Bounded mixed regression models using Johnson-SB type distributions
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da USP |
Texto Completo: | https://www.teses.usp.br/teses/disponiveis/104/104131/tde-19052021-133907/ |
Resumo: | This work considers a flexible mechanism for constructing probability distributions in the (0,1) interval called GF-quantile distributions. The focus is on a new derivation of the GF-quantile distributions called the JSB class of distributions. New mixed-effects models for bounded longitudinal data in the interval (0;1) based on the JSB distributions are presented. The penalized likelihood estimators are obtained by maximizing the penalized likelihood and are computed by the Rigby and Stasinopoulos (RS) algorithm. From the Bayesian perspective, the No-UTurn- Sampler (NUTS) is used to sample from the posterior distribution. Residual analysis is performed considering randomized quantile residuals. Simulation studies considering robustness to outliers from the distributions and extensions of the models to support 0 and 1 observations are presented. Three real data sets motivate the use of the new models. The first dataset contains the proportion of individuals vulnerable to poverty of the 645 municipalities from São Paulo state in Brazil and does not contain any covariate. The second dataset incorporates the proportion of votes obtained by a political party in five Brazilian presidential elections, every four years, from 1994 to 2010, from the 75 municipalities from Sergipe state in Brazil. The third dataset comes from the public health area in Brazilian states. It contains the mortality rates from bronchial and lung cancer from the 27 Brazilian states over the last 30 years. The aim is to identify if factors like sex, age, and the Municipal Human Development Index of the state can influence the mortality rate. The JSB mixed regression models and the Beta mixed model were applied. The JSB mixed models display lower values than the Beta mixed model for the model comparison criteria. The results and the residual analysis reveal that the JSB models can be an alternative to the Beta model. |
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Bounded mixed regression models using Johnson-SB type distributionsModelos de regressão mista para resposta limitada usando distribuições do tipo Johnson-SBBayesian estimationBounded responseDados longitudinaisDistribuição Johson-SbEstimação BayesianaJohnson-Sb distributionLongitudinal dataMixed modelsModelos mistosPenalized likelihood estimationResposta limitadaVerossimilhança penalizadaThis work considers a flexible mechanism for constructing probability distributions in the (0,1) interval called GF-quantile distributions. The focus is on a new derivation of the GF-quantile distributions called the JSB class of distributions. New mixed-effects models for bounded longitudinal data in the interval (0;1) based on the JSB distributions are presented. The penalized likelihood estimators are obtained by maximizing the penalized likelihood and are computed by the Rigby and Stasinopoulos (RS) algorithm. From the Bayesian perspective, the No-UTurn- Sampler (NUTS) is used to sample from the posterior distribution. Residual analysis is performed considering randomized quantile residuals. Simulation studies considering robustness to outliers from the distributions and extensions of the models to support 0 and 1 observations are presented. Three real data sets motivate the use of the new models. The first dataset contains the proportion of individuals vulnerable to poverty of the 645 municipalities from São Paulo state in Brazil and does not contain any covariate. The second dataset incorporates the proportion of votes obtained by a political party in five Brazilian presidential elections, every four years, from 1994 to 2010, from the 75 municipalities from Sergipe state in Brazil. The third dataset comes from the public health area in Brazilian states. It contains the mortality rates from bronchial and lung cancer from the 27 Brazilian states over the last 30 years. The aim is to identify if factors like sex, age, and the Municipal Human Development Index of the state can influence the mortality rate. The JSB mixed regression models and the Beta mixed model were applied. The JSB mixed models display lower values than the Beta mixed model for the model comparison criteria. The results and the residual analysis reveal that the JSB models can be an alternative to the Beta model.Este trabalho considera um mecanismo flexível para a construção de distribuições de probabilidade no intervalo (0,1) denominado distribuições GF-quantile . O foco está em uma nova derivação das distribuições GF-quantile, chamada de classe de distribuições JSB. Novos modelos mistos para dados longitudinais limitados no intervalo (0;1) com base nas distribuições JSB são apresentados. Os estimadores de verossimilhança penalizada são obtidos maximizando a verossimilhança penalizada e calculados pelo algoritmo de Rigby e Stasinopoulos (RS). Na abordagem bayesiana, o algoritmo No-U-Turn-Sampler (NUTS) é usado para simular valores da distribuição a posterior. A análise de resíduos é realizada considerando os resíduos quantílicos. São apresentados estudos de simulação considerando a robustez a outliers das distribuições e extensões dos modelos para suportar observações 0 e 1. Três conjuntos de dados reais motivam o uso dos novos modelos. O primeiro conjunto de dados contém a proporção de indivíduos vulneráveis à pobreza dos 645 municípios do estado de São Paulo no Brasil e não contém nenhuma covariável. O segundo conjunto de dados contém a proporção de votos obtidos por um partido político em cinco eleições presidenciais brasileiras, a cada quatro anos, de 1994 a 2010, nos 75 municípios do estado de Sergipe no Brasil. O terceiro conjunto de dados é proveniente da área de saúde pública dos estados brasileiros. Ele contém as taxas de mortalidade por câncer brônquico e de pulmão nos 27 estados brasileiros nos últimos 30 anos. O objetivo é identificar se fatores como sexo, idade e Índice de Desenvolvimento Humano Municipal do estado podem influenciar