Approximate Bayesian approaches and semiparametric methods for handling missing data

This thesis consists of four research papers focusing on estimation and inference in missing data. In the first paper (Chapter 2), an approximate Bayesian approach is developed to handle unit nonresponse with parametric model assumptions on the response probability, but without model assumptions for the outcome variable. The proposed Bayesian method is also extended to incorporate the auxiliary information from full sample. In second paper (Chapter 3), a new Bayesian method using the Spike-and-Slab prior is proposed to handle the sparse propensity score estimation. The proposed method is not based on any model assumption on the outcome variable and is computationally efficient. In third paper (Chapter 4), we develop a robust semiparametric method based on the profile likelihood obtained from semiparametric response model. The proposed method uses the observed regression model and the semiparametric response model to achieve robustness. An efficient algorithm using fractional imputation is developed. The bootstrap testing procedure is also proposed to test ignorability assumption. In last paper (Chapter 5), we propose a novel semiparametric fractional imputation method using Gaussian mixture model for handling multivariate missingness. The proposed method is computationally efficient and leads to robust estimation. The proposed method is further extended to incorporate the categorical auxiliary information. Asymptotic properties are developed for each proposed methods. Both simulation studies and real data applications are conducted to check the performance of the proposed methods in this thesis

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

Estimation and Applications of Quantile Regression for Binary Longitudinal Data

This paper develops a framework for quantile regression in binary longitudinal data settings. A novel Markov chain Monte Carlo (MCMC) method is designed to fit the model and its computational efficiency is demonstrated in a simulation study. The proposed approach is flexible in that it can account for common and individual-specific parameters, as well as multivariate heterogeneity associated with several covariates. The methodology is applied to study female labor force participation and home ownership in the United States. The results offer new insights at the various quantiles, which are of interest to policymakers and researchers alike

Additive quantile regression for clustered data with an application to children's physical activity

Additive models are flexible regression tools that handle linear as well as nonlinear terms. The latter are typically modelled via smoothing splines. Additive mixed models extend additive models to include random terms when the data are sampled according to cluster designs (e.g., longitudinal). These models find applications in the study of phenomena like growth, certain disease mechanisms and energy consumption in humans, when repeated measurements are available. In this paper, we propose a novel additive mixed model for quantile regression. Our methods are motivated by an application to physical activity based on a dataset with more than half million accelerometer measurements in children of the UK Millennium Cohort Study. In a simulation study, we assess the proposed methods against existing alternatives.Comment: 50 pages, 4 figures, 2 tables (18 supplementary tables