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Parametric and semi-parametric modelos for longitudinal limited response

Grant number: 18/26784-1
Support type:Scholarships in Brazil - Master
Effective date (Start): June 01, 2019
Effective date (End): February 28, 2021
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics
Principal Investigator:Caio Lucidius Naberezny Azevedo
Grantee:Áurea Fonseca Lopes Galindo
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this project we will develop two approaches, the first one involving extensions of the zero and/or one augmented beta, simplex and rectangular beta models considering semi-parametric structures to the respective response means, to analyze limited data. The advantage of this extension is that it will be possible to satisfactorily model linear and non-linear phenomena. In the second approach, the focus is on correlated data that may present linear or non-linear relationship between the mean and covariates of interest. In this way, regression models based on the above distributions will be developed under the parametric and semi-parametric approaches, with the differential of the inclusion of a correlation structure via Generalized Estimation Equations (EEG). The two approaches will be developed using some linking functions, among them different from some often used in the literature, in order to study the sensitivity of the results with respect to that choice. Model selection and diagnostic tools will be developed for all models. Finally, simulations and real data analysis will be done to illustrate the potential of the proposed methodologies. We will consider the frequentist approach for the two model classes and for the development of all the mentioned tools.