- Shopping Bag ( 0 items )
Other sellers (Hardcover)
-
All (12) from $31.45
-
New (6) from $81.91
-
Used (6) from $31.45
More About This Textbook
Overview
The book is aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis. The book is suitable for a course in a M.S. program in statistics, provided that the section of further results and technical notes in each of the first four chapters is skipped. If these four sections are included, the book may be used for a course in a Ph.D. program in statistics. A first course in mathematical statistics, the ability to use computers for data analysis, and familiarity with calculus and linear algebra are prerequisites. Additional statistical courses such as regression analysis and a good knowledge about matrices would be helpful.
About the Author:
Jiming Jiang is Professor of Statistics and Director of the Statistical Laboratory at UC-Davis
Editorial Reviews
From the Publisher
From the reviews:
"This book is an up to date description of linear mixed models, LMM, and generalized linear mixed models, GLMM. The material is complete enough to cover a course in a Ph.D. program in statistics. The contribution of this book is that of pointing and developing the inference and estimation issues for non-Gaussion LMMs." (Nicoleta Breaz, Zentrablatt MATH, 2009, 1152)
"The book deals with Gaussian and non-Gaussian linear mixed models. … This book is suitable for a course in statistics at the MSc level … . This book contains many examples, exercises and some useful appendices, making it suitable for use in statistics courses. … The book has a nice lay-out and the index make it easy to jump to a topic of interest. … A nice feature of the book are the many real-life data examples." (M. Moerbeek, Kwantitatieve Methoden, August, 2007)
"This book, which has grown out of the author's research on this area, deserves close attention. It provides a good reference source for an advanced graduate course and would prove useful for research workers who wish to learn about theoretical developments in this area...[T]his book will be a useful source for obtaining the theoreteical skills required for further developments in this area." (Youngjo Lee, Biometrics, December 2007)
"As noted by the author, there have been many new developments in mixed effects models in the past decade. This volume is intended to provide an up-to-date treatment of both theory and methods. … it is full of important results and examples, including significant contributions by the author to the treatment of mixed effects models. As a textbook, it is aimed at MS students in statistics, but includes supplementary material more suitable for PhD candidates. … be useful as such for many GLMM users." (Donald E. Myers, Technometrics, Vol. 50 (1), 2008)
"The book under review covers both LMMs and GLMMs and offers an up-to-date account of theory and methods in the analysis of the models as well as their applications in biological and the medical research, animal and human genetics, and small area estimation. The examples of applications appear near the end of each chapter. … The book is aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis." (Alexander G. Kukush, Mathematical Reviews, Issue 2007 m)
"Jiming Jiang’s book on mixed models covers a lot of material in surprisingly few pages. … On the whole, it is a rather technical book, both in terms of the mathematical level and in terms of notation … . Undoubtedly there is a lot one may learn from the book … . useful for the professional who wishes to know more about the technical results of the topic … ." (Søren Feodor Nielsen, Journal of Applied Statistics, Vol. 35 (4), 2008)
Product Details
Related Subjects
Table of Contents
Linear Mixed Models: Part I 1
Introduction 1
Effect of Air Pollution Episodes on Children 2
Prediction of Maize Single-Cross Performance 3
Small Area Estimation of Income 3
Types of Linear Mixed Models 4
Gaussian Mixed Models 4
Non-Gaussian Linear Mixed Models 8
Estimation in Gaussian Models 9
Maximum Likelihood 9
Restricted Maximum Likelihood 12
Estimation in Non-Gaussian Models 15
Quasi-Likelihood Method 16
Partially Observed Information 18
Iterative Weighted Least Squares 20
Jackknife Method 24
Other Methods of Estimation 25
Analysis of Variance Estimation 25
Minimum Norm Quadratic Unbiased Estimation 28
Notes on Computation and Software 29
Notes on Computation 29
Notes on Software 33
Real-Life Data Examples 34
Analysis of Birth Weights of Lambs 35
Analysis of Hip Replacements Data 37
Further Results and Technical Notes 39
Exercises 48
Linear Mixed Models: Part II 51
Tests in Linear Mixed Models 51
Tests in Gaussian Mixed Models 51
Tests in Non-Gaussian Linear Mixed Models 56
Confidence Intervals in Linear Mixed Models 66
Confidence Intervals in Gaussian Mixed Models 66
Confidence Intervals in Non-Gaussian Linear Mixed Models 72
Prediction 74
Prediction of Mixed Effect 74
Prediction of Future Observation 80
Model Checking and Selection 88
Model Diagnostics 88
Model Selection 93
Bayesian Inference 99
Inference about Variance Components 100
Inference about Fixed and Random Effects 101
Real-Life Data Examples 102
Analysis of the Birth Weights of Lambs (Continued) 102
The Baseball Example 103
Further Results and Technical Notes 105
Exercises 113
Generalized Linear Mixed Models: Part I 119
Introduction 119
Generalized Linear Mixed Models 120
Real-Life Data Examples 122
The Salamander Mating Experiments 122
A Log-Linear Mixed Model for Seizure Counts 124
Small Area Estimation of Mammography Rates 124
Likelihood Function under GLMM 125
Approximate Inference 127
Laplace Approximation 127
Penalized Quasi-Likelihood Estimation 128
Tests of Zero Variance Components 132
Maximum Hierarchical Likelihood 134
Prediction of Random Effects 136
Joint Estimation of Fixed and Random Effects 136
Empirical Best Prediction 142
A Simulated Example 149
Further Results and Technical Notes 151
More on NLGSA 151
Asymptotic Properties of PQWLS Estimators 152
MSE of EBP 155
MSPE of the Model-Assisted EBP 158
Exercises 161
Generalized Linear Mixed Models: Part II 163
Likelihood-Based Inference 163
A Monte Carlo EM Algorithm for Binary Data 164
Extensions 167
MCEM with I.I.D. Sampling 170
Automation 171
Maximization by Parts 174
Bayesian Inference 178
Estimating Equations 183
Generalized Estimating Equations (GEE) 184
Iterative Estimating Equations 186
Method of Simulated Moments 190
Robust Estimation in GLMM 196
GLMM Selection 199
A General Principle for Model Selection 200
A Simulated Example 203
Real-Life Data Examples 205
Fetal Mortality in Mouse Litters 205
Analysis of Ge Genotype Data: An Application of the Fence Method 207
The Salamander-Mating Experiments: Various Applications of GLMM 209
Further Results and Technical Notes 214
Proof of Theorem 4.3 214
Linear Convergence and Asymptotic Properties of IEE 214
Incorporating Informative Missing Data in IEE 217
Consistency of MSM Estimator 218
Asymptotic Properties of First and Second-Step Estimators 221
Further Results of the Fence Method 225
Exercises 229
List of Notations 231
Matrix Algebra 233
Kronecker Products 233
Matrix Differentiation 233
Projection 234
Generalized Inverse 235
Decompositions of Matrices 235
The Eigenvalue Perturbation Theory 236
Some Results in Statistics 237
Multivariate Normal Distribution 237
Quadratic Forms 237
Op and op 238
Convolution 238
Exponential Family and Generalized Linear Models 239
References 241
Index 255