Estimation and incommutativity in mixed models

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

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)58-67
Number of pages10
JournalJournal of Multivariate Analysis
Publication statusPublished - 1 Sept 2017


  • Inference
  • Mixed models
  • Variance components


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