Bivariate beta regression models: a Bayesian approach applied to educational data

In this paper we propose a bivariate beta regression model, de¯ning the beta distribution derived from Farlie-Gumbel-Morgenstern (FGM) copulas. This model could be a good alternative to analyze pairs of proportions, when they are not independent. To ¯t the proposed models we apply standard existing...

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Autores:
Cepeda Cuervo, Edilberto
Achcar, Jorge Alberto
Garrido Lopera, B. Liliana
Tipo de recurso:
Work document
Fecha de publicación:
2019
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
eng
OAI Identifier:
oai:repositorio.unal.edu.co:unal/9058
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/9058
http://bdigital.unal.edu.co/5851/
Palabra clave:
31 Colecciones de estadística general / Statistics
51 Matemáticas / Mathematics
Beta distribution
Beta regression models
bivariate random variables
MCMC methods
Bayesian methodology
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
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oai_identifier_str oai:repositorio.unal.edu.co:unal/9058
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Cepeda Cuervo, Edilberto8f2ae6e2-1778-4f83-a496-0d49efcbe66a300Achcar, Jorge Alberto99c161ab-6e01-4ba5-bf64-a6528c49b480300Garrido Lopera, B. Liliana900089f7-8bc5-43d2-9689-fe73999255bc3002019-06-24T17:52:45Z2019-06-24T17:52:45Zhttps://repositorio.unal.edu.co/handle/unal/9058http://bdigital.unal.edu.co/5851/In this paper we propose a bivariate beta regression model, de¯ning the beta distribution derived from Farlie-Gumbel-Morgenstern (FGM) copulas. This model could be a good alternative to analyze pairs of proportions, when they are not independent. To ¯t the proposed models we apply standard existing MCMC (Markov Chain Monte Carlo) methods to simulate samples for the joint posterior of interest, using the Bayesian methodology proposed by Cepeda and Gamerman (2001) and Cepeda and Gamerman (2005). Two examples are introduced to illustrate the proposed methodology: an example with simulated bivariate data and an example with a real data set.application/pdfengUniversidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de EstadísticaDepartamento de EstadísticaCepeda Cuervo, Edilberto and Achcar, Jorge Alberto and Garrido Lopera, B. Liliana Bivariate beta regression models: a Bayesian approach applied to educational data. Reporte técnico. Sin Definir. (No publicado)31 Colecciones de estadística general / Statistics51 Matemáticas / MathematicsBeta distributionBeta regression modelsbivariate random variablesMCMC methodsBayesian methodologyBivariate beta regression models: a Bayesian approach applied to educational dataDocumento de trabajoinfo:eu-repo/semantics/workingPaperinfo:eu-repo/semantics/drafthttp://purl.org/coar/resource_type/c_8042http://purl.org/coar/version/c_b1a7d7d4d402bcceTexthttp://purl.org/redcol/resource_type/WPORIGINALedilbertocepedacuervo.2012.pdfapplication/pdf217643https://repositorio.unal.edu.co/bitstream/unal/9058/1/edilbertocepedacuervo.2012.pdfc698f8bdbb56a237b6e193c3ef299c1dMD51THUMBNAILedilbertocepedacuervo.2012.pdf.jpgedilbertocepedacuervo.2012.pdf.jpgGenerated Thumbnailimage/jpeg3627https://repositorio.unal.edu.co/bitstream/unal/9058/2/edilbertocepedacuervo.2012.pdf.jpg35b4183fab9d576b7380e2ddde3f4404MD52unal/9058oai:repositorio.unal.edu.co:unal/90582023-09-04 23:09:51.297Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Bivariate beta regression models: a Bayesian approach applied to educational data
title Bivariate beta regression models: a Bayesian approach applied to educational data
spellingShingle Bivariate beta regression models: a Bayesian approach applied to educational data
31 Colecciones de estadística general / Statistics
51 Matemáticas / Mathematics
Beta distribution
Beta regression models
bivariate random variables
MCMC methods
Bayesian methodology
title_short Bivariate beta regression models: a Bayesian approach applied to educational data
title_full Bivariate beta regression models: a Bayesian approach applied to educational data
title_fullStr Bivariate beta regression models: a Bayesian approach applied to educational data
title_full_unstemmed Bivariate beta regression models: a Bayesian approach applied to educational data
title_sort Bivariate beta regression models: a Bayesian approach applied to educational data
dc.creator.fl_str_mv Cepeda Cuervo, Edilberto
Achcar, Jorge Alberto
Garrido Lopera, B. Liliana
dc.contributor.author.spa.fl_str_mv Cepeda Cuervo, Edilberto
Achcar, Jorge Alberto
Garrido Lopera, B. Liliana
dc.subject.ddc.spa.fl_str_mv 31 Colecciones de estadística general / Statistics
51 Matemáticas / Mathematics
topic 31 Colecciones de estadística general / Statistics
51 Matemáticas / Mathematics
Beta distribution
Beta regression models
bivariate random variables
MCMC methods
Bayesian methodology
dc.subject.proposal.spa.fl_str_mv Beta distribution
Beta regression models
bivariate random variables
MCMC methods
Bayesian methodology
description In this paper we propose a bivariate beta regression model, de¯ning the beta distribution derived from Farlie-Gumbel-Morgenstern (FGM) copulas. This model could be a good alternative to analyze pairs of proportions, when they are not independent. To ¯t the proposed models we apply standard existing MCMC (Markov Chain Monte Carlo) methods to simulate samples for the joint posterior of interest, using the Bayesian methodology proposed by Cepeda and Gamerman (2001) and Cepeda and Gamerman (2005). Two examples are introduced to illustrate the proposed methodology: an example with simulated bivariate data and an example with a real data set.
publishDate 2019
dc.date.accessioned.spa.fl_str_mv 2019-06-24T17:52:45Z
dc.date.available.spa.fl_str_mv 2019-06-24T17:52:45Z
dc.type.spa.fl_str_mv Documento de trabajo
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/workingPaper
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/draft
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_8042
dc.type.coarversion.spa.fl_str_mv http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.content.spa.fl_str_mv Text
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format http://purl.org/coar/resource_type/c_8042
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dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/9058
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/5851/
url https://repositorio.unal.edu.co/handle/unal/9058
http://bdigital.unal.edu.co/5851/
dc.language.iso.eng.fl_str_mv eng
language eng
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de Estadística
Departamento de Estadística
dc.relation.references.spa.fl_str_mv Cepeda Cuervo, Edilberto and Achcar, Jorge Alberto and Garrido Lopera, B. Liliana Bivariate beta regression models: a Bayesian approach applied to educational data. Reporte técnico. Sin Definir. (No publicado)
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/9058/1/edilbertocepedacuervo.2012.pdf
https://repositorio.unal.edu.co/bitstream/unal/9058/2/edilbertocepedacuervo.2012.pdf.jpg
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repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
repository.mail.fl_str_mv repositorio_nal@unal.edu.co
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