Semiparametric analysis of regression models for longitudinal data - Gu, Xiecheng (2013)
In this thesis, we investigate new methods, extending the marginal and mixed effects models to deal with more practical and complicated cases in longitudinal data. First, to analyze the longitudinal data with large number of covariates, we propose a regularized QIF incorporating regularization technique and specify a new quadratic penalty based on SCAD in order to enhance its performance in variable selection. Theoretical properties are well derived under the scenario of diverging number of covariates. Extensive simulation studies have been conducted to assess the performance of our proposed modeling approaches. Next, modeling longitudinal data with mismeasured covariates, we consider partially linear mixed effects models. In particular, the regression linear predictor is set to incorporate a combination of linear and nonlinear effects to improve model fitting efficiency. To deal with measurement error in covariates, a two-step estimation method including multiple imputation and penalized quasi-likelihood is specified. We further propose an iterative procedure and illustrate its behavior via a simulation study. The simulation result coincides with the asymptotic inference we have derived. A real example from public health study is provided to demonstrate its application.