na taxa de mortalidade. Os modelos de regressão misto JSB e o modelo misto Beta foram aplicados. Os modelos mistos JSB exibem valores mais baixos do que o modelo misto Beta para os critérios de comparação de modelos. Os resultados e a análise residual revelam que os modelos JSB podem ser uma alternativa ao modelo Beta.Biblioteca Digitais de Teses e Dissertações da USPGuzmán, Jorge Luis BazánPiccirilli, Giovanni Pastori2021-03-10info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfhttps://www.teses.usp.br/teses/disponiveis/104/104131/tde-19052021-133907/reponame:Biblioteca Digital de Teses e Dissertações da USPinstname:Universidade de São Paulo (USP)instacron:USPLiberar o conteúdo para acesso público.info:eu-repo/semantics/openAccesseng2021-05-19T19:44:02Zoai:teses.usp.br:tde-19052021-133907Biblioteca Digital de Teses e Dissertaçõeshttp://www.teses.usp.br/PUBhttp://www.teses.usp.br/cgi-bin/mtd2br.plvirginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.bropendoar:27212021-05-19T19:44:02Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP)false |
dc.title.none.fl_str_mv |
Bounded mixed regression models using Johnson-SB type distributions Modelos de regressão mista para resposta limitada usando distribuições do tipo Johnson-SB |
title |
Bounded mixed regression models using Johnson-SB type distributions |
spellingShingle |
Bounded mixed regression models using Johnson-SB type distributions Piccirilli, Giovanni Pastori Bayesian estimation Bounded response Dados longitudinais Distribuição Johson-Sb Estimação Bayesiana Johnson-Sb distribution Longitudinal data Mixed models Modelos mistos Penalized likelihood estimation Resposta limitada Verossimilhança penalizada |
title_short |
Bounded mixed regression models using Johnson-SB type distributions |
title_full |
Bounded mixed regression models using Johnson-SB type distributions |
title_fullStr |
Bounded mixed regression models using Johnson-SB type distributions |
title_full_unstemmed |
Bounded mixed regression models using Johnson-SB type distributions |
title_sort |
Bounded mixed regression models using Johnson-SB type distributions |
author |
Piccirilli, Giovanni Pastori |
author_facet |
Piccirilli, Giovanni Pastori |
author_role |
author |
dc.contributor.none.fl_str_mv |
Guzmán, Jorge Luis Bazán |
dc.contributor.author.fl_str_mv |
Piccirilli, Giovanni Pastori |
dc.subject.por.fl_str_mv |
Bayesian estimation Bounded response Dados longitudinais Distribuição Johson-Sb Estimação Bayesiana Johnson-Sb distribution Longitudinal data Mixed models Modelos mistos Penalized likelihood estimation Resposta limitada Verossimilhança penalizada |
topic |
Bayesian estimation Bounded response Dados longitudinais Distribuição Johson-Sb Estimação Bayesiana Johnson-Sb distribution Longitudinal data Mixed models Modelos mistos Penalized likelihood estimation Resposta limitada Verossimilhança penalizada |
description |
This work considers a flexible mechanism for constructing probability distributions in the (0,1) interval called GF-quantile distributions. The focus is on a new derivation of the GF-quantile distributions called the JSB class of distributions. New mixed-effects models for bounded longitudinal data in the interval (0;1) based on the JSB distributions are presented. The penalized likelihood estimators are obtained by maximizing the penalized likelihood and are computed by the Rigby and Stasinopoulos (RS) algorithm. From the Bayesian perspective, the No-UTurn- Sampler (NUTS) is used to sample from the posterior distribution. Residual analysis is performed considering randomized quantile residuals. Simulation studies considering robustness to outliers from the distributions and extensions of the models to support 0 and 1 observations are presented. Three real data sets motivate the use of the new models. The first dataset contains the proportion of individuals vulnerable to poverty of the 645 municipalities from São Paulo state in Brazil and does not contain any covariate. The second dataset incorporates the proportion of votes obtained by a political party in five Brazilian presidential elections, every four years, from 1994 to 2010, from the 75 municipalities from Sergipe state in Brazil. The third dataset comes from the public health area in Brazilian states. It contains the mortality rates from bronchial and lung cancer from the 27 Brazilian states over the last 30 years. The aim is to identify if factors like sex, age, and the Municipal Human Development Index of the state can influence the mortality rate. The JSB mixed regression models and the Beta mixed model were applied. The JSB mixed models display lower values than the Beta mixed model for the model comparison criteria. The results and the residual analysis reveal that the JSB models can be an alternative to the Beta model. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-03-10 |
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://www.teses.usp.br/teses/disponiveis/104/104131/tde-19052021-133907/ |
url |
https://www.teses.usp.br/teses/disponiveis/104/104131/tde-19052021-133907/ |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
|
dc.rights.driver.fl_str_mv |
Liberar o conteúdo para acesso público. info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Liberar o conteúdo para acesso público. |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.coverage.none.fl_str_mv |
|
dc.publisher.none.fl_str_mv |
Biblioteca Digitais de Teses e Dissertações da USP |
publisher.none.fl_str_mv |
Biblioteca Digitais de Teses e Dissertações da USP |
dc.source.none.fl_str_mv |
reponame:Biblioteca Digital de Teses e Dissertações da USP instname:Universidade de São Paulo (USP) instacron:USP |
instname_str |
Universidade de São Paulo (USP) |
instacron_str |
USP |
institution |
USP |
reponame_str |
Biblioteca Digital de Teses e Dissertações da USP |
collection |
Biblioteca Digital de Teses e Dissertações da USP |
repository.name.fl_str_mv |
Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP) |
repository.mail.fl_str_mv |
virginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.br |
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1809090861144735744 |