Modelos de regressão GJS longitudinais

• Ano de defesa: 2024
• Autor(a) principal: Santos, Paulo César dos
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Rio Grande do Norte; Brasil; UFRN; PROGRAMA DE PÓS-GRADUAÇÃO EM MATEMÁTICA APLICADA E ESTATÍSTICA
• Palavras-chave em Português: Estatística matemática; Dados proporcionais longitudinais; Distribuição GJS; Modelos de regressão GJS longitudinais; Modelos para taxas e proporções; Modelos lineares generalizados mistos; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufrn.br/handle/123456789/58288

Weextend the class of GJS regression models that model continuous variables with support in the interval (0,1) to the case of correlated data, such as those coming from repeated measures, longitudinal or grouped data studies. The extension was carried out using the generalized linear mixed model methodology and parameter estimates are obtained based on the maximum likelihood (MV) method. The computational implementation combines the Gauss-Hermite quadrature to obtain the marginal density of the response variable and the BFGS non-linear optimization algorithm, implemented in the optim function of the computational software R. Monte Carlo simulations were performed to verify the performance of the MV estimators of the model parameters in samples of finite size. The simulation results suggest that the MV approach provides estimators with good properties. Additionally, we propose the randomized quantile residual to ascertain the quality of the f it. Furthermore, the effectiveness of the proposed residue in detecting some forms of model inadequacy was verified. Finally, we illustrate the methodology developed by applying it to a set of real data.