Modelos alternativos da TRI para dados politômicos
Autor(a) principal: | |
---|---|
Data de Publicação: | 2019 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/11293 |
Resumo: | The item response theory (IRT) models for polytomous data are frequently used in the analysis of data coming from the behavioral and social sciences. From a practical point of view, polytomous data are more informative than dichotomous data, since it considers more than two response categories in each test item, making the models assigned to this type of data attractive. The purpose of this research is to explore alternative polytomous IRT models and their multidimensional extensions, filling some gaps in the literature. Specifically, the chapters of this work follow a construction sequence of IRT modeling. Firstly, we conducted a study to assist readers in choosing between two of the major polytomous IRT models in the one-dimensional context: the graded response (GR) model and the generalized partial credit (GPC) model. We conducted a sensitivity analysis of priors to choose a suitable priors scenario for each model and we verified the performance of some model comparison criteria against these models through a simulation study. Then, we extend the one-dimensional GPC model to the bifactor context, proposing the GPC-bifactor model, in which a global latent trait and specific latent traits are considered through an additive structure in its formulation. In addition, we flexibilize the structure of the GPC-bifactor model, making possible its use with other link functions beyond the usual logit, such as probit and clog-log. Then, we incorporate the relation between the items and the latent trait dimensions of the individuals in the formulation of the multidimensional item response theory (MIRT) models through the Q-matrix, a component present in the vast majority of cognitive diagnostic models (CDM), making it easy for users to express the item-trait relationship in MIRT models. Finally, we propose a validation method using the Q-matrix in MIRT models. In particular, we used in the study the multidimensional GPC model with Q-matrix embedded in its formulation. The different simulation studies and the applications performed in this research showed that these models are alternative models for the analysis of polytomous data and that can be used by the users in practice. |
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Silva, Marcelo Andrade daBazán Guzmán, Jorge Luishttp://lattes.cnpq.br/7302778157579178http://lattes.cnpq.br/5641187629276460aac931d2-6aac-4813-9805-8ceeb1a4aed22019-04-23T13:49:42Z2019-04-23T13:49:42Z2019-03-22SILVA, Marcelo Andrade da. Modelos alternativos da TRI para dados politômicos. 2019. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2019. Disponível em: https://repositorio.ufscar.br/handle/ufscar/11293.https://repositorio.ufscar.br/handle/ufscar/11293The item response theory (IRT) models for polytomous data are frequently used in the analysis of data coming from the behavioral and social sciences. From a practical point of view, polytomous data are more informative than dichotomous data, since it considers more than two response categories in each test item, making the models assigned to this type of data attractive. The purpose of this research is to explore alternative polytomous IRT models and their multidimensional extensions, filling some gaps in the literature. Specifically, the chapters of this work follow a construction sequence of IRT modeling. Firstly, we conducted a study to assist readers in choosing between two of the major polytomous IRT models in the one-dimensional context: the graded response (GR) model and the generalized partial credit (GPC) model. We conducted a sensitivity analysis of priors to choose a suitable priors scenario for each model and we verified the performance of some model comparison criteria against these models through a simulation study. Then, we extend the one-dimensional GPC model to the bifactor context, proposing the GPC-bifactor model, in which a global latent trait and specific latent traits are considered through an additive structure in its formulation. In addition, we flexibilize the structure of the GPC-bifactor model, making possible its use with other link functions beyond the usual logit, such as probit and clog-log. Then, we incorporate the relation between the items and the latent trait dimensions of the individuals in the formulation of the multidimensional item response theory (MIRT) models through the Q-matrix, a component present in the vast majority of cognitive diagnostic models (CDM), making it easy for users to express the item-trait relationship in MIRT models. Finally, we propose a validation method using the Q-matrix in MIRT models. In particular, we used in the study the multidimensional GPC model