[下载]Linear and Generalized Linear Mixed Models and Their Applications

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[下载]Linear and Generalized Linear Mixed Models and Their Applications
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<P>这本书很有特色的</P>
<P>作者Jiming Jiang（统计的牛人呀）<BR>书名Linear and Generalized Linear Mixed Models  and Their Applications</P>
<P>出版年代2007</P>
<P>出版商 Springer</P>
<P>页数268</P>
<P>1 Linear Mixed Models: Part I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1<BR>1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1<BR>1.1.1 Effect of Air Pollution Episodes on Children . . . . . . . . . . 2<BR>1.1.2 Prediction of Maize Single-Cross Performance . . . . . . . . . 3<BR>1.1.3 Small Area Estimation of Income . . . . . . . . . . . . . . . . . . . . 3<BR>1.2 Types of Linear Mixed Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4<BR>1.2.1 Gaussian Mixed Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4<BR>1.2.2 Non-Gaussian Linear Mixed Models . . . . . . . . . . . . . . . . . 8<BR>1.3 Estimation in Gaussian Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9<BR>1.3.1 Maximum Likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9<BR>1.3.2 Restricted Maximum Likelihood. . . . . . . . . . . . . . . . . . . . . 12<BR>1.4 Estimation in Non-Gaussian Models . . . . . . . . . . . . . . . . . . . . . . . 15<BR>1.4.1 Quasi-Likelihood Method. . . . . . . . . . . . . . . . . . . . . . . . . . . 16<BR>1.4.2 Partially Observed Information. . . . . . . . . . . . . . . . . . . . . . 18<BR>1.4.3 Iterative Weighted Least Squares . . . . . . . . . . . . . . . . . . . . 20<BR>1.4.4 Jackknife Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24<BR>1.5 Other Methods of Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25<BR>1.5.1 Analysis of Variance Estimation . . . . . . . . . . . . . . . . . . . . . 25<BR>1.5.2 Minimum Norm Quadratic Unbiased Estimation . . . . . . 28<BR>1.6 Notes on Computation and Software . . . . . . . . . . . . . . . . . . . . . . . 29<BR>1.6.1 Notes on Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29<BR>1.6.2 Notes on Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33<BR>1.7 Real-Life Data Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34<BR>1.7.1 Analysis of Birth Weights of Lambs . . . . . . . . . . . . . . . . . . 35<BR>1.7.2 Analysis of Hip Replacements Data . . . . . . . . . . . . . . . . . . 37<BR>1.8 Further Results and Technical Notes . . . . . . . . . . . . . . . . . . . . . . . 39<BR>1.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48</P>
<P>2 Linear Mixed Models: Part II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51<BR>2.1 Tests in Linear Mixed Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51<BR>2.1.1 Tests in Gaussian Mixed Models . . . . . . . . . . . . . . . . . . . . 51<BR>2.1.2 Tests in Non-Gaussian Linear Mixed Models . . . . . . . . . . 56<BR>2.2 Confidence Intervals in Linear Mixed Models . . . . . . . . . . . . . . . . 66<BR>2.2.1 Confidence Intervals in Gaussian Mixed Models . . . . . . . 66<BR>2.2.2 Confidence Intervals in Non-Gaussian Linear Mixed<BR>Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72<BR>2.3 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74<BR>2.3.1 Prediction of Mixed Effect . . . . . . . . . . . . . . . . . . . . . . . . . . 74<BR>2.3.2 Prediction of Future Observation . . . . . . . . . . . . . . . . . . . . 80<BR>2.4 Model Checking and Selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88<BR>2.4.1 Model Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88<BR>2.4.2 Model Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93<BR>2.5 Bayesian Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99<BR>2.5.1 Inference about Variance Components . . . . . . . . . . . . . . . 100<BR>2.5.2 Inference about Fixed and Random Effects . . . . . . . . . . . 101<BR>2.6 Real-Life Data Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102</P>
<P>2.6.1 Analysis of the Birth Weights of Lambs (Continued) . . . 102<BR>2.6.2 The Baseball Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103<BR>2.7 Further Results and Technical Notes . . . . . . . . . . . . . . . . . . . . . . . 105<BR>2.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113<BR>3 Generalized Linear Mixed Models: Part I . . . . . . . . . . . . . . . . . . 119<BR>3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119<BR>3.2 Generalized Linear Mixed Models . . . . . . . . . . . . . . . . . . . . . . . . . 120<BR>3.3 Real-Life Data Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122<BR>3.3.1 The Salamander Mating Experiments . . . . . . . . . . . . . . . . 122<BR>3.3.2 A Log-Linear Mixed Model for Seizure Counts . . . . . . . . 124<BR>3.3.3 Small Area Estimation of Mammography Rates . . . . . . . 124<BR>3.4 Likelihood Function under GLMM. . . . . . . . . . . . . . . . . . . . . . . . . 