Banca de DEFESA: PAULO CÉSAR DOS SANTOS

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : PAULO CÉSAR DOS SANTOS
DATE: 21/03/2024
TIME: 14:30
LOCAL: Auditório do CCET
TITLE:

Longitudinal GJS regression models

KEY WORDS:

Longitudinal proportional data; GJS Distribution; Longitudinal GJS Regression
Models; Models for rates and proportions; Generalized linear mixed models;

PAGES: 106
BIG AREA: Ciências Exatas e da Terra
AREA: Probabilidade e Estatística
SUMMARY:

We extend 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
longitudinal studies or pooled data. The proposed model is based on the class of generalized
linear mixed models and parameter estimates are obtained based on the marginal maximum
likelihood (ML) method. The computational implementation combines the Gauss-Hermite
quadrature to obtain the marginal density of the response variable and the non-linear
optimization algorithm of Broyden, Fletcher, Goldfarb and Shanno (BFGS), implemented in the
optim package of the R software. Monte Carlo to verify the performance of the ML estimators.
The simulation results suggest that the ML approach provides unbiased and consistent

estimators for all model parameters. The motivation for this proposal is the absence of a class
of GJS regression models for correlated data and the fact that longitudinal data in the interval
(0, 1) generally present asymmetry or are more concentrated around one of the limits of the
interval. Therefore, to obtain consistent parameter estimates, methods that are robust in the
presence of asymmetry are necessary, as is the case with GJS regression models that model
the median of the response variable. Additionally, we propose the quantile residue for this
new class of models and apply the global influence technique based on the conditional Cook
distance with the aim of identifying possible influential points. Finally, we illustrate the
methodology developed by applying it to a real dataset.

COMMITTEE MEMBERS:
Presidente - 2310429 - ARTUR JOSE LEMONTE
Externo à Instituição - FRANCISCO FELIPE DE QUEIROZ - USP
Externa ao Programa - 2083593 - LUZ MILENA ZEA FERNANDEZ - null