Conditions for D_A-Maximin Marginal Designs for Generalized Linear Mixed Models to be Uniform

Abstract

Optimal design theory deals with the assessment of the optimal joint distribution of all independent variables prior to data collection. In many practical situations, however, covariates are involved for which the distribution is not previously determined. The optimal design problem may then be reformulated in terms of finding the optimal marginal distribution for a specific set of variables. In general, the optimal solution may depend on the unknown (conditional) distribution of the covariates. This article discusses the D _A -maximin procedure to account for the uncertain distribution of the covariates. Sufficient conditions will be given under which the uniform design of a subset of independent discrete variables is D _A -maximin. The sufficient conditions are formulated for Generalized Linear Mixed Models with an arbitrary number of quantitative and qualitative independent variables and random effects.

Keywords:

• GLMM
• D _A -Maximin marginal design
• D _A -Optimal marginal design
• Relative efficiency
• Uniform marginal design

Mathematics Subject Classification:

• 62K05

Acknowledgment

The author thanks the two anonymous reviewers and the Associate Editor for their valuable suggestions leading to the current version of the article.