with respect to precision of important terms, lack of fit and also excellent bias properties with respect to a true assumed model in various simulation studies.status: publishe