Generalized, Linear, and Mixed Models / Edition 2

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Overview

This book provides a unified treatment of the use of mixed models for analyzing correlated data. Models for non-normal data, i.e. binary or count data, and generalized linear and nonlinear models are described and illustrated. The first few chapters of the book introduce all the major ideas in a context that will be familiar to most students of statistics. This text provides an accessible treatment of many of the newer statistical models for correlated, non-normally distributed data. The book's unified treatment addresses the needs of applications-oriented users of statistical packages and also graduate students in statistics.

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Editorial Reviews

From the Publisher
"I strongly recommend…[it] for inclusion in math and statistics libraries and in the personal libraries of professional statisticians." (Journal of the American Statistical Association, December 2006)

"…well written and suitable to be a textbook…I enjoyed reading this book and recommend it highly to statisticians." (Journal of Statistical Computation and Simulation, January 2006)

"This text is to be highly recommended as one that provides a modern perspective on fitting models to data." (Short Book Reviews, Vol. 21, No. 2, August 2001)

"For graduate students and statisticians, McCulloch and Searle begin by reviewing the basics of linear models and linear mixed models..." (SciTech Book News, Vol. 25, No. 4, December 2001)

"...a very good reference book." (Zentralblatt MATH, Vol. 964, 2001/14)

"...another fine contribution to the statistics literature from these respected authors..." (Technometrics, Vol. 45, No. 1, February 2003)

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Product Details

Meet the Author

Charles E. McCulloch, PhD, is Professor and Head of theDivision of Biostatistics in the School of Medicine at theUniversity of California, San Francisco. A Fellow of the AmericanStatistical Association, Dr. McCulloch is the author of numerouspublished articles in the areas of longitudinal data analysis,generalized linear mixed models, and latent class models and theirapplications.

Shayle R. Searle, PhD, is Professor Emeritus in theDepartment of Biological Statistics and Computational Biology atCornell University. Dr. Searle is the author of LinearModels, Linear Models for Unbalanced Data, MatrixAlgebra Useful for Statistics, and Variance Components,all published by Wiley.

John M. Neuhaus, PhD, is Professor of Biostatistics inthe School of Medicine at the University of California, SanFrancisco. A Fellow of the American Statistical Association and theRoyal Statistical Society, Dr. Neuhaus has authored or coauthorednumerous journal articles on statistical methods for analyzingcorrelated response data and assessments on the effects ofstatistical model misspecification.

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Table of Contents

Preface.

Preface to the First Edition.

