Estimation and incommutativity in mixed models

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 confid...

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Bibliographic Details
Main Author: Ferreira, Dário (author)
Other Authors: Ferreira, Sandra S. (author), Nunes, Célia (author), Fonseca, Miguel (author), Silva, Adilson (author), Mexia, João T. (author)
Format: article
Language:eng
Published: 2020
Subjects:
Inference
Mixed models
Variance components
Online Access:http://hdl.handle.net/10400.6/9069
Country:Portugal
Oai:oai:ubibliorum.ubi.pt:10400.6/9069
Description
Summary: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.

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