with Q-matrix embedded in its formulation. The different simulation studies and the applications performed in this research showed that these models are alternative models for the analysis of polytomous data and that can be used by the users in practice.Os modelos da teoria da resposta ao item (TRI) para dados politômicos são frequentemente utilizados na análise de dados provenientes das ciências comportamentais e sociais. Do ponto de vista prático, dados politômicos são mais informativos do que dados dicotômicos, uma vez que considera mais de duas categorias de resposta em cada item do teste, tornando atrativos os modelos designados a esse tipo de dados. A proposta desta pesquisa é explorar modelos alternativos da TRI para dados politômicos e suas extensões multidimensionais, preenchendo algumas lacunas existentes na literatura. Especificamente, os capítulos deste trabalho seguem uma sequência de construção da modelagem da TRI. Primeiramente, realizamos um estudo para auxiliar os leitores na escolha entre dois dos principais modelos da TRI para dados politômicos no contexto unidimensional: o modelo de resposta gradual (RG) e o modelo de crédito parcial generalizado (CPG). Conduzimos uma análise de sensibilidade de prioris para escolher um cenário de prioris adequado para cada modelo e verificamos o desempenho de alguns critérios de comparação de modelos frente a estes modelos através de um estudo de simulação. Em seguida, estendemos o modelo CPG unidimensional para o contexto bifator, propondo o modelo CPG-bifator, em que são considerados um traço latente global e traços latentes específicos através de uma estrutura aditiva em sua formulação. Além disso, flexibilizamos a estrutura do modelo CPG-bifator, tornando possível o seu uso com outras funções de ligação além da usual logito, tais como probito e clog-log. Na sequência, incorporamos a relação entre os itens do teste e as dimensões do traço latente dos indivíduos na formulação dos modelos da teoria da resposta ao item multidimensionais (TRIM) através da matriz Q, um componente presente na grande maioria dos modelos de diagnóstico cognitivo (MDC), tornando acessível aos usuários uma maneira simples de expressar a relação item-traço nos modelos da TRIM. Por fim, propomos um método de validação de matriz Q em modelos da TRIM. Em particular, utilizamos no estudo o modelo CPG multidimensional com matriz Q incorporada em sua formulação. Os diferentes estudos de simulação e as aplicações realizadas nesta pesquisa mostraram que estes modelos são modelos alternativos para a análise de dados politômicos e que podem ser utilizados pelos usuários na prática.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)CAPES: Código de Financiamento 001porUniversidade Federal de São CarlosCâmpus São CarlosPrograma Interinstitucional de Pós-Graduação em Estatística - PIPGEsUFSCarInferência bayesianaModelos da TRI multidimensionaisModelos para dados politômicosTeoria da resposta ao itemVariáveis latentesBayesian inferenceMultidimensiona lIRT modelsModels for polytomous dataItem response theoryLatent variablesCIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::ANALISE DE DADOSModelos alternativos da TRI para dados politômicosAlternative polytomous IRT modelsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisOnline712d7773-fe6a-4a4f-a2f1-42684ef30b44info:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALtese ufscar.pdftese ufscar.pdfTeseapplication/pdf2920864https://repositorio.ufscar.br/bitstream/ufscar/11293/1/tese%20ufscar.pdf8b3cbbd345764d7446372a926b663c27MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81957https://repositorio.ufscar.br/bitstream/ufscar/11293/3/license.txtae0398b6f8b235e40ad82cba6c50031dMD53TEXTtese ufscar.pdf.txttese ufscar.pdf.txtExtracted texttext/plain253655https://repositorio.ufscar.br/bitstream/ufscar/11293/4/tese%20ufscar.pdf.txt727515bb821f95d959ee2fdd3726b9efMD54THUMBNAILtese ufscar.pdf.jpgtese ufscar.pdf.jpgIM Thumbnailimage/jpeg4990https://repositorio.ufscar.br/bitstream/ufscar/11293/5/tese%20ufscar.pdf.jpg4db8d7b6bf06df24267737f20c59c09aMD55ufscar/112932023-09-18 18:31:22.019oai:repositorio.ufscar.br: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Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:31:22Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.por.fl_str_mv |
Modelos alternativos da TRI para dados politômicos |
dc.title.alternative.eng.fl_str_mv |
Alternative polytomous IRT models |
title |
Modelos alternativos da TRI para dados politômicos |
spellingShingle |
Modelos alternativos da TRI para dados politômicos Silva, Marcelo Andrade da Inferência bayesiana Modelos da TRI multidimensionais Modelos para dados politômicos Teoria da resposta ao item Variáveis latentes Bayesian inference Multidimensiona lIRT models Models for polytomous data Item response theory Latent variables CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::ANALISE DE DADOS |