1. Introduction.

1.1 Models.

1.2 Factors, Levels, Cells, Effects And Data.

1.3 Fixed Effects Models.

1.4 Random Effects Models.

1.5 Linear Mixed Models (Lmms).

1.6 Fixed Or Random?

1.7 Inference.

1.8 Computer Software.

1.9 Exercises.

2. One-Way Classifications.

2.1 Normality And Fixed Effects.

2.2 Normality, Random Effects And MLE.

2.3 Normality, Random Effects And REM1.

2.4 More On Random Effects And Normality.

2.5 Binary Data: Fixed Effects.

2.6 Binary Data: Random Effects.

2.7 Computing.

2.8 Exercises.

3. Single-Predictor Regression.

3.1 Introduction.

3.2 Normality: Simple Linear Regression.

3.3 Normality: A Nonlinear Model.

3.4 Transforming Versus Linking.

3.5 Random Intercepts: Balanced Data.

3.6 Random Intercepts: Unbalanced Data.

3.7 Bernoulli - Logistic Regression.

3.8 Bernoulli - Logistic With Random Intercepts.

3.9 Exercises.

4. Linear Models (LMs).

4.1 A General Model.

4.2 A Linear Model For Fixed Effects.

4.3 Mle Under Normality.

4.4 Sufficient Statistics.

4.5 Many Apparent Estimators.

4.6 Estimable Functions.

4.7 A Numerical Example.

4.8 Estimating Residual Variance.

4.9 Comments On The 1- And 2-Way Classifications.

4.10 Testing Linear Hypotheses.

4.11 T-Tests And Confidence Intervals.

4.12 Unique Estimation Using Restrictions.

4.13 Exercises.

5. Generalized Linear Models (GLMs).

5.1 Introduction.

5.2 Structure Of The Model.

5.3 Transforming Versus Linking.

5.4 Estimation By Maximum Likelihood.

5.5 Tests Of Hypotheses.

5.6 Maximum Quasi-Likelihood.

5.7 Exercises.

6. Linear Mixed Models (LMMs).

6.1 A General Model.

6.2 Attributing Structure To VAR(y).

6.3 Estimating Fixed Effects For V Known.

6.4 Estimating Fixed Effects For V Unknown.

6.5 Predicting Random Effects For V Known.

6.6 Predicting Random Effects For V Unknown.

6.7 Anova Estimation Of Variance Components.

6.8 Maximum Likelihood (Ml) Estimation.

6.9 Restricted Maximum Likelihood (REMl).

6.10 Notes And Extensions.

6.11 Appendix For Chapter 6.

6.12 Exercises.

7. Generalized Linear Mixed Models.

7.1 Introduction.

7.2 Structure Of The Model.

7.3 Consequences Of Having Random Effects.

7.4 Estimation By Maximum Likelihood.

7.5 Other Methods Of Estimation.

7.6 Tests Of Hypotheses.

7.7 Illustration: Chestnut Leaf Blight.

7.8 Exercises.

8. Models for Longitudinal data.

8.1 Introduction.

8.2 A Model For Balanced Data.

8.3 A Mixed Model Approach.

8.4 Random Intercept And Slope Models.

8.5 Predicting Random Effects.

8.6 Estimating Parameters.

8.7 Unbalanced Data.

8.8 Models For Non-Normal Responses.

8.9 A Summary Of Results.

8.10 Appendix.

8.11 Exercises.

9. Marginal Models.

9.1 Introduction.

9.2 Examples Of Marginal Regression Models.

9.3 Generalized Estimating Equations.

9.4 Contrasting Marginal And Conditional Models.

9.5 Exercises.

10. Multivariate Models.

10.1 Introduction.

10.2 Multivariate Normal Outcomes.

10.3 Non-Normally Distributed Outcomes.

10.4 Correlated Random Effects.

10.5 Likelihood Based Analysis.

10.6 Example: Osteoarthritis Initiative.

10.7 Notes And Extensions.

10.8 Exercises.

11. Nonlinear Models.

11.1 Introduction.

11.2 Example: Corn Photosynthesis.

11.3 Pharmacokinetic Models.

11.4 Computations For Nonlinear Mixed Models.

11.5 Exercises.

12. Departures From Assumptions.

12.1 Introduction.

12.2 Misspecifications Of Conditional Model For Response.

12.3 Misspecifications Of Random Effects Distribution.

12.4 Methods To Diagnose And Correct For Misspecifications.

12.5 Exercises.

13. Prediction.

13.1 Introduction.

13.2 Best Prediction (BP).

13.3 Best Linear Prediction (BLP).

13.4 Linear Mixed Model Prediction (BLUP).

13.5 Required Assumptions.

13.6 Estimated Best Prediction.

13.7 Henderson’s Mixed Model Equations.

13.8 Appendix.

13.9 Exercises.

14. Computing.

14.1 Introduction.

14.2 Computing Ml Estimates For LMMs.

14.3 Computing Ml Estimates For GLMMs.

14.4 Penalized Quasi-Likelihood And Laplace.

14.5 Exercises.

Appendix M: Some Matrix Results.

M.1 Vectors And Matrices Of Ones.

M.2 Kronecker (Or Direct) Products.

M.3 A Matrix Notation.

M.4 Generalized Inverses.

M.5 Differential Calculus.

Appendix S: Some Statistical Results.

S.1 Moments.

S.2 Normal Distributions.

S.3 Exponential Families.

S.4 Maximum Likelihood.

S.5 Likelihood Ratio Tests.

S.6 MLE Under Normality.

References.

Index.

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