Fixed effects selection in the linear mixed-effects model using adaptive ridge procedure for L0 penalty performance

This paper is concerned with the selection of fixed effects along with the estimation of fixed effects, random effects and variance components in the linear mixed-effects model. We introduce a selection procedure based on an adaptive ridge (AR) penalty of the profiled likelihood, where the covariance matrix of the random effects is Cholesky factorized. This selection procedure is intended to both low and high-dimensional settings where the number of fixed effects is allowed to grow exponentially with the total sample size, yielding technical difficulties due to the non-convex optimization problem induced by L0 penalties. Through extensive simulation studies, the procedure is compared to the LASSO selection and appears to enjoy the model selection consistency as well as the estimation consistency

Functional mapping of reaction norms to multiple environmental signals through nonparametric covariance estimation

<p>Abstract</p> <p>Background</p> <p>The identification of genes or quantitative trait loci that are expressed in response to different environmental factors such as temperature and light, through functional mapping, critically relies on precise modeling of the covariance structure. Previous work used separable parametric covariance structures, such as a Kronecker product of autoregressive one [AR(1)] matrices, that do not account for interaction effects of different environmental factors.</p> <p>Results</p> <p>We implement a more robust nonparametric covariance estimator to model these interactions within the framework of functional mapping of reaction norms to two signals. Our results from Monte Carlo simulations show that this estimator can be useful in modeling interactions that exist between two environmental signals. The interactions are simulated using nonseparable covariance models with spatio-temporal structural forms that mimic interaction effects.</p> <p>Conclusions</p> <p>The nonparametric covariance estimator has an advantage over separable parametric covariance estimators in the detection of QTL location, thus extending the breadth of use of functional mapping in practical settings.</p

Estimação e diagnóstico em modelos multivariados para dados censurados

Orientadores: Víctor Hugo Lachos Dávila, Luis Mauricio Castro CeperoTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: Em alguns ensaios clínicos da síndrome da imunodeficiência adquirida (AIDS), as medições dos ácidos ribonucleicos do vírus da imunodeficiência humana (HIV-1) são coletadas periodicamente ao longo do tempo e muitas vezes estão sujeitas a limites de detecção inferiores ou superiores, dependendo dos ensaios de quantificação que foram utilizados. Assim, estas respostas podem ser censuradas à esquerda ou à direita. Na prática, dados longitudinais provenientes de estudos de acompanhamento do HIV, podem ser modelados utilizando modelos lineares e não-lineares de efeitos mistos censurados e também modelos de regressão censurados com estruturas de correlação específicas sobre os erros. Uma complicação adicional surge quando duas ou mais variáveis respostas são coletadas de forma irregular e repetidamente em cada sujeito durante um certo período de tempo. Os modelos lineares multivariados de efeitos mistos com respostas censuradas são ferramentas bastante utilizadas para análise conjunta de mais de uma série de respostas de dados longitudinais. Nesta tese desenvolvemos métodos inferenciais para lidar com dados censurados com estrutura longitudinal sob uma perspectiva clássica. Como resultado, conclusões importantes foram obtidas a partir da análise dos modelos propostosAbstract: In some acquired immunodeficiency syndrome (AIDS) clinical trials, the human immunodeficiency virus-1 ribonucleic acid measurements are collected irregularly over time and are often subject to some upper and lower detection limits, depending on the quantification assays. Hence, these responses are either left- or right-censored. In practice, longitudinal data coming from those follow-up studies can be modelled using censored linear and nonlinear mixed-effects models and also censored regression models with a specific correlation structures on the error terms. A complication arises when more than one series of responses are repeatedly collected on each subject at irregularly occasions over a period of time. The multivariate censored linear mixed model is a frequently used tool for a joint analysis of more than one series of longitudinal data. In this thesis we develop a series of essays in which different models and techniques to deal with censored data are applied. As result, we had several works to carry out censored dataDoutoradoEstatisticaDoutora em Estatística2011/22063-9, 2015/05385-3FAPES

A family of linear mixed-effects models using the generalized Laplace distribution

We propose a new family of linear mixed-effects models based on the generalized Laplace distribution. Special cases include the classical normal mixed-effects model, models with Laplace random effects and errors, and models where Laplace and normal variates interchange their roles as random effects and errors. By using a scale-mixture representation of the generalized Laplace, we develop a maximum likelihood estimation approach based on Gaussian quadrature. For model selection, we propose likelihood ratio testing and we account for the situation in which the null hypothesis is at the boundary of the parameter space. In a simulation study, we investigate the finite sample properties of our proposed estimator and compare its performance to other flexible linear mixed-effects specifications. In two real data examples, we demonstrate the flexibility of our proposed model to solve applied problems commonly encountered in clustered data analysis. The newly proposed methods discussed in this paper are implemented in the R package nlmm