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Flexible modeling of complex longitudinal data using skew-elliptical distributions


In recent years, the study of statistical models for longitudinal data analysis has received an increasing attention in the statistical literature. In this context, a common practice to analyze longitudinal measures is to use mixed effects models under assumptions such as the normality or symmetry of random errors and random effects, the absence of missing observations and the absence of measurement error-in-covariates. Although longitudinal data present complex features as skewness, heavy or light tails, outliers or influential observations, non-ignorable missingness, censored responses, covariate measurement errors among many others, most of the published researches have been concentrated only on capturing specific aspects of the motivating case studies. The objective of this research project is to study mixed effects models for complex longitudinal data features, using a particular family of skew-elliptical distributions such as the scale mixtures of skew-normal (SMSN) class. The emphasis of this research will be based mainly on the following aspects: (A)The study of censored mixed effects models with covariate measurement errors.(B)The study of non-linear mixed effects models based on smoothing functions such as P-splines.(C)The study of mixed effects models considering non-ignorable missingness (NMAR scheme). For (A), the main objective is to propose a robust generalization of the Tobit model by considering on one hand, a time-varying covariate that suffers from random measurement error, and on the other hand, a random effect and error term joint distribution belonging to the SMSN class. For (B), the main focus is to propose a non-linear mixed effects modeling based on smoothing functions techniques as the penalized spline fitting. The use of the smoothing functions to model the non-linear relationship of the response variable, covariates and random effects and also to model the random effects distribution will be considered. Finally, for (C) the main objective is to study the effect on inference when the longitudinal data present missing values and the joint distribution for the random effect and the error term belongs to the SMSN class. (AU)

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Scientific publications (6)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
GARAY, ALDO M.; CASTRO, LUIS M.; LESKOW, JACEK; LACHOS, VICTOR H. Censored linear regression models for irregularly observed longitudinal data using the multivariate-t distribution. STATISTICAL METHODS IN MEDICAL RESEARCH, v. 26, n. 2, p. 542-566, APR 2017. Web of Science Citations: 7.
ALEJANDRO GONZALEZ, JOSE; MAURICIO CASTRO, LUIS; LACHOS, VICTOR HUGO; PATRIOTA, ALEXANDRE GALVAO. A Confidence Set Analysis for Observed Samples: A Fuzzy Set Approach. Entropy, v. 18, n. 6 JUN 2016. Web of Science Citations: 3.
CASTRO, LUIS MAURICIO; COSTA, DENISE REIS; PRATES, MARCOS OLIVEIRA; LACHOS, VICTOR HUGO. Likelihood-based inference for Tobit confirmatory factor analysis using the multivariate Student-t distribution. STATISTICS AND COMPUTING, v. 25, n. 6, p. 1163-1183, NOV 2015. Web of Science Citations: 4.
MATOS, LARISSA A.; BANDYOPADHYAY, DIPANKAR; CASTRO, LUIS M.; LACHOS, VICTOR H. Influence assessment in censored mixed-effects models using the multivariate Student's-t distribution. JOURNAL OF MULTIVARIATE ANALYSIS, v. 141, p. 104-117, OCT 2015. Web of Science Citations: 3.
BANDYOPADHYAY, DIPANKAR; CASTRO, LUIS M.; LACHOS, VICTOR H.; PINHEIRO, HILDETE P. Robust Joint Non-linear Mixed-Effects Models and Diagnostics for Censored HIV Viral Loads with CD4 Measurement Error. JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS, v. 20, n. 1, p. 121-139, MAR 2015. Web of Science Citations: 7.
CASTRO, LUIS M.; LACHOS, VICTOR H.; FERREIRA, GUILLERMO P.; ARELLANO-VALLE, REINALDO B. Partially linear censored regression models using heavy-tailed distributions: A Bayesian approach. STATISTICAL METHODOLOGY, v. 18, p. 14-31, MAY 2014. Web of Science Citations: 7.

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