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Estimation and incommutativity in mixed models

Author

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  • Ferreira, Dário
  • Ferreira, Sandra
  • Nunes, Célia
  • Fonseca, Miguel
  • Silva, Adilson
  • Mexia, João T.

Abstract

In this paper we present a treatment for the estimation of variance components and estimable vectors in linear mixed models in which the relation matrices may not commute. To overcome this difficulty, we partition the mixed model in sub-models using orthogonal matrices. In addition, we obtain confidence regions and derive tests of hypothesis for the variance components. A numerical example is included. There we illustrate the estimation of the variance components using our treatment and compare the obtained estimates with the ones obtained by the ANOVA method. Besides this, we also present the restricted and unrestricted maximum likelihood estimates.

Suggested Citation

  • Ferreira, Dário & Ferreira, Sandra & Nunes, Célia & Fonseca, Miguel & Silva, Adilson & Mexia, João T., 2017. "Estimation and incommutativity in mixed models," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 58-67.
    • Handle: RePEc:eee:jmvana:v:161:y:2017:i:c:p:58-67
    DOI: 10.1016/j.jmva.2017.07.002
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    References listed on IDEAS

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    1. J. Srivastava, 1966. "On testing hypotheses regarding a class of covariance structures," Psychometrika, Springer;The Psychometric Society, vol. 31(2), pages 147-164, June.
    2. J. Srivastava & R. Maik, 1967. "On a new property of partially balanced association schemes useful in psychometric structural analysis," Psychometrika, Springer;The Psychometric Society, vol. 32(3), pages 279-289, September.
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