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Longitudinal data modelling based on centred skew scale mixture of distributions: parametric and semi-parametric approaches

Grant number: 18/26780-6
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:João Victor Bastos de Freitas
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 classes of regression models for continuous data. One for independent data and another for longitudinal data, making data modeling that presents asymmetry and / or heavy tails flexible. More specifically, we will consider the parametric and semi-parametric approaches using Generalized Estimation Equations (EEG) and Generalized Partial Additives Models (MLPAG), respectively. In the case of independent observations, we will consider centered skew scale mixture of normal distributions with semi-parametric predictor (independent MLPAG). In the case of data with repeated measures, we will extend this approach, via EEG and MLPAG. In these two latter cases, we will assume that the (marginal) distribution of the response variable follows skew scale mixture of normal distributions, considering appropriate measure mixing (such as gamma, beta, and binary distributions). We will develop estimation methods, measures of goodness of fit and diagnostics for these models, under the frequentist perspective. Other mixtures, not yet used in the literature, will be considered, namely: generalized gamma, Birnbaum-Saunders and beta-prime. Computational routines will be developed for the methodologies of this project, as well as simulation studies will be conducted to asses the performance of the methodologies to be developed. Also, real data analysis will be performed in order to illustrate the potential of such methodologies.