Multiple factor analysis model with scale mixture of normal distributions in the latent factors
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFPE |
Texto Completo: | https://repositorio.ufpe.br/handle/123456789/32306 |
Resumo: | Statistical tools for modeling covariance structures have been shown useful in Medicine for studies in genetics. In that context, factor analysis models stand out for its ability in identifying latent factors capable of reducing data dimensionality and explaining observed variability. Usually, latent factors are interpreted as unobserved physiological mechanisms underlying the studied phenomenon. Confirmatory factor analysis models are characterized by allowing the researcher to pre-specify model’s elements, as for example, the number of latent factors, the loading matrix structure and linear restrictions on the parameters. Those models allow the validation of hypothesis in gene co-expression studies. Confirmatory factor analysis models under normality assumption for the data are well consolidated in the literature. Our aim is to develop a more general class capable of integrate several independent populations extending the data’s normality assumption to a more flexible class of distributions, the class of scale mixture of normal (SMN). The class of scale mixture of normal includes, as special cases, the normal distribution and distributions with heavy tails as the t-Student, contaminated normal ans slash. This model allows to specify parameter restrictions, which leads to important particular cases of covariance structures, making it more flexible in its specification and distributional assumptions. Model identifiability is studied, with necessary and/or sufficient conditions for parameter identification being presented. To estimate the model’s parameters we propose an ECM algorithm and the estimators’ performance in finite samples is evaluated through Monte Carlo simulation studies. We conclude the study with an illustration considering a confirmatory model for the pathological dynamic of pancreas cancer based on actual gene expression data. |
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MARQUES, Alexandre Henrique Carvalhohttp://lattes.cnpq.br/3091837880986468http://lattes.cnpq.br/6628260142102150GARAY, Aldo William MedinaCYSNEIROS, Francisco José de Azevedo2019-09-05T22:22:13Z2019-09-05T22:22:13Z2018-07-27https://repositorio.ufpe.br/handle/123456789/32306Statistical tools for modeling covariance structures have been shown useful in Medicine for studies in genetics. In that context, factor analysis models stand out for its ability in identifying latent factors capable of reducing data dimensionality and explaining observed variability. Usually, latent factors are interpreted as unobserved physiological mechanisms underlying the studied phenomenon. Confirmatory factor analysis models are characterized by allowing the researcher to pre-specify model’s elements, as for example, the number of latent factors, the loading matrix structure and linear restrictions on the parameters. Those models allow the validation of hypothesis in gene co-expression studies. Confirmatory factor analysis models under normality assumption for the data are well consolidated in the literature. Our aim is to develop a more general class capable of integrate several independent populations extending the data’s normality assumption to a more flexible class of distributions, the class of scale mixture of normal (SMN). The class of scale mixture of normal includes, as special cases, the normal distribution and distributions with heavy tails as the t-Student, contaminated normal ans slash. This model allows to specify parameter restrictions, which leads to important particular cases of covariance structures, making it more flexible in its specification and distributional assumptions. Model identifiability is studied, with necessary and/or sufficient conditions for parameter identification being presented. To estimate the model’s parameters we propose an ECM algorithm and the estimators’ performance in finite samples is evaluated through Monte Carlo simulation studies. We conclude the study with an illustration considering a confirmatory model for the pathological dynamic of pancreas cancer based on actual gene expression data.CAPESFerramentas estatísticas voltadas para a modelagem de estruturas de covariâncias têm se mostrado úteis em medicina para estudos genéticos. Nesse contexto, modelos de análise fatorial destacam-se por sua habilidade em identificar fatores latentes capazes de reduzir a dimensionalidade dos dados e explicar a variabilidade observada. Comumente, fatores latentes são interpretados como mecanismos fisiológicos não observáveis subjacentes ao fenômeno estudado. Modelos de análise fatorial confirmatória caracterizam-se por possibilitar ao pesquisador a pré-especificação de elementos do modelo, como por exemplo, o número de fatores latentes, a estrutura da matriz de loadings e restrições lineares nos parâmetros. Tais modelos permitem a validação de hipotéses em estudos de coexpressão gênica. Modelos de análise fatorial confirmatório sob suposição de normalidade de dados estão bem consolidados na literatura. Nosso objetivo é desenvolver uma classe mais geral capaz de integrar várias populações independentes estendendo a suposição de normalidade de dados para uma classe mais flexível de distribuições, a classe de misturas de escala da distribuição normal (SMN). A classe SMN contém, como casos especiais, a distribuição normal e distribuições com caudas pesadas tais como t-Student, normal contaminada e slash. Este modelo permite especificar restrições nos parâmetros, as quais levam a importantes casos particulares de estruturas de covariância, tornando-o mais flexível em sua especificação e em suas suposições distribucionais. A identificabilidade do modelo é estudada e condições necessárias e/ou suficientes para identificação dos parâmetros são apresentadas. Para a estimação dos parâmetros do modelo propomos um algoritmo ECM e a performance dos estimadores em amostras finitas é avaliada através de estudos de simulação de Monte Carlo. Finalizamos nosso estudo com uma ilustração considerando o modelo confirmatório para a dinâmica patológica do câncer de pâncreas utilizando dados reais de expressão gênica.