125<BR>3.5 Approximate Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127<BR>3.5.1 Laplace Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127<BR>3.5.2 Penalized Quasi-Likelihood Estimation . . . . . . . . . . . . . . . 128<BR>3.5.3 Tests of Zero Variance Components . . . . . . . . . . . . . . . . . . 132<BR>3.5.4 Maximum Hierarchical Likelihood . . . . . . . . . . . . . . . . . . . 134<BR>3.6 Prediction of Random Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136<BR>3.6.1 Joint Estimation of Fixed and Random Effects . . . . . . . . 136<BR>3.6.2 Empirical Best Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . 142<BR>3.6.3 A Simulated Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149<BR>3.7 Further Results and Technical Notes . . . . . . . . . . . . . . . . . . . . . . . 151<BR>3.7.1 More on NLGSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151<BR>3.7.2 Asymptotic Properties of PQWLS Estimators . . . . . . . . . 152<BR>3.7.3 MSE of EBP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155<BR>3.7.4 MSPE of the Model-Assisted EBP . . . . . . . . . . . . . . . . . . . 158</P>
<P>3.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161<BR>4 Generalized Linear Mixed Models: Part II . . . . . . . . . . . . . . . . . 163<BR>4.1 Likelihood-Based Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163<BR>4.1.1 A Monte Carlo EM Algorithm for Binary Data . . . . . . . . 164<BR>4.1.2 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167<BR>4.1.3 MCEM with I.I.D. Sampling . . . . . . . . . . . . . . . . . . . . . . . . 170<BR>4.1.4 Automation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171<BR>4.1.5 Maximization by Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174<BR>4.1.6 Bayesian Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178<BR>4.2 Estimating Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183<BR>4.2.1 Generalized Estimating Equations (GEE) . . . . . . . . . . . . 184<BR>4.2.2 Iterative Estimating Equations . . . . . . . . . . . . . . . . . . . . . . 186<BR>4.2.3 Method of Simulated Moments . . . . . . . . . . . . . . . . . . . . . . 190<BR>4.2.4 Robust Estimation in GLMM . . . . . . . . . . . . . . . . . . . . . . . 196<BR>4.3 GLMM Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199<BR>4.3.1 A General Principle for Model Selection . . . . . . . . . . . . . . 200<BR>4.3.2 A Simulated Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203<BR>4.4 Real-Life Data Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205<BR>4.4.1 Fetal Mortality in Mouse Litters . . . . . . . . . . . . . . . . . . . . 205<BR>4.4.2 Analysis of Gc Genotype Data: An Application of the<BR>Fence Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207</P>
<P>4.4.3 The Salamander-Mating Experiments: Various<BR>Applications of GLMM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209<BR>4.5 Further Results and Technical Notes . . . . . . . . . . . . . . . . . . . . . . . 214<BR>4.5.1 Proof of Theorem 4.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214<BR>4.5.2 Linear Convergence and Asymptotic Properties<BR>of IEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214<BR>4.5.3 Incorporating Informative Missing Data in IEE . . . . . . . 217<BR>4.5.4 Consistency of MSM Estimator . . . . . . . . . . . . . . . . . . . . . 218<BR>4.5.5 Asymptotic Properties of First and<BR>Second-Step Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221<BR>4.5.6 Further Results of the Fence Method. . . . . . . . . . . . . . . . . 225<BR>4.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229<BR>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230<BR>A List of Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231<BR>B Matrix Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233<BR>B.1 Kronecker Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233<BR>B.2 Matrix Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233<BR>B.3 Projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234<BR>B.4 Generalized Inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235<BR>B.5 Decompositions of Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235<BR>B.6 The Eigenvalue Perturbation Theory . . . . . . . . . . . . . . . . . . . . . . . 236</P>
<P>C Some Results in Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237<BR>C.1 Multivariate Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 237<BR>C.2 Quadratic Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237<BR>C.3 OP and oP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238<BR>C.4 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238<BR>C.5 Exponential Family and Generalized Linear Models . . . . . . . . . . 239<BR>References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241<BR>Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255</P>

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