The parametric, semiparametric and random effect regression model based on the extension of the generalized inverse Gaussian distribution

• Ano de defesa: 2021
• Autor(a) principal: Vasconcelos, Julio Cezar Souza
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Additive model; Efeito aleatório; Gerador odd log-logístico; Modelo aditivo; Modelo parcial; Modelo semiparamétrico; Odd log-logistic generator; Partial model; Random effect; Semiparametric model
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/11/11134/tde-28052021-151316/

We propose a regression model based on the four-parameter distribution called generalized inverse Gaussian odd log-logistic (OLLGIG) with two systematic components suitable for unimodal and bimodal data that extends the heteroscedastic GIG regression model. Additive, partial or semi-parametric regression models can be an option when the response variable and the explanatory variable have a nonlinear relationship, that is, the fundamental assumption of linearity between these variables does not hold. With this in mind, three flexible models are proposed, namely additive, partial and semiparametric regression models based on the OLLGIG distribution with a systematic structure, considering three different types of penalized smoothings generated by splines. Many studies in the areas of public health, economics, agronomics, medicine, biology and social sciences, among others, involve repeated observations of a response variable. The expression \"repeated measures\" is used to designate measurements obtained for the same variable or in the same experimental unit on more than one occasion. Various experimental designs with repeated measurements exist, such as split-plot, crossover and longitudinal. These types of investigations are called studies of correlated data and play a fundamental role in the analysis of results, where it is possible to characterize changes in the characteristics of an individual by associating these variations to a set of covariates. Due to their nature, the repeated measures have a correlation structure that plays an important role in the analysis of these types of data. In addition, the distribution of the response variable may present asymmetry or bimodality. Thus, a regression with a normal random intercept is introduced based on the OLLGIG distribution. In linear and random regressions, the maximum likelihood method is adopted for the models: additive, partial and semiparametric OLLGIG and the penalized maximum likelihood method are used to estimate the parameters of the proposed models. In addition, several simulations are performed for different parameter configurations and sample sizes to verify the accuracy of the maximum likelihood and penalized maximum likelihood estimators. Diagnostic analyses based on case-deletion and quantile residuals are performed. To prove the potential of the proposed regression models, adjustments are made with real data.