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em EstatisticaUFPEBrasilAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessEstatísticaAnálise fatorialMultiple factor analysis model with scale mixture of normal distributions in the latent factorsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesismestradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPETHUMBNAILDISSERTAÇÃO Alexandre Henrique Carvalho Marques.pdf.jpgDISSERTAÇÃO Alexandre Henrique Carvalho Marques.pdf.jpgGenerated Thumbnailimage/jpeg1298https://repositorio.ufpe.br/bitstream/123456789/32306/5/DISSERTA%c3%87%c3%83O%20Alexandre%20Henrique%20Carvalho%20Marques.pdf.jpgddf8c7f39d4e2a359882cf871e3258d9MD55ORIGINALDISSERTAÇÃO Alexandre Henrique Carvalho Marques.pdfDISSERTAÇÃO Alexandre Henrique Carvalho Marques.pdfapplication/pdf873296https://repositorio.ufpe.br/bitstream/123456789/32306/1/DISSERTA%c3%87%c3%83O%20Alexandre%20Henrique%20Carvalho%20Marques.pdff1e3cc3596048871a1a0332868e86cd6MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.pt_BR.fl_str_mv |
Multiple factor analysis model with scale mixture of normal distributions in the latent factors |
title |
Multiple factor analysis model with scale mixture of normal distributions in the latent factors |
spellingShingle |
Multiple factor analysis model with scale mixture of normal distributions in the latent factors MARQUES, Alexandre Henrique Carvalho Estatística Análise fatorial |
title_short |
Multiple factor analysis model with scale mixture of normal distributions in the latent factors |
title_full |
Multiple factor analysis model with scale mixture of normal distributions in the latent factors |
title_fullStr |
Multiple factor analysis model with scale mixture of normal distributions in the latent factors |
title_full_unstemmed |
Multiple factor analysis model with scale mixture of normal distributions in the latent factors |
title_sort |
Multiple factor analysis model with scale mixture of normal distributions in the latent factors |
author |
MARQUES, Alexandre Henrique Carvalho |
author_facet |
MARQUES, Alexandre Henrique Carvalho |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/3091837880986468 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/6628260142102150 |
dc.contributor.author.fl_str_mv |
MARQUES, Alexandre Henrique Carvalho |
dc.contributor.advisor1.fl_str_mv |
GARAY, Aldo William Medina |
dc.contributor.advisor-co1.fl_str_mv |
CYSNEIROS, Francisco José de Azevedo |
contributor_str_mv |
GARAY, Aldo William Medina CYSNEIROS, Francisco José de Azevedo |
dc.subject.por.fl_str_mv |
Estatística Análise fatorial |
topic |
Estatística Análise fatorial |
description |
Statistical tools for modeling covariance structures have been shown useful in Medicine for studies in genetics. In that context, factor analysis models stand out for its ability in identifying latent factors capable of reducing data dimensionality and explaining observed variability. Usually, latent factors are interpreted as unobserved physiological mechanisms underlying the studied phenomenon. Confirmatory factor analysis models are characterized by allowing the researcher to pre-specify model’s elements, as for example, the number of latent factors, the loading matrix structure and linear restrictions on the parameters. Those models allow the validation of hypothesis in gene co-expression studies. Confirmatory factor analysis models under normality assumption for the data are well consolidated in the literature. Our aim is to develop a more general class capable of integrate several independent populations extending the data’s normality assumption to a more flexible class of distributions, the class of scale mixture of normal (SMN). The class of scale mixture of normal includes, as special cases, the normal distribution and distributions with heavy tails as the t-Student, contaminated normal ans slash. This model allows to specify parameter restrictions, which leads to important particular cases of covariance structures, making it more flexible in its specification and distributional assumptions. Model identifiability is studied, with necessary and/or sufficient conditions for parameter identification being presented. To estimate the model’s parameters we propose an ECM algorithm and the estimators’ performance in finite samples is evaluated through Monte Carlo simulation studies. We conclude the study with an illustration considering a confirmatory model for the pathological dynamic of pancreas cancer based on actual gene expression data. |
publishDate |
2018 |
dc.date.issued.fl_str_mv |
2018-07-27 |
dc.date.accessioned.fl_str_mv |
2019-09-05T22:22:13Z |
dc.date.available.fl_str_mv |
2019-09-05T22:22:13Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufpe.br/handle/123456789/32306 |
url |
https://repositorio.ufpe.br/handle/123456789/32306 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
dc.publisher.program.fl_str_mv |
Programa de Pos Graduacao em Estatistica |
dc.publisher.initials.fl_str_mv |
UFPE |
dc.publisher.country.fl_str_mv |
Brasil |
publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
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reponame:Repositório Institucional da UFPE instname:Universidade Federal de Pernambuco (UFPE) instacron:UFPE |
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UFPE |
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UFPE |
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Repositório Institucional da UFPE |
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Repositório Institucional da UFPE |
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