A new class of discrete models for the analysis of zero-modified count data
Autor(a) principal: | |
---|---|
Data de Publicação: | 2020 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/13249 |
Resumo: | In this work, a new class of discrete models for the analysis of zero-modified count data has been introduced. The proposed class is composed of hurdle versions of the Poisson-Lindley, Poisson-Shanker, and Poisson-Sujatha baseline distributions, which are uniparametric Poisson mixtures that can accommodate different levels of overdispersion. Unlike the traditional formulation of zero-modified distributions, the primary assumption under hurdle models is that the positive observations are entirely represented by zero-truncated distributions. In the sense of extending the applicability of the theoretical models, it has also been developed a fixed-effects regression framework, in which the probability of zero-valued observations being generated as well as the average number of positive observations per individual could be modeled in the presence of covariates. Besides, an even more flexible structure allowing the inclusion of both fixed and random-effects in the linear predictors of the hurdle models has also been developed. In the derived mixed-effects structure, it has been considered the use of scalar random-effects to quantify the within-subjects heterogeneity arising from clustering or repeated measurements. In this work, all inferential procedures were conducted under a fully Bayesian perspective. Different prior distributions have been considered (e.g., Jeffreys' and g-prior), and the task of generating pseudo-random values from a posterior distribution without closed-form has been performed by one out of the three following algorithms (depending on the structure of each model): Rejection Sampling, Random-walk Metropolis, and Adaptive Metropolis. Intensive Monte Carlo simulation studies were performed in order to evaluate the performance of the adopted Bayesian methodologies. The usefulness of the proposed zero-modified models was illustrated by using several real datasets presenting different structures and sources of variation. Beyond parameter estimation, it has been performed sensitivity analyses to identify influent points, and, in order to evaluate the fitted models, it has been computed the Bayesian p-values, the randomized quantile residuals, among other measures. Finally, when compared with well-established distributions for the analysis of count data, the competitiveness of the proposed models has been proved in all provided examples. |
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Silva, Wesley Bertoli daLouzada Neto, Franciscohttp://lattes.cnpq.br/0994050156415890http://lattes.cnpq.br/7852733762870256acaba91b-03a5-4cc9-b90b-984065e77ee12020-09-18T10:15:24Z2020-09-18T10:15:24Z2020-04-03SILVA, Wesley Bertoli da. A new class of discrete models for the analysis of zero-modified count data. 2020. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2020. Disponível em: https://repositorio.ufscar.br/handle/ufscar/13249.https://repositorio.ufscar.br/handle/ufscar/13249In this work, a new class of discrete models for the analysis of zero-modified count data has been introduced. The proposed class is composed of hurdle versions of the Poisson-Lindley, Poisson-Shanker, and Poisson-Sujatha baseline distributions, which are uniparametric Poisson mixtures that can accommodate different levels of overdispersion. Unlike the traditional formulation of zero-modified distributions, the primary assumption under hurdle models is that the positive observations are entirely represented by zero-truncated distributions. In the sense of extending the applicability of the theoretical models, it has also been developed a fixed-effects regression framework, in which the probability of zero-valued observations being generated as well as the average number of positive observations per individual could be modeled in the presence of covariates. Besides, an even more flexible structure allowing the inclusion of both fixed and random-effects in the linear predictors of the hurdle models has also been developed. In the derived mixed-effects structure, it has been considered the use of scalar random-effects to quantify the within-subjects heterogeneity arising from clustering or repeated measurements. In this work, all inferential procedures were conducted under a fully Bayesian perspective. Different prior distributions have been considered (e.g., Jeffreys' and g-prior), and the task of generating pseudo-random values from a posterior distribution without closed-form has been performed by one out of the three following algorithms (depending on the structure of each model): Rejection Sampling, Random-walk Metropolis, and Adaptive Metropolis. Intensive Monte Carlo simulation studies were performed in order to evaluate the performance of the adopted Bayesian methodologies. The usefulness of the proposed zero-modified models was illustrated by using several real datasets presenting different structures and sources of variation. Beyond parameter estimation, it has been performed sensitivity analyses to identify influent points, and, in order to evaluate the fitted models, it has been computed the Bayesian p-values, the randomized quantile residuals, among other measures. Finally, when compared with well-established distributions for the analysis of count data, the competitiveness of the proposed models has been proved in all provided examples.Neste trabalho, uma nova classe de modelos discretos para a análise de contagens zero modificados foi introduzida. A classe proposta é composta pelas versões hurdle das distribuições de Poisson-Lindley, Poisson-Shanker