RESUMO
The interest for nonlinear mixed-effects models comes from application areas as pharmacokinetics, growth curves and HIV viral dynamics. However, the modeling procedure usually leads to many difficulties, as the inclusion of random effects, the estimation process and the model sensitivity to atypical or nonnormal data. The scale mixture of normal distributions include heavy-tailed models, as the Student-t, slash and contaminated normal distributions, and provide competitive alternatives to the usual models, enabling the obtention of robust estimates against outlying observations. Our proposal is to compare two estimation methods in nonlinear mixed-effects models where the random components follow a multivariate scale mixture of normal distributions. For this purpose, a Monte Carlo expectation-maximization algorithm (MCEM) and an efficient likelihood-based approximate method are developed. Results show that the approximate method is much faster and enables a fairly efficient likelihood maximization, although a slightly larger bias may be produced, especially for the fixed-effects parameters. A discussion on the robustness aspects of the proposed models are also provided. Two real nonlinear applications are discussed and a brief simulation study is presented.
RESUMO
Continuous clustered proportion data often arise in various areas of the social and political sciences where the response variable of interest is a proportion (or percentage). An example is the behavior of the proportion of voters favorable to a political party in municipalities (or cities) of a country over time. This behavior can be different depending on the region of the country, giving rise to groups (or clusters) with similar profiles. For this kind of data, we propose a finite mixture of a random effects regression model based on the L-Logistic distribution. A Markov chain Monte Carlo algorithm is tailored to obtain posterior distributions of the unknown quantities of interest through a Bayesian approach. To illustrate the proposed method, with emphasis on analysis of clusters, we analyze the proportion of votes for a political party in presidential elections in different municipalities observed over time, and then identify groups according to electoral behavior at different levels of favorable votes.