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D-optimal designs for multi-response linear mixed models

Author

Listed:
  • Xin Liu

    (Donghua University)

  • Rong-Xian Yue

    (Shanghai Normal University)

  • Weng Kee Wong

    (University of California)

Abstract

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.

Suggested Citation

  • Xin Liu & Rong-Xian Yue & Weng Kee Wong, 2019. "D-optimal designs for multi-response linear mixed models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 87-98, January.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:1:d:10.1007_s00184-018-0679-7
    DOI: 10.1007/s00184-018-0679-7
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    References listed on IDEAS

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    1. Maryna Prus & Rainer Schwabe, 2016. "Optimal designs for the prediction of individual parameters in hierarchical models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 175-191, January.
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    Cited by:

    1. Mavrogonatou, Lida & Sun, Yuxuan & Robertson, David S. & Villar, Sofía S., 2022. "A comparison of allocation strategies for optimising clinical trial designs under variance heterogeneity," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    2. Prus, Maryna, 2023. "Optimal designs for prediction of random effects in two-groups models with multivariate response," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    3. Lei He & Rong-Xian Yue, 2021. "D-optimal designs for hierarchical linear models with intraclass covariance structure," Statistical Papers, Springer, vol. 62(3), pages 1349-1361, June.
    4. Renata Eirini Tsirpitzi & Frank Miller & Carl-Fredrik Burman, 2023. "Robust optimal designs using a model misspecification term," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(7), pages 781-804, October.
    5. He, Lei & He, Daojiang, 2020. "R-optimal designs for individual prediction in random coefficient regression models," Statistics & Probability Letters, Elsevier, vol. 159(C).

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