Modelos não lineares assimétricos com efeitos mistos

Abstract

PEREIRA, M. A. A. Nonlinear mixed-effects models with scale mixture of skew-normal distributions. 2019. 150 p. Tese (Doutorado em Estatística – Programa Interinstitucional de PósGraduação em Estatística) – Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos – SP, 2019. This work aims to develop asymmetric nonlinear regression models with mixed-effects, which provide alternatives to the use of normal distribution and other symmetric distributions, in order to avoid the sensitivity in the estimates to atypical observations and asymmetry. Nonlinear models with mixed-effects are explored in several areas of knowledge, especially when data are correlated, such as longitudinal data, repeated measures and multilevel data, in particular, for their flexibility in dealing with measures of areas such as biology and pharmacokinetics. However, there are difficulties in obtaining explicit estimators for the parameters in these models. At present, many studies have been developed with the family scale mixtures of skew-normal distribution (SMSN) that encompasses distributions with light and heavy tails, such as skewnormal, skew-Student-t, skew-contaminated normal and skew-slash, as well as symmetrical versions of these distributions. In this work, nonlinear regression models with mixed-effects are presented in which the random components have distributions belonging to the SMSN family. For the parameters estimation, a numerical solution via the EM algorithm and its extensions and Newton-Raphson algorithm is obtained. Analyzes for real data sets are performed with this new proposal, such as the study of drug kinetics in humans, as well as diagnostic analyzes, through residual analysis and influence diagnostics. Simulation studies are conducted to verify the maximum likelihood properties of the estimators.