Contribuições em modelos de regressão com erro de medida multiplicativo

• Ano de defesa: 2016
• Autor(a) principal: Silva, Eveliny Barroso da
• Orientador(a): Diniz, Carlos Alberto Ribeiro
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de São Carlos; Câmpus São Carlos
• Programa de Pós-Graduação: Programa Interinstitucional de Pós-Graduação em Estatística - PIPGEs
• Palavras-chave em Português: Erro de medida nas covariáveis; Erro de medida multiplicativo; Pseudo verossimilhança; Análise de diagnóstico; Quadratura de Gauss- Hermite
• Palavras-chave em Inglês: Regression models with measurement error; Multiplicative measu- rement error; Pseudo-likelihood; Diagnostic analysis; Gauss-hermite quadrature; Modified power series regression models
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA
• Link de acesso: https://repositorio.ufscar.br/handle/20.500.14289/7738

In regression models in which a covariate is measured with error, it is common to use structures that correlate the observed covariate with the true non-observed covariate. Such structures are usually additive or multiplicative. In the literature there are several interesting works that deal with regression models having an additive measurement error, many of which are linear models with covariate and measurement error normally distributed. For models having a multiplicative measurement error, one does not find in the literature the same theoretical amount of works as one finds for models in which the measurement error is additive. The same happens in situations where the supositions of normality for the covariates and the measurement errors do not apply. The present work proposes the construction, definition, estimation methods, and diagnostic analysis for the regression models with a multiplicative measurement error in one of the covariates. For these models it is considered that the response variable may belong either to the class of modified power series regression models or to the exponential family. The list of distributions belonging to the family modified power series is rather comprehensive; for this reason this work develops, firstly and in a general way, the models estimation and validation theory, and, as an example, presents the model of negative binomial regression with measurement error. In the case where the response variable belongs to the exponential family, the model of beta regression with multiplicative measurement error is presented. All proposed models were analysed through simulation studies and applied to real data sets.