Mixed Effects Models for Complex Data
Features
- Covers widely used mixed effects models, including LME models, GLMMs, NLME models, frailty models, and semiparametric and nonparametric mixed effects models
- Links each mixed effects model with the corresponding class of regression model for cross-sectional data
- Discusses various computational strategies for likelihood estimations of mixed effects models
- Offers brief descriptions of GEE methods and Bayesian mixed effects models
- Includes real-world data examples throughout that encompass studies on mental distress, AIDS, and more
- Explains how to implement standard models using R and S-Plus
Summary
Although standard mixed effects models are useful in a range of studies, other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts, missing data, measurement errors, censoring, and outliers. For each class of mixed effects model, the author reviews the corresponding class of regression model for cross-sectional data.
An overview of general models and methods, along with motivating examples
After presenting real data examples and outlining general approaches to the analysis of longitudinal/clustered data and incomplete data, the book introduces linear mixed effects (LME) models, generalized linear mixed models (GLMMs), nonlinear mixed effects (NLME) models, and semiparametric and nonparametric mixed effects models. It also includes general approaches for the analysis of complex data with missing values, measurement errors, censoring, and outliers.
Self-contained coverage of specific topics
Subsequent chapters delve more deeply into missing data problems, covariate measurement errors, and censored responses in mixed effects models. Focusing on incomplete data, the book also covers survival and frailty models, joint models of survival and longitudinal data, robust methods for mixed effects models, marginal generalized estimating equation (GEE) models for longitudinal or clustered data, and Bayesian methods for mixed effects models.
Background material
In the appendix, the author provides background information, such as likelihood theory, the Gibbs sampler, rejection and importance sampling methods, numerical integration methods, optimization methods, bootstrap, and matrix algebra.
Failure to properly address missing data, measurement errors, and other issues in statistical analyses can lead to severely biased or misleading results. This book explores the biases that arise when naïve methods are used and shows which approaches should be used to achieve accurate results in longitudinal data analysis.
Table of Contents
Introduction
Introduction
Longitudinal Data and Clustered Data
Some Examples
Regression Models
Mixed Effects Models
Complex or Incomplete Data
Software
Outline and Notation
Mixed Effects Models
Introduction
Linear Mixed Effects (LME) Models
Nonlinear Mixed Effects (NLME) Models
Generalized Linear Mixed Models (GLMMs)
Nonparametric and Semiparametric Mixed Effects Models
Computational Strategies
Further Topics
Software
Missing Data, Measurement Errors, and Outliers
Introduction
Missing Data Mechanisms and Ignorability
General Methods for Missing Data
EM Algorithms
Multiple Imputation
General Methods for Measurement Errors
General Methods for Outliers
Software
Mixed Effects Models with Missing Data
Introduction
Mixed Effects Models with Missing Covariates
Approximate Methods
Mixed Effects Models with Missing Responses
Multiple Imputation Methods
Computational Strategies
Examples
Mixed Effects Models with Covariate Measurement Errors
Introduction
Measurement Error Models and Methods
Two-Step Methods and Regression Calibration Methods
Likelihood Methods
Approximate Methods
Measurement Error and Missing Data
Mixed Effects Models with Censoring
Introduction
Mixed Effects Models with Censored Responses
Mixed Effects Models with Censoring and Measurement Errors
Mixed Effects Models with Censoring and Missing Data
Appendix
Survival Mixed Effects (Frailty) Models
Introduction
Survival Models
Frailty Models
Survival and Frailty Models with Missing Covariates
Frailty Models with Measurement Errors
Joint Modeling Longitudinal and Survival Data
Introduction
Joint Modeling for Longitudinal Data and Survival Data
Two-Step Methods
Joint Likelihood Inference
Joint Models with Incomplete Data
Joint Modeling of Several Longitudinal Processes
Robust Mixed Effects Models
Introduction
Robust Methods
Mixed Effects Models with Robust Distributions
M-Estimators for Mixed Effects Models
Robust Inference for Mixed Effects Models with Incomplete Data
Generalized Estimating Equations (GEEs)
Introduction
Marginal Models
Estimating Equations with Incomplete Data
Discussion
Bayesian Mixed Effects Models
Introduction
Bayesian Methods
Bayesian Mixed Effects Models
Bayesian Mixed Models with Missing Data
Bayesian Models with Covariate Measurement Errors
Bayesian Joint Models of Longitudinal and Survival Data
Appendix: Background Materials
Likelihood Methods
The Gibbs Sampler and MCMC Methods
Rejection Sampling and Importance Sampling Methods
Numerical Integration and the Gauss–Hermite Quadrature Method
Optimization Methods and the Newton–Raphson Algorithm
Bootstrap Methods
Matrix Algebra and Vector Differential Calculus
References
Index
Abstract
Author Bio(s)
Lang Wu is an associate professor in the Department of Statistics at the University of British Columbia in Vancouver, Canada.
Editorial Reviews
This book could serve as a text for an advanced course at the Ph.D. level and as a reference to analysts who are familiar with basic statistical methodology for mixed effects models.
—Tena I. Katsaounis, Technometrics, November 2011
What I was most impressed by was the sheer breadth of complex models considered. Furthermore, unlike much of the research in the area, the book examines each of the complications, not merely in isolation, but in various combinations. … Considering the complexity of some of these models, the fact that the book does a good job of describing how to fit them in a clear manner is noteworthy. … The book is clear and lucidly written. It is set at an appropriate level for graduates and should be accessible to practitioners with at least some knowledge of mixed model methodology. It should also be of interest to researchers who might want to learn different modelling techniques.
—John T. Ormerod, Statistics in Medicine, 2011, 30
… as an introduction to what it says in the title of the book, the author has done an excellent job—the coverage is pretty comprehensive, detailed without too much mathematical technicality, and (most importantly) readable. I believe that it will become a useful reference in many libraries, personal and public.
—International Statistical Review (2010), 78, 3
