Estimation and incommutativity in mixed models

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

doi:10.1016/j.jmva.2017.07.002

Estimation and incommutativity in mixed models

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

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	58-67
Number of pages	10
Journal	Journal of Multivariate Analysis
Volume	161
DOIs	https://doi.org/10.1016/j.jmva.2017.07.002
Publication status	Published - 1 Sept 2017

Keywords

Inference
Mixed models
Variance components

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10.1016/j.jmva.2017.07.002Licence: CC BY-NC-ND

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title = "Estimation and incommutativity in mixed models",

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.",

keywords = "Inference, Mixed models, Variance components",

author = "D{\'a}rio Ferreira and Sandra Ferreira and C{\'e}lia Nunes and Miguel Fonseca and Adilson Silva and Mexia, {Jo{\~a}o T.}",

note = "sem pdf conforme despacho. Center of Mathematics and Applications, Faculty of Sciences, University of Beira Interior - PEst-OE/MAT/UI0212/2014 ; Center for Mathematics and Applications, Faculty of Science and Technology, New University of Lisbon - PEst-OE/MAT/UI0297/2011. ",

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doi = "10.1016/j.jmva.2017.07.002",

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T1 - Estimation and incommutativity in mixed models

AU - Ferreira, Dário

AU - Ferreira, Sandra

AU - Nunes, Célia

AU - Fonseca, Miguel

AU - Silva, Adilson

AU - Mexia, João T.

N1 - sem pdf conforme despacho. Center of Mathematics and Applications, Faculty of Sciences, University of Beira Interior - PEst-OE/MAT/UI0212/2014 ; Center for Mathematics and Applications, Faculty of Science and Technology, New University of Lisbon - PEst-OE/MAT/UI0297/2011.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - 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.

AB - 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.

KW - Inference

KW - Mixed models

KW - Variance components

UR - http://www.scopus.com/inward/record.url?scp=85026788479&partnerID=8YFLogxK

U2 - 10.1016/j.jmva.2017.07.002

DO - 10.1016/j.jmva.2017.07.002

M3 - Article

AN - SCOPUS:85026788479

SN - 0047-259X

VL - 161

SP - 58

EP - 67

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

ER -

Estimation and incommutativity in mixed models

Abstract

Keywords

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