Robust transformation mixed-effects models for longitudinal continuous proportional data

The authors propose a robust transformation linear mixed-effects model for longitudinal continuous proportional data when some of the subjects exhibit outlying trajectories over time. It becomes troublesome when including or excluding such subjects in the data analysis results in different statistical conclusions. To robustify the longitudinal analysis using the mixed-effects model, they utilize the multivariate t distribution for random effects or/and error terms. Estimation and inference in the proposed model are established and illustrated by a real data example from an ophthalmology study. Simulation studies show a substantial robustness gain by the proposed model in comparison to the mixed-effects model based on Aitchison's logit-normal approach. As a result, the data analysis benefits from the robustness of making consistent conclusions in the presence of influential outliers. The Canadian Journal of Statistics © 2009 Statistical Society of CanadaPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/63085/1/10015_ftp.pd

Regressão quantílica para modelos de efeitos mistos

Orientador: Víctor Hugo Lachos DávilaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: Os dados longitudinais são frequentemente analisados usando modelos de efeitos mistos normais. Além disso, os métodos de estimação tradicionais baseiam-se em regressão na média da distribuição considerada, o que leva a estimação de parâmetros não robusta quando a distribuição do erro não é normal. Em comparação com a abordagem de regressão na média convencional, a regressão quantílica (RQ) pode caracterizar toda a distribuição condicional da variável de resposta e é mais robusta na presença de outliers e especificações erradas da distribuição do erro. Esta tese desenvolve uma abordagem baseada em verossimilhança para analisar modelos de RQ para dados longitudinais contínuos correlacionados através da distribuição Laplace assimétrica (DLA). Explorando a conveniente representação hierárquica da DLA, a nossa abordagem clássica segue a aproximação estocástica do algoritmo EM (SAEM) para derivar estimativas de máxima verossimilhança (MV) exatas dos efeitos fixos e componentes de variância em modelos lineares e não lineares de efeitos mistos. Nós avaliamos o desempenho do algoritmo em amostras finitas e as propriedades assintóticas das estimativas de MV através de experimentos empíricos e aplicações para quatro conjuntos de dados reais. Os algoritmos SAEMs propostos são implementados nos pacotes do R qrLMM() e qrNLMM() respectivamenteAbstract: Longitudinal data are frequently analyzed using normal mixed effects models. Moreover, the traditional estimation methods are based on mean regression, which leads to non-robust parameter estimation for non-normal error distributions. Compared to the conventional mean regression approach, quantile regression (QR) can characterize the entire conditional distribution of the outcome variable and is more robust to the presence of outliers and misspecification of the error distribution. This thesis develops a likelihood-based approach to analyzing QR models for correlated continuous longitudinal data via the asymmetric Laplace distribution (ALD). Exploiting the nice hierarchical representation of the ALD, our classical approach follows the stochastic Approximation of the EM (SAEM) algorithm for deriving exact maximum likelihood (ML) estimates of the fixed-effects and variance components in linear and nonlinear mixed effects models. We evaluate the finite sample performance of the algorithm and the asymptotic properties of the ML estimates through empirical experiments and applications to four real life datasets. The proposed SAEMs algorithms are implemented in the R packages qrLMM() and qrNLMM() respectivelyMestradoEstatisticaMestre em Estatístic

Robust MM-Estimation and Inference in Mixed Linear Models

Mixed linear models are used to analyse data in many settings. These models generally rely on the normality assumption and are often fitted by means of the maximum likelihood estimator (MLE) or the restricted maximum likelihood estimator (REML). However, the sensitivity of these estimation techniques and related tests to this underlying assumption has been identified as a weakness that can even lead to wrong interpretations. Recently Copt and Victoria-Feser(2005) proposed a high breakdown estimator, namely an S-estimator, for general mixed linear models. It has the advantage of being easy to compute - even for highly structured variance matrices - and allow the computation of a robust score test. However this proposal cannot be used to define a likelihood ratio type test which is certainly the most direct route to robustify an F-test. As the latter is usually a key tool to test hypothesis in mixed linear models, we propose two new robust estimators that allow the desired extension. They also lead to resistant Wald-type tests useful for testing contrasts and covariate efects. We study their properties theoretically and by means of simulations. An analysis of a real data set illustrates the advantage of the new approach in the presence of outlying observations.

Discussion paper. Conditional growth charts

Growth charts are often more informative when they are customized per subject, taking into account prior measurements and possibly other covariates of the subject. We study a global semiparametric quantile regression model that has the ability to estimate conditional quantiles without the usual distributional assumptions. The model can be estimated from longitudinal reference data with irregular measurement times and with some level of robustness against outliers, and it is also flexible for including covariate information. We propose a rank score test for large sample inference on covariates, and develop a new model assessment tool for longitudinal growth data. Our research indicates that the global model has the potential to be a very useful tool in conditional growth chart analysis.Comment: This paper discussed in: [math/0702636], [math/0702640], [math/0702641], [math/0702642]. Rejoinder in [math.ST/0702643]. Published at http://dx.doi.org/10.1214/009053606000000623 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org