title_short |
Modelos alternativos da TRI para dados politômicos |
title_full |
Modelos alternativos da TRI para dados politômicos |
title_fullStr |
Modelos alternativos da TRI para dados politômicos |
title_full_unstemmed |
Modelos alternativos da TRI para dados politômicos |
title_sort |
Modelos alternativos da TRI para dados politômicos |
author |
Silva, Marcelo Andrade da |
author_facet |
Silva, Marcelo Andrade da |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/5641187629276460 |
dc.contributor.author.fl_str_mv |
Silva, Marcelo Andrade da |
dc.contributor.advisor1.fl_str_mv |
Bazán Guzmán, Jorge Luis |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/7302778157579178 |
dc.contributor.authorID.fl_str_mv |
aac931d2-6aac-4813-9805-8ceeb1a4aed2 |
contributor_str_mv |
Bazán Guzmán, Jorge Luis |
dc.subject.por.fl_str_mv |
Inferência bayesiana Modelos da TRI multidimensionais Modelos para dados politômicos Teoria da resposta ao item Variáveis latentes |
topic |
Inferência bayesiana Modelos da TRI multidimensionais Modelos para dados politômicos Teoria da resposta ao item Variáveis latentes Bayesian inference Multidimensiona lIRT models Models for polytomous data Item response theory Latent variables CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::ANALISE DE DADOS |
dc.subject.eng.fl_str_mv |
Bayesian inference Multidimensiona lIRT models Models for polytomous data Item response theory Latent variables |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::ANALISE DE DADOS |
description |
The item response theory (IRT) models for polytomous data are frequently used in the analysis of data coming from the behavioral and social sciences. From a practical point of view, polytomous data are more informative than dichotomous data, since it considers more than two response categories in each test item, making the models assigned to this type of data attractive. The purpose of this research is to explore alternative polytomous IRT models and their multidimensional extensions, filling some gaps in the literature. Specifically, the chapters of this work follow a construction sequence of IRT modeling. Firstly, we conducted a study to assist readers in choosing between two of the major polytomous IRT models in the one-dimensional context: the graded response (GR) model and the generalized partial credit (GPC) model. We conducted a sensitivity analysis of priors to choose a suitable priors scenario for each model and we verified the performance of some model comparison criteria against these models through a simulation study. Then, we extend the one-dimensional GPC model to the bifactor context, proposing the GPC-bifactor model, in which a global latent trait and specific latent traits are considered through an additive structure in its formulation. In addition, we flexibilize the structure of the GPC-bifactor model, making possible its use with other link functions beyond the usual logit, such as probit and clog-log. Then, we incorporate the relation between the items and the latent trait dimensions of the individuals in the formulation of the multidimensional item response theory (MIRT) models through the Q-matrix, a component present in the vast majority of cognitive diagnostic models (CDM), making it easy for users to express the item-trait relationship in MIRT models. Finally, we propose a validation method using the Q-matrix in MIRT models. In particular, we used in the study the multidimensional GPC model with Q-matrix embedded in its formulation. The different simulation studies and the applications performed in this research showed that these models are alternative models for the analysis of polytomous data and that can be used by the users in practice. |
publishDate |
2019 |
dc.date.accessioned.fl_str_mv |
2019-04-23T13:49:42Z |
dc.date.available.fl_str_mv |
2019-04-23T13:49:42Z |
dc.date.issued.fl_str_mv |
2019-03-22 |
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, Marcelo Andrade da. Modelos alternativos da TRI para dados politômicos. 2019. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2019. Disponível em: https://repositorio.ufscar.br/handle/ufscar/11293. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/11293 |
identifier_str_mv |
SILVA, Marcelo Andrade da. Modelos alternativos da TRI para dados politômicos. 2019. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2019. Disponível em: https://repositorio.ufscar.br/handle/ufscar/11293. |
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https://repositorio.ufscar.br/handle/ufscar/11293 |
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por |
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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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