On the derivation of complex linear models from simpler ones
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/20.500.12207/5695 |
Resumo: | Linear mixed models are useful in biology, genetics, medical research, agriculture, industry, and many other fields, providing a flexible approach in situations of correlated data. Based on the structure of the variance-covariance matrix, emerged a special class of linear mixed models, those of models with orthogonal block structure, which allows optimal estimation for variance components of blocks and contrasts of treatments. This approach triggered a more restrict class of mixed models, models with commutative orthogonal block structure, whose interest lies in the possibility of achieving least squares estimators giving best linear unbiased estimators for estimable vectors. Exploring the possibility of joint analysis of linear mixed models, obtained independently, and focusing on the approach based on the algebraic structure of the models, some authors have investigated the conditions in which the good properties of the estimators are preserved. In this work we intend to highlight the ideas underlying the techniques for the joint analysis of models, since these aspects were underexplored in the works where the theoretical formulation of the techniques were introduced. Given that these techniques were developed involving models with commutative orthogonal block structure, we provide a selective review of the literature focusing on the contributions addressing this special class of mixed linear models. |
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On the derivation of complex linear models from simpler onesCommutative orthogonal block structuremodels crossingmodels nestingmodels joiningIndexação ScopusLinear mixed models are useful in biology, genetics, medical research, agriculture, industry, and many other fields, providing a flexible approach in situations of correlated data. Based on the structure of the variance-covariance matrix, emerged a special class of linear mixed models, those of models with orthogonal block structure, which allows optimal estimation for variance components of blocks and contrasts of treatments. This approach triggered a more restrict class of mixed models, models with commutative orthogonal block structure, whose interest lies in the possibility of achieving least squares estimators giving best linear unbiased estimators for estimable vectors. Exploring the possibility of joint analysis of linear mixed models, obtained independently, and focusing on the approach based on the algebraic structure of the models, some authors have investigated the conditions in which the good properties of the estimators are preserved. In this work we intend to highlight the ideas underlying the techniques for the joint analysis of models, since these aspects were underexplored in the works where the theoretical formulation of the techniques were introduced. Given that these techniques were developed involving models with commutative orthogonal block structure, we provide a selective review of the literature focusing on the contributions addressing this special class of mixed linear models.IEOM Society2023-01-04T16:24:20Z2020-08-01T00:00:00Z2020-08info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/20.500.12207/5695eng978-0-9855497-8-72169-8767Santos, CarlaDias, CristinaNunes, CéliaMexia, JoãoTiagoinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-01-05T07:45:14ZPortal AgregadorONG |
dc.title.none.fl_str_mv |
On the derivation of complex linear models from simpler ones |
title |
On the derivation of complex linear models from simpler ones |
spellingShingle |
On the derivation of complex linear models from simpler ones Santos, Carla Commutative orthogonal block structure models crossing models nesting models joining Indexação Scopus |
title_short |
On the derivation of complex linear models from simpler ones |
title_full |
On the derivation of complex linear models from simpler ones |
title_fullStr |
On the derivation of complex linear models from simpler ones |
title_full_unstemmed |
On the derivation of complex linear models from simpler ones |
title_sort |
On the derivation of complex linear models from simpler ones |
author |
Santos, Carla |
author_facet |
Santos, Carla Dias, Cristina Nunes, Célia Mexia, JoãoTiago |
author_role |
author |
author2 |
Dias, Cristina Nunes, Célia Mexia, JoãoTiago |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Santos, Carla Dias, Cristina Nunes, Célia Mexia, JoãoTiago |
dc.subject.por.fl_str_mv |
Commutative orthogonal block structure models crossing models nesting models joining Indexação Scopus |
topic |
Commutative orthogonal block structure models crossing models nesting models joining Indexação Scopus |
description |
Linear mixed models are useful in biology, genetics, medical research, agriculture, industry, and many other fields, providing a flexible approach in situations of correlated data. Based on the structure of the variance-covariance matrix, emerged a special class of linear mixed models, those of models with orthogonal block structure, which allows optimal estimation for variance components of blocks and contrasts of treatments. This approach triggered a more restrict class of mixed models, models with commutative orthogonal block structure, whose interest lies in the possibility of achieving least squares estimators giving best linear unbiased estimators for estimable vectors. Exploring the possibility of joint analysis of linear mixed models, obtained independently, and focusing on the approach based on the algebraic structure of the models, some authors have investigated the conditions in which the good properties of the estimators are preserved. In this work we intend to highlight the ideas underlying the techniques for the joint analysis of models, since these aspects were underexplored in the works where the theoretical formulation of the techniques were introduced. Given that these techniques were developed involving models with commutative orthogonal block structure, we provide a selective review of the literature focusing on the contributions addressing this special class of mixed linear models. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-08-01T00:00:00Z 2020-08 2023-01-04T16:24:20Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/20.500.12207/5695 |
url |
http://hdl.handle.net/20.500.12207/5695 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
978-0-9855497-8-7 2169-8767 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
IEOM Society |
publisher.none.fl_str_mv |
IEOM Society |
dc.source.none.fl_str_mv |
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instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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1777301721631948800 |