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

Frans E. S. Tan*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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.
Original languageEnglish
Pages (from-to)255-266
JournalCommunications in Statistics - Theory and Methods
Issue number2
Publication statusPublished - 2011


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


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