Mixed Effects Models for Complex Data

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 topicsSubsequent 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 materialIn 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.

Lang Wu is an associate professor in the Department of Statistics at the University of British Columbia in Vancouver, Canada.

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