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Linear and generalized linear mixed models and their applications / Jiming Jiang.

By: Jiang, Jiming.
Material type: TextTextSeries: Springer series in statistics.Publisher: New York ; London : Springer, c2007Description: xiv, 257 p. : ill. ; 24 cm.ISBN: 9780387479415 (acidfree paper); 0387479414 (acidfree paper); 9780387479460 (eISBN); 0387479465 (eISBN).Subject(s): Mathematical statistics | Linear models (Statistics)DDC classification: 519.5 Online resources: Publisher description | WorldCat details | E-book Fulltext
Contents:
Table of contents Cover -- TOC$Contents -- Preface -- CH$1 Linear Mixed Models: Part I -- 1.1 Introduction -- 1.1.1 Effect of Air Pollution Episodes on Children -- 1.1.2 Prediction of Maize Single-Cross Performance -- 1.1.3 Small Area Estimation of Income -- 1.2 Types of Linear Mixed Models -- 1.2.1 Gaussian Mixed Models -- 1.2.2 Non-Gaussian Linear Mixed Models -- 1.3 Estimation in Gaussian Models -- 1.3.1 Maximum Likelihood -- 1.3.2 Restricted Maximum Likelihood -- 1.4 Estimation in Non-Gaussian Models -- 1.4.1 Quasi-Likelihood Method -- 1.4.2 Partially Observed Information -- 1.4.3 Iterative Weighted Least Squares -- 1.4.4 Jackknife Method -- 1.5 Other Methods of Estimation -- 1.5.1 Analysis of Variance Estimation -- 1.5.2 Minimum Norm Quadratic Unbiased Estimation -- 1.6 Notes on Computation and Software -- 1.6.1 Notes on Computation -- 1.6.2 Notes on Software -- 1.7 Real-Life Data Examples -- 1.7.1 Analysis of Birth Weights of Lambs -- 1.7.2 Analysis of Hip Replacements Data -- 1.8 Further Results and Technical Notes -- 1.9 Exercises -- CH$2 Linear Mixed Models: Part II -- 2.1 Tests in Linear Mixed Models -- 2.1.1 Tests in Gaussian Mixed Models -- 2.1.2 Tests in Non-Gaussian Linear Mixed Models -- 2.2 Confidence Intervals in Linear Mixed Models -- 2.2.1 Confidence Intervals in Gaussian Mixed Models -- 2.2.2 Confidence Intervals in Non-Gaussian Linear Mixed Models -- 2.3 Prediction -- 2.3.1 Prediction of Mixed Effect -- 2.3.2 Prediction of Future Observation -- 2.4 Model Checking and Selection -- 2.4.1 Model Diagnostics -- 2.4.2 Model Selection -- 2.5 Bayesian Inference -- 2.5.1 Inference about Variance Components -- 2.5.2 Inference about Fixed and Random Effects -- 2.6 Real-Life Data Examples -- 2.6.1 Analysis of the Birth Weights of Lambs (Continued) -- 2.6.2 The Baseball Example -- 2.7 Further Results and Technical Notes -- 2.8 Exercises -- CH$3 Generalized Linear Mixed Models: Part I -- 3.1 Introduction -- 3.2 Generalized Linear Mixed Models -- 3.3 Real-Life Data Examples -- 3.3.1 The Salamander Mating Experiments -- 3.3.2 A Log-Linear Mixed Model for Seizure Counts -- 3.3.3 Small Area Estimation of Mammography Rates -- 3.4 Likelihood Function under GLMM -- 3.5 Approximate Inference -- 3.5.1 Laplace Approximation -- 3.5.2 Penalized Quasi-Likelihood Estimation -- 3.5.3 Tests of Zero Variance Components -- 3.5.4 Maximum Hierarchical Likelihood -- 3.6 Prediction of Random Effects -- 3.6.1 Joint Estimation of Fixed and Random Effects -- 3.6.2 Empirical Best Prediction -- 3.6.3 A Simulated Example -- 3.7 Further Results and Technical Notes -- 3.7.1 More on NLGSA -- 3.7.2 Asymptotic Properties of PQWLS Estimators -- 3.7.3 MSE of EBP -- 3.7.4 MSPE of the Model-Assisted EBP -- 3.8 Exercises -- CH$4 Generalized Linear Mixed Models: Part II -- 4.1 Likelihood-Based Inference -- 4.1.1 A Monte Carlo EM Algorithm for Binary Data -- 4.1.2 Extensions -- 4&#
Summary: Summary: "This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models, and it presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it has included recently developed methods, such as mixed Read more...
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Includes bibliographical references and index.

