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.