, Volume 82, Issue 1, pp 87–98 | Cite as

D-optimal designs for multi-response linear mixed models

  • Xin Liu
  • Rong-Xian YueEmail author
  • Weng Kee Wong


Linear mixed models have become popular in many statistical applications during recent years. However design issues for multi-response linear mixed models are rarely discussed. The main purpose of this paper is to investigate D-optimal designs for multi-response linear mixed models. We provide two equivalence theorems to characterize the optimal designs for the estimation of the fixed effects and the prediction of random effects, respectively. Two examples of the D-optimal designs for multi-response linear mixed models are given for illustration.


D-optimal designs Multi-response Linear mixed model Equivalence theorem 



Dr. Yue and Dr. Liu were partially supported by the National Natural Science Foundation of China under Grants 11471216 and 11871143. Dr. Wong was partially supported by a Grant from the National Institute of General Medical Sciences of the National Institutes of Health under Award Number R01GM107639. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of ScienceDonghua UniversityShanghaiChina
  2. 2.Department of MathematicsShanghai Normal UniversityShanghaiChina
  3. 3.Department of BiostatisticsUniversity of CaliforniaLos AngelesUSA

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