Browsing by Author "Daowen Zhang, Committee Chair"

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Model Selection and Estimation in Additive Regression Models
(2009-09-14) Miao, Huiping; Hao Zhang, Committee Member; Marie Davidian, Committee Member; Dennis Boos, Committee Member; Daowen Zhang, Committee Chair
We propose a method of simultaneous model selection and estimation in additive regression models (ARMs) for independent normal data. We use the mixed model representation of the smoothing spline estimators of the nonparametric functions in ARMs, where the importance of these functions is controlled by treating the inverse of the smoothing parameters as extra variance components. The selection of important nonparametric functions is achieved by maximizing the penalized likelihood with an adaptive LASSO. A unified EM algorithm is provided to obtain the maximum penalized likelihood estimates of the nonparametric functions and the residual variance. In the same framework, we also consider forward selection based on score tests, and a two stage approach that imposes an early stage screening using an individual score test on each induced variance component of the smoothing parameter. For longitudinal data, we propose to extend the adaptive LASSO and the two-stage selection with score test screening to the additive mixed models (AMMs), by introducing subject-specific random effects to the additive models to accommodate the correlation in responses. We use the eigenvalue-eigenvector decomposition approach to approximate the working random effects in the linear mixed model presentation of the AMMs, so as to reduce the dimensions of matrices involved in the algorithm while keeping most data information, hence to tackle the computational problems caused by large sample sizes in longitudinal data. Simulation studies are provided and the methods are illustrated with data applications.
Quantitative Trait Loci (QTL) Mapping With Longitudinal Traits
(2008-08-08) Yu, Miao; Zhao-Bang Zeng, Committee Member; Wenbin Lu, Committee Co-Chair; Daowen Zhang, Committee Chair; Jung-Ying Tzeng, Committee Member
Semiparametric Mixed Models for Censored Longitudinal Data.
(2010-11-01) Huang, Mingyan; Daowen Zhang, Committee Chair; Hao Zhang, Committee Chair; Marie Davidian, Committee Member; Wenbin Lu, Committee Member; Richard Braham, Committee Member
Topics in Application of Nonparametric Smoothing Splines
(2005-12-14) Lin, Jiang; Marie Davidian, Committee Co-Chair; John Monahan, Committee Member; Hao (Helen) Zhang, Committee Member; Daowen Zhang, Committee Chair
There are two topics in this dissertation. The first topic is 'Smoothing Parameter Selection in Nonparametric Generalized Linear Models via Sixth-order Laplace Approximation' and the second topic is 'Smoothing Spline-based Score Tests for Proportional Hazards Models'. We present a new approach for the automatic selection of the smoothing parameter in nonparametric smoothing spline Generalized Linear Models (GLMs), using the Restricted Maximum Likelihood (REML) method and the sixth-order Laplace approximation of Raudenbush et al. (2000). The proposed approach is compared with Generalized Additive Mixed Model (GAMM, Lin and Zhang 1999) and Generalized Approximate Cross-Validation (GACV, Gu and Xiang 2001) through simulations and is shown to be effective. We propose 'score-type' tests for the proportional hazards assumption and for covariate effects in the Cox model, using the natural smoothing spline representation of the corresponding nonparametric functions of time or covariate. The tests are based on the penalized partial likelihood. By treating the inverse of the smoothing parameter as a variance component, we derive the score tests by testing an equivalent null hypothesis that the corresponding variance component is zero. The tests are shown to have size close to the nominal level and to provide good power against general alternatives in simulations. We apply the proposed tests to data from a cancer clinical trial.
Variable Selection in Linear Mixed Model for Longitudinal Data
(2006-08-17) Lan, Lan; Daowen Zhang, Committee Chair; Hao Helen Zhang, Committee Co-Chair; Marie Davidian, Committee Member; Dennis Boos, Committee Member
Fan and Li (JASA, 2001) proposed a family of variable selection procedures for certain parametric models via a nonconcave penalized likelihood approach, where significant variable selection and parameter estimation were done simultaneously, and the procedures were shown to have the oracle property. In this presentation, we extend the nonconcave penalized likelihood approach to linear mixed models for longitudinal data. Two new approaches are proposed to select significant covariates and estimate fixed effect parameters and variance components. In particular, we show the new approaches also possess the oracle property when the tuning parameter is chosen appropriately. We assess the performance of the proposed approaches via simulation and apply the procedures to data from the Multicenter AIDS Cohort Study.
Variable Selection in Partial Linear Models and Semiparametric Mixed Models
(2008-07-25) Ni, Xiao; Hao Helen Zhang, Committee Co-Chair; Marie Davidian, Committee Member; Jason Osborne, Committee Member; Daowen Zhang, Committee Chair
Variable Selection Procedures for Generalized Linear Mixed Models in Longitudinal Data Analysis
(2007-08-03) Yang, Hongmei; Daowen Zhang, Committee Chair; Hao Helen Zhang, Committee Co-Chair; Dennis Boos, Committee Member; Marie Davidian, Committee Member
Model selection is important for longitudinal data analysis. But up to date little work has been done on variable selection for generalized linear mixed models (GLMM). In this paper we propose and study a class of variable selection methods. Full likelihood (FL) approach is proposed for simultaneous model selection and parameter estimation. Due to the intensive computation involved in FL approach, Penalized Quasi-Likelihood (PQL) procedure is developed so that model selection in GLMMs can proceed in the framework of linear mixed models. Since the PQL approach will produce biased parameter estimates for sparse binary longitudinal data, Two-stage Penalized Quasi-Likelihood approach (TPQL) is proposed to bias correct PQL in terms of estimation: use PQL to do model selection at the first stage and existing software to do parameter estimation at the second stage. Marginal approach for some special types of data is also developed. A robust estimator of standard error for the fitted parameters is derived based on a sandwich formula. A bias correction is proposed to improve the estimation accuracy of PQL for binary data. The sampling performance of four proposed procedures is evaluated through extensive simulations and their application to real data analysis. In terms of model selection, all of them perform closely. As for parameter estimation, FL, AML and TPQL yield similar results. Compared with FL, the other procedures greatly reduce computational load. The proposed procedures can be extended to longitudinal data analysis involving missing data, and the shrinkage penalty based approach allows them to work even when the number of observations n is less than the number of parameters d.