Table of contents Cover --
TOC$Contents --
Preface --
CH$1 Linear Mixed Models: Part I --
1.1 Introduction --
1.1.1 Effect of Air Pollution Episodes on Children --
1.1.2 Prediction of Maize Single-Cross Performance --
1.1.3 Small Area Estimation of Income --
1.2 Types of Linear Mixed Models --
1.2.1 Gaussian Mixed Models --
1.2.2 Non-Gaussian Linear Mixed Models --
1.3 Estimation in Gaussian Models --
1.3.1 Maximum Likelihood --
1.3.2 Restricted Maximum Likelihood --
1.4 Estimation in Non-Gaussian Models --
1.4.1 Quasi-Likelihood Method --
1.4.2 Partially Observed Information --
1.4.3 Iterative Weighted Least Squares --
1.4.4 Jackknife Method --
1.5 Other Methods of Estimation --
1.5.1 Analysis of Variance Estimation --
1.5.2 Minimum Norm Quadratic Unbiased Estimation --
1.6 Notes on Computation and Software --
1.6.1 Notes on Computation --
1.6.2 Notes on Software --
1.7 Real-Life Data Examples --
1.7.1 Analysis of Birth Weights of Lambs --
1.7.2 Analysis of Hip Replacements Data --
1.8 Further Results and Technical Notes --
1.9 Exercises --
CH$2 Linear Mixed Models: Part II --
2.1 Tests in Linear Mixed Models --
2.1.1 Tests in Gaussian Mixed Models --
2.1.2 Tests in Non-Gaussian Linear Mixed Models --
2.2 Confidence Intervals in Linear Mixed Models --
2.2.1 Confidence Intervals in Gaussian Mixed Models --
2.2.2 Confidence Intervals in Non-Gaussian Linear Mixed Models --
2.3 Prediction --
2.3.1 Prediction of Mixed Effect --
2.3.2 Prediction of Future Observation --
2.4 Model Checking and Selection --
2.4.1 Model Diagnostics --
2.4.2 Model Selection --
2.5 Bayesian Inference --
2.5.1 Inference about Variance Components --
2.5.2 Inference about Fixed and Random Effects --
2.6 Real-Life Data Examples --
2.6.1 Analysis of the Birth Weights of Lambs (Continued) --
2.6.2 The Baseball Example --
2.7 Further Results and Technical Notes --
2.8 Exercises --
CH$3 Generalized Linear Mixed Models: Part I --
3.1 Introduction --
3.2 Generalized Linear Mixed Models --
3.3 Real-Life Data Examples --
3.3.1 The Salamander Mating Experiments --
3.3.2 A Log-Linear Mixed Model for Seizure Counts --
3.3.3 Small Area Estimation of Mammography Rates --
3.4 Likelihood Function under GLMM --
3.5 Approximate Inference --
3.5.1 Laplace Approximation --
3.5.2 Penalized Quasi-Likelihood Estimation --
3.5.3 Tests of Zero Variance Components --
3.5.4 Maximum Hierarchical Likelihood --
3.6 Prediction of Random Effects --
3.6.1 Joint Estimation of Fixed and Random Effects --
3.6.2 Empirical Best Prediction --
3.6.3 A Simulated Example --
3.7 Further Results and Technical Notes --
3.7.1 More on NLGSA --
3.7.2 Asymptotic Properties of PQWLS Estimators --
3.7.3 MSE of EBP --
3.7.4 MSPE of the Model-Assisted EBP --
3.8 Exercises --
CH$4 Generalized Linear Mixed Models: Part II --
4.1 Likelihood-Based Inference --
4.1.1 A Monte Carlo EM Algorithm for Binary Data --
4.1.2 Extensions --
4&#

Summary:
"This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models, and it presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it has included recently developed methods, such as mixed Read more...

Applied Statistics

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