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An optimal test for variance components of multivariate mixed-effects linear models

Author

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  • Aryal, Subhash
  • Bhaumik, Dulal K.
  • Mathew, Thomas
  • Gibbons, Robert D.

Abstract

In this article we derive an optimal test for testing the significance of covariance matrices of random-effects of two multivariate mixed-effects linear models. We compute the power of this newly derived test via simulation for various alternative hypotheses in a bivariate set up for unbalanced designs and observe that power responds sharply when sample size and alternative hypotheses are changed. For some balanced designs we compare power of the optimal test to that of the likelihood ratio test via simulation, and find that the proposed test has greater power than the likelihood ratio test. The results are illustrated using real data on human growth. Other relevant applications of the model are highlighted.

Suggested Citation

  • Aryal, Subhash & Bhaumik, Dulal K. & Mathew, Thomas & Gibbons, Robert D., 2014. "An optimal test for variance components of multivariate mixed-effects linear models," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 166-178.
    • Handle: RePEc:eee:jmvana:v:124:y:2014:i:c:p:166-178
    DOI: 10.1016/j.jmva.2013.10.014
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    References listed on IDEAS

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    1. Mathew, T. & Niyogi, A. & Sinha, B. K., 1994. "Improved Nonnegative Estimation of Variance Components in Balanced Multivariate Mixed Models," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 83-101, October.
    2. Franklin Satterthwaite, 1941. "Synthesis of variance," Psychometrika, Springer;The Psychometric Society, vol. 6(5), pages 309-316, October.
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