e Poisson-Sujatha, que são misturas uniparamétricas de Poisson, capazes de acomodar diferentes níveis de sobredispersão. Diferentemente da formulação tradicional das distribuições zero modificadas, a principal suposição acerca de um modelo hurdle é que as observações positivas são inteiramente representadas por distribuições zero-truncadas. No sentido de estender a aplicabilidade dos modelos teóricos, também foi desenvolvida uma estrutura de regressão com efeitos fixos, na qual tanto a probabilidade de se observar o valor zero, quanto o número médio de observações positivas por indivíduo, puderam ser modelados na presença de covariáveis. Além disso, também foi desenvolvida uma estrutura ainda mais flexível, permitindo a inclusão simultânea de efeitos fixos e aleatórios nos preditores lineares do modelo hurdle. Na estrutura de efeitos mistos derivada, considerou-se o uso de efeitos aleatórios escalares para quantificar a heterogeneidade entre as observações de um mesmo indivíduo, que decorre de agrupamentos ou medidas repetidas. Neste trabalho, todos os procedimentos inferenciais foram conduzidos sob uma perspectiva totalmente Bayesiana. Diferentes distribuições a priori foram consideradas (por exemplo, Jeffreys' e g-prior), e a tarefa de gerar valores pseudo- aleatórios de uma distribuição a posteriori sem forma fechada foi realizada por um dos três algoritmos a seguir (dependendo da estrutura de cada modelo): Amostragem por Rejeição, Random-walk Metropolis, e Metropolis Adaptativo. Estudos intensivos de simulação de Monte Carlo foram realizados como forma de avaliar o desempenho das metodologias Bayesianas adotadas. A utilidade dos modelos zero modificados propostos foi ilustrada usando vários conjuntos de dados reais que apresentavam diferentes estruturas e fontes de variação. Além de estimar os parâmetros, foram realizadas análises de sensibilidade para identificar pontos influentes e, para avaliar os modelos ajustados, foram computados os p-valores Bayesianos, os resíduos quantílicos aleatorizados, entre outras medidas. Por fim, quando comparados com distribuições bem estabelecidas que são úteis para a análise de dados de contagem, a competitividade dos modelos propostos foi comprovada em todos os exemplos fornecidos.Fundação Araucária de Apoio ao Desenvolvimento Científico e Tecnológico do Paraná (FAADCT/PR)FAADCT/PR: CP 18/2015engUniversidade Federal de São CarlosCâmpus São CarlosPrograma Interinstitucional de Pós-Graduação em Estatística - PIPGEsUFSCarAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessBayesian MethodsMixed-effects Hurdle ModelsOverdispersionPoisson Mixture DistributionsZero-modified DataDados Zero ModificadosDistribuições de Mistura de PoissonMétodos BayesianosModelo Hurdle com Efeitos MistosSobredispersãoCIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICACIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA PARAMETRICACIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::REGRESSAO E CORRELACAOA new class of discrete models for the analysis of zero-modified count dataUma nova classe de modelos discretos para a análise de dados de contagem zero-modificadosinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis600d0f3b31a-38c4-4c28-aa5b-837ad377108ereponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALtese_wesley_final.pdftese_wesley_final.pdfTese de Doutoradoapplication/pdf7548868https://repositorio.ufscar.br/bitstream/ufscar/13249/1/tese_wesley_final.pdfa39149fc7cee9cd90aa8bc6b10c88d7eMD51cartacomprovantepipges.pdfcartacomprovantepipges.pdfCarta Comprovante (Orientador)application/pdf131060https://repositorio.ufscar.br/bitstream/ufscar/13249/3/cartacomprovantepipges.pdfca4164e0165a568f5376914b420795c2MD53CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufscar.br/bitstream/ufscar/13249/4/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD54TEXTtese_wesley_final.pdf.txttese_wesley_final.pdf.txtExtracted texttext/plain610367https://repositorio.ufscar.br/bitstream/ufscar/13249/5/tese_wesley_final.pdf.txt0e1bafcb8b11e09f62f2ac49ab5cdae7MD55cartacomprovantepipges.pdf.txtcartacomprovantepipges.pdf.txtExtracted texttext/plain1194https://repositorio.ufscar.br/bitstream/ufscar/13249/7/cartacomprovantepipges.pdf.txt1b3a282e5410d9cfdae105c40cc303c3MD57THUMBNAILtese_wesley_final.pdf.jpgtese_wesley_final.pdf.jpgIM Thumbnailimage/jpeg7415https://repositorio.ufscar.br/bitstream/ufscar/13249/6/tese_wesley_final.pdf.jpg4ea9abf77baf6ace9c7e8f5fcf091be3MD56cartacomprovantepipges.pdf.jpgcartacomprovantepipges.pdf.jpgIM Thumbnailimage/jpeg7669https://repositorio.ufscar.br/bitstream/ufscar/13249/8/cartacomprovantepipges.pdf.jpgadaee24a71a839429244e76484edf6cfMD58ufscar/132492023-09-18 18:32:00.725oai:repositorio.ufscar.br:ufscar/13249Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:32Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.eng.fl_str_mv |
A new class of discrete models for the analysis of zero-modified count data |
dc.title.alternative.por.fl_str_mv |
Uma nova classe de modelos discretos para a análise de dados de contagem zero-modificados |
title |
A new class of discrete models for the analysis of zero-modified count data |
spellingShingle |
A new class of discrete models for the analysis of zero-modified count data Silva, Wesley Bertoli da Bayesian Methods Mixed-effects Hurdle Models Overdispersion Poisson Mixture Distributions Zero-modified Data Dados Zero Modificados Distribuições de Mistura de Poisson Métodos Bayesianos Modelo Hurdle com Efeitos Mistos Sobredispersão CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA PARAMETRICA CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::REGRESSAO E CORRELACAO |
title_short |
A new class of discrete models for the analysis of zero-modified count data |
