Robust Designs for Generalized Linear Mixed Models

• Activity Number: 51
• Type: Contributed
• Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
• Sponsor: Biometrics Section*
• Author(s): Martijn Berger*+
• Affiliation(s): University of Maastricht
• Keywords: Maximin ; D-optimality ; Optimal Design ; Random Effects ; Relative Efficiency

Abstract

It is well-known that an optimal design for one model may not be optimal for other models. It is therefore quite difficult for applied researchers to choose an optimal design, when the best fitting model is not exactly known in advance. This problem will be handled in the present paper by proposing robust designs, which are highly efficient for a set of alternative models. The problem of finding D-optimal designs for Generalized Linear Mixed Models (GLMM) is hampered by local optimality, i.e. by their dependence on the actual combinations of parameter values. In this paper a maximum strategy is proposed which not only deals with local optimality, but also leads to robust designs which have a high relative efficiency under alternative models. The results are obtained by numerical computation and consist of robust designs for first, second and third degree polynomial mixed effects models, with random intercepts and slopes. It is shown that the relative efficiency of these designs is higher than 0.8, meaning that only 20% more data are needed to obtain the same efficiency as that of the optimal design.