
Linear and Generalized Linear Mixed Models and Their Applications
By: Jiming Jiang
Hardcover | 1 January 2007
At a Glance
276 Pages
23.39 x 15.6 x 1.75
Hardcover
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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 offersan 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 ... ." (Soren Feodor Nielsen, Journal of Applied Statistics, Vol. 35 (4), 2008)
| Preface | p. VII |
| Linear Mixed Models: Part I | p. 1 |
| Introduction | p. 1 |
| Effect of Air Pollution Episodes on Children | p. 2 |
| Prediction of Maize Single-Cross Performance | p. 3 |
| Small Area Estimation of Income | p. 3 |
| Types of Linear Mixed Models | p. 4 |
| Gaussian Mixed Models | p. 4 |
| Non-Gaussian Linear Mixed Models | p. 8 |
| Estimation in Gaussian Models | p. 9 |
| Maximum Likelihood | p. 9 |
| Restricted Maximum Likelihood | p. 12 |
| Estimation in Non-Gaussian Models | p. 15 |
| Quasi-Likelihood Method | p. 16 |
| Partially Observed Information | p. 18 |
| Iterative Weighted Least Squares | p. 20 |
| Jackknife Method | p. 24 |
| Other Methods of Estimation | p. 25 |
| Analysis of Variance Estimation | p. 25 |
| Minimum Norm Quadratic Unbiased Estimation | p. 28 |
| Notes on Computation and Software | p. 29 |
| Notes on Computation | p. 29 |
| Notes on Software | p. 33 |
| Real-Life Data Examples | p. 34 |
| Analysis of Birth Weights of Lambs | p. 35 |
| Analysis of Hip Replacements Data | p. 37 |
| Further Results and Technical Notes | p. 39 |
| Exercises | p. 48 |
| Linear Mixed Models: Part II | p. 51 |
| Tests in Linear Mixed Models | p. 51 |
| Tests in Gaussian Mixed Models | p. 51 |
| Tests in Non-Gaussian Linear Mixed Models | p. 56 |
| Confidence Intervals in Linear Mixed Models | p. 66 |
| Confidence Intervals in Gaussian Mixed Models | p. 66 |
| Confidence Intervals in Non-Gaussian Linear Mixed Models | p. 72 |
| Prediction | p. 74 |
| Prediction of Mixed Effect | p. 74 |
| Prediction of Future Observation | p. 80 |
| Model Checking and Selection | p. 88 |
| Model Diagnostics | p. 88 |
| Model Selection | p. 93 |
| Bayesian Inference | p. 99 |
| Inference about Variance Components | p. 100 |
| Inference about Fixed and Random Effects | p. 101 |
| Real-Life Data Examples | p. 102 |
| Analysis of the Birth Weights of Lambs (Continued) | p. 102 |
| The Baseball Example | p. 103 |
| Further Results and Technical Notes | p. 105 |
| Exercises | p. 113 |
| Generalized Linear Mixed Models: Part I | p. 119 |
| Introduction | p. 119 |
| Generalized Linear Mixed Models | p. 120 |
| Real-Life Data Examples | p. 122 |
| The Salamander Mating Experiments | p. 122 |
| A Log-Linear Mixed Model for Seizure Counts | p. 124 |
| Small Area Estimation of Mammography Rates | p. 124 |
| Likelihood Function under GLMM | p. 125 |
| Approximate Inference | p. 127 |
| Laplace Approximation | p. 127 |
| Penalized Quasi-Likelihood Estimation | p. 128 |
| Tests of Zero Variance Components | p. 132 |
| Maximum Hierarchical Likelihood | p. 134 |
| Prediction of Random Effects | p. 136 |
| Joint Estimation of Fixed and Random Effects | p. 136 |
| Empirical Best Prediction | p. 142 |
| A Simulated Example | p. 149 |
| Further Results and Technical Notes | p. 151 |
| More on NLGSA | p. 151 |
| Asymptotic Properties of PQWLS Estimators | p. 152 |
| MSE of EBP | p. 155 |
| MSPE of the Model-Assisted EBP | p. 158 |
| Exercises | p. 161 |
| Generalized Linear Mixed Models: Part II | p. 163 |
| Likelihood-Based Inference | p. 163 |
| A Monte Carlo EM Algorithm for Binary Data | p. 164 |
| Extensions | p. 167 |
| MCEM with I.I.D. Sampling | p. 170 |
| Automation | p. 171 |
| Maximization by Parts | p. 174 |
| Bayesian Inference | p. 178 |
| Estimating Equations | p. 183 |
| Generalized Estimating Equations (GEE) | p. 184 |
| Iterative Estimating Equations | p. 186 |
| Method of Simulated Moments | p. 190 |
| Robust Estimation in GLMM | p. 196 |
| GLMM Selection | p. 199 |
| A General Principle for Model Selection | p. 200 |
| A Simulated Example | p. 203 |
| Real-Life Data Examples | p. 205 |
| Fetal Mortality in Mouse Litters | p. 205 |
| Analysis of Ge Genotype Data: An Application of the Fence Method | p. 207 |
| The Salamander-Mating Experiments: Various Applications of GLMM | p. 209 |
| Further Results and Technical Notes | p. 214 |
| Proof of Theorem 4.3 | p. 214 |
| Linear Convergence and Asymptotic Properties of IEE | p. 214 |
| Incorporating Informative Missing Data in IEE | p. 217 |
| Consistency of MSM Estimator | p. 218 |
| Asymptotic Properties of First and Second-Step Estimators | p. 221 |
| Further Results of the Fence Method | p. 225 |
| Exercises | p. 229 |
| List of Notations | p. 231 |
| Matrix Algebra | p. 233 |
| Kronecker Products | p. 233 |
| Matrix Differentiation | p. 233 |
| Projection | p. 234 |
| Generalized Inverse | p. 235 |
| Decompositions of Matrices | p. 235 |
| The Eigenvalue Perturbation Theory | p. 236 |
| Some Results in Statistics | p. 237 |
| Multivariate Normal Distribution | p. 237 |
| Quadratic Forms | p. 237 |
| Op and op | p. 238 |
| Convolution | p. 238 |
| Exponential Family and Generalized Linear Models | p. 239 |
| References | p. 241 |
| Index | p. 255 |
| Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9780387479415
ISBN-10: 0387479414
Series: Springer Series in Statistics
Published: 1st January 2007
Format: Hardcover
Language: English
Number of Pages: 276
Audience: General Adult
Publisher: Springer Nature B.V.
Country of Publication: US
Dimensions (cm): 23.39 x 15.6 x 1.75
Weight (kg): 0.51
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