Mixed Effects Models for Complex Data

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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