Mixed Effects Models for Complex Data: 1st Edition (Hardback) book cover

Mixed Effects Models for Complex Data

1st Edition

By Lang Wu

Chapman and Hall/CRC

440 pages | 22 B/W Illus.

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pub: 2009-11-11
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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.


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

Table of Contents



Longitudinal Data and Clustered Data

Some Examples

Regression Models

Mixed Effects Models

Complex or Incomplete Data


Outline and Notation

Mixed Effects Models


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


Missing Data, Measurement Errors, and Outliers


Missing Data Mechanisms and Ignorability

General Methods for Missing Data

EM Algorithms

Multiple Imputation

General Methods for Measurement Errors

General Methods for Outliers


Mixed Effects Models with Missing Data


Mixed Effects Models with Missing Covariates

Approximate Methods

Mixed Effects Models with Missing Responses

Multiple Imputation Methods

Computational Strategies


Mixed Effects Models with Covariate Measurement Errors


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


Mixed Effects Models with Censored Responses

Mixed Effects Models with Censoring and Measurement Errors

Mixed Effects Models with Censoring and Missing Data


Survival Mixed Effects (Frailty) Models


Survival Models

Frailty Models

Survival and Frailty Models with Missing Covariates

Frailty Models with Measurement Errors

Joint Modeling Longitudinal and Survival Data


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


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)


Marginal Models

Estimating Equations with Incomplete Data


Bayesian Mixed Effects Models


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




About the Author/Editors

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

About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General