title_full |
A new class of discrete models for the analysis of zero-modified count data |
title_fullStr |
A new class of discrete models for the analysis of zero-modified count data |
title_full_unstemmed |
A new class of discrete models for the analysis of zero-modified count data |
title_sort |
A new class of discrete models for the analysis of zero-modified count data |
author |
Silva, Wesley Bertoli da |
author_facet |
Silva, Wesley Bertoli da |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/7852733762870256 |
dc.contributor.author.fl_str_mv |
Silva, Wesley Bertoli da |
dc.contributor.advisor1.fl_str_mv |
Louzada Neto, Francisco |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/0994050156415890 |
dc.contributor.authorID.fl_str_mv |
acaba91b-03a5-4cc9-b90b-984065e77ee1 |
contributor_str_mv |
Louzada Neto, Francisco |
dc.subject.eng.fl_str_mv |
Bayesian Methods Mixed-effects Hurdle Models Overdispersion Poisson Mixture Distributions Zero-modified Data |
topic |
Bayesian Methods Mixed-effects Hurdle Models Overdispersion Poisson Mixture Distributions Zero-modified Data Dados Zero Modificados Distribuições de Mistura de Poisson Métodos Bayesianos Modelo Hurdle com Efeitos Mistos Sobredispersão CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA PARAMETRICA CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::REGRESSAO E CORRELACAO |
dc.subject.Por.fl_str_mv |
Dados Zero Modificados |
dc.subject.por.fl_str_mv |
Distribuições de Mistura de Poisson Métodos Bayesianos Modelo Hurdle com Efeitos Mistos Sobredispersão |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA PARAMETRICA CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::REGRESSAO E CORRELACAO |
description |
In this work, a new class of discrete models for the analysis of zero-modified count data has been introduced. The proposed class is composed of hurdle versions of the Poisson-Lindley, Poisson-Shanker, and Poisson-Sujatha baseline distributions, which are uniparametric Poisson mixtures that can accommodate different levels of overdispersion. Unlike the traditional formulation of zero-modified distributions, the primary assumption under hurdle models is that the positive observations are entirely represented by zero-truncated distributions. In the sense of extending the applicability of the theoretical models, it has also been developed a fixed-effects regression framework, in which the probability of zero-valued observations being generated as well as the average number of positive observations per individual could be modeled in the presence of covariates. Besides, an even more flexible structure allowing the inclusion of both fixed and random-effects in the linear predictors of the hurdle models has also been developed. In the derived mixed-effects structure, it has been considered the use of scalar random-effects to quantify the within-subjects heterogeneity arising from clustering or repeated measurements. In this work, all inferential procedures were conducted under a fully Bayesian perspective. Different prior distributions have been considered (e.g., Jeffreys' and g-prior), and the task of generating pseudo-random values from a posterior distribution without closed-form has been performed by one out of the three following algorithms (depending on the structure of each model): Rejection Sampling, Random-walk Metropolis, and Adaptive Metropolis. Intensive Monte Carlo simulation studies were performed in order to evaluate the performance of the adopted Bayesian methodologies. The usefulness of the proposed zero-modified models was illustrated by using several real datasets presenting different structures and sources of variation. Beyond parameter estimation, it has been performed sensitivity analyses to identify influent points, and, in order to evaluate the fitted models, it has been computed the Bayesian p-values, the randomized quantile residuals, among other measures. Finally, when compared with well-established distributions for the analysis of count data, the competitiveness of the proposed models has been proved in all provided examples. |
publishDate |
2020 |
dc.date.accessioned.fl_str_mv |
2020-09-18T10:15:24Z |
dc.date.available.fl_str_mv |
2020-09-18T10:15:24Z |
dc.date.issued.fl_str_mv |
2020-04-03 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
SILVA, Wesley Bertoli da. A new class of discrete models for the analysis of zero-modified count data. 2020. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2020. Disponível em: https://repositorio.ufscar.br/handle/ufscar/13249. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/13249 |
identifier_str_mv |
SILVA, Wesley Bertoli da. A new class of discrete models for the analysis of zero-modified count data. 2020. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2020. Disponível em: https://repositorio.ufscar.br/handle/ufscar/13249. |
url |
https://repositorio.ufscar.br/handle/ufscar/13249 |
dc.language.iso.fl_str_mv |
eng |
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eng |
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600 |
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d0f3b31a-38c4-4c28-aa5b-837ad377108e |
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 |
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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 São Carlos Câmpus São Carlos |
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Programa Interinstitucional de Pós-Graduação em Estatística - PIPGEs |
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UFSCar |
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Universidade Federal de São Carlos Câmpus São Carlos |
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