Linear and Generalized Linear Mixed Models and Their Applications

ISBN-10: 0387479414
ISBN-13: 9780387479415
Edition: 2007
Authors: Jiming Jiang
List price: $169.00 Buy it from $69.14
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Description: Aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis, this book covers two major classes of mixed effects models, linear mixed models and generalised linear mixed models, with  More...

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Book details

List price: $169.00
Copyright year: 2007
Publisher: Springer
Publication date: 3/9/2007
Binding: Hardcover
Pages: 257
Size: 6.25" wide x 9.50" long x 0.50" tall
Weight: 1.100
Language: English

Aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis, this book covers two major classes of mixed effects models, linear mixed models and generalised linear mixed models, with the intention of offering an up-to-date account of theory and methods.

Preface
Linear Mixed Models: Part I
Introduction
Effect of Air Pollution Episodes on Children
Prediction of Maize Single-Cross Performance
Small Area Estimation of Income
Types of Linear Mixed Models
Gaussian Mixed Models
Non-Gaussian Linear Mixed Models
Estimation in Gaussian Models
Maximum Likelihood
Restricted Maximum Likelihood
Estimation in Non-Gaussian Models
Quasi-Likelihood Method
Partially Observed Information
Iterative Weighted Least Squares
Jackknife Method
Other Methods of Estimation
Analysis of Variance Estimation
Minimum Norm Quadratic Unbiased Estimation
Notes on Computation and Software
Notes on Computation
Notes on Software
Real-Life Data Examples
Analysis of Birth Weights of Lambs
Analysis of Hip Replacements Data
Further Results and Technical Notes
Exercises
Linear Mixed Models: Part II
Tests in Linear Mixed Models
Tests in Gaussian Mixed Models
Tests in Non-Gaussian Linear Mixed Models
Confidence Intervals in Linear Mixed Models
Confidence Intervals in Gaussian Mixed Models
Confidence Intervals in Non-Gaussian Linear Mixed Models
Prediction
Prediction of Mixed Effect
Prediction of Future Observation
Model Checking and Selection
Model Diagnostics
Model Selection
Bayesian Inference
Inference about Variance Components
Inference about Fixed and Random Effects
Real-Life Data Examples
Analysis of the Birth Weights of Lambs (Continued)
The Baseball Example
Further Results and Technical Notes
Exercises
Generalized Linear Mixed Models: Part I
Introduction
Generalized Linear Mixed Models
Real-Life Data Examples
The Salamander Mating Experiments
A Log-Linear Mixed Model for Seizure Counts
Small Area Estimation of Mammography Rates
Likelihood Function under GLMM
Approximate Inference
Laplace Approximation
Penalized Quasi-Likelihood Estimation
Tests of Zero Variance Components
Maximum Hierarchical Likelihood
Prediction of Random Effects
Joint Estimation of Fixed and Random Effects
Empirical Best Prediction
A Simulated Example
Further Results and Technical Notes
More on NLGSA
Asymptotic Properties of PQWLS Estimators
MSE of EBP
MSPE of the Model-Assisted EBP
Exercises
Generalized Linear Mixed Models: Part II
Likelihood-Based Inference
A Monte Carlo EM Algorithm for Binary Data
Extensions
MCEM with I.I.D. Sampling
Automation
Maximization by Parts
Bayesian Inference
Estimating Equations
Generalized Estimating Equations (GEE)
Iterative Estimating Equations
Method of Simulated Moments
Robust Estimation in GLMM
GLMM Selection
A General Principle for Model Selection
A Simulated Example
Real-Life Data Examples
Fetal Mortality in Mouse Litters
Analysis of Ge Genotype Data: An Application of the Fence Method
The Salamander-Mating Experiments: Various Applications of GLMM
Further Results and Technical Notes
Proof of Theorem 4.3
Linear Convergence and Asymptotic Properties of IEE
Incorporating Informative Missing Data in IEE
Consistency of MSM Estimator
Asymptotic Properties of First and Second-Step Estimators
Further Results of the Fence Method
Exercises
List of Notations
Matrix Algebra
Kronecker Products
Matrix Differentiation
Projection
Generalized Inverse
Decompositions of Matrices
The Eigenvalue Perturbation Theory
Some Results in Statistics
Multivariate Normal Distribution
Quadratic Forms
Op and op
Convolution
Exponential Family and Generalized Linear Models
References
Index

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