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, whilean accessible treatment of many of the newer statistical models for correlated, non-normally distributed data is also provided. The book's unified approachaddresses the needs of applications-oriented users of statistical packages and graduate students in statistics alike. INDICE: Preface. 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 ForFixed 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 VersusLinking. 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 AnovaEstimation 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. GlMMs. 7.1 Introduction. 7.2 Structure OfThe 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. 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. 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 HendersonS 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.
- ISBN: 978-0-470-07371-1
- Editorial: John Wiley & Sons
- Encuadernacion: Cartoné
- Páginas: 416
- Fecha Publicación: 04/07/2008
- Nº Volúmenes: 1
- Idioma: Inglés