| |
| |
| Preface | |
| |
| |
| |
| Linear Mixed Models: Part I | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Effect of Air Pollution Episodes on Children | |
| |
| |
| |
| Prediction of Maize Single-Cross Performance | |
| |
| |
| |
| Small Area Estimation of Income | |
| |
| |
| |
| Types of Linear Mixed Models | |
| |
| |
| |
| Gaussian Mixed Models | |
| |
| |
| |
| Non-Gaussian Linear Mixed Models | |
| |
| |
| |
| Estimation in Gaussian Models | |
| |
| |
| |
| Maximum Likelihood | |
| |
| |
| |
| Restricted Maximum Likelihood | |
| |
| |
| |
| Estimation in Non-Gaussian Models | |
| |
| |
| |
| Quasi-Likelihood Method | |
| |
| |
| |
| Partially Observed Information | |
| |
| |
| |
| Iterative Weighted Least Squares | |
| |
| |
| |
| Jackknife Method | |
| |
| |
| |
| Other Methods of Estimation | |
| |
| |
| |
| Analysis of Variance Estimation | |
| |
| |
| |
| Minimum Norm Quadratic Unbiased Estimation | |
| |
| |
| |
| Notes on Computation and Software | |
| |
| |
| |
| Notes on Computation | |
| |
| |
| |
| Notes on Software | |
| |
| |
| |
| Real-Life Data Examples | |
| |
| |
| |
| Analysis of Birth Weights of Lambs | |
| |
| |
| |
| Analysis of Hip Replacements Data | |
| |
| |
| |
| Further Results and Technical Notes | |
| |
| |
| |
| Exercises | |
| |
| |
| |
| Linear Mixed Models: Part II | |
| |
| |
| |
| Tests in Linear Mixed Models | |
| |
| |
| |
| Tests in Gaussian Mixed Models | |
| |
| |
| |
| Tests in Non-Gaussian Linear Mixed Models | |
| |
| |
| |
| Confidence Intervals in Linear Mixed Models | |
| |
| |
| |
| Confidence Intervals in Gaussian Mixed Models | |
| |
| |
| |
| Confidence Intervals in Non-Gaussian Linear Mixed Models | |
| |
| |
| |
| Prediction | |
| |
| |
| |
| Prediction of Mixed Effect | |
| |
| |
| |
| Prediction of Future Observation | |
| |
| |
| |
| Model Checking and Selection | |
| |
| |
| |
| Model Diagnostics | |
| |
| |
| |
| Model Selection | |
| |
| |
| |
| Bayesian Inference | |
| |
| |
| |
| Inference about Variance Components | |
| |
| |
| |
| Inference about Fixed and Random Effects | |
| |
| |
| |
| Real-Life Data Examples | |
| |
| |
| |
| Analysis of the Birth Weights of Lambs (Continued) | |
| |
| |
| |
| The Baseball Example | |
| |
| |
| |
| Further Results and Technical Notes | |
| |
| |
| |
| Exercises | |
| |
| |
| |
| Generalized Linear Mixed Models: Part I | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Generalized Linear Mixed Models | |
| |
| |
| |
| Real-Life Data Examples | |
| |
| |
| |
| The Salamander Mating Experiments | |
| |
| |
| |
| A Log-Linear Mixed Model for Seizure Counts | |
| |
| |
| |
| Small Area Estimation of Mammography Rates | |
| |
| |
| |
| Likelihood Function under GLMM | |
| |
| |
| |
| Approximate Inference | |
| |
| |
| |
| Laplace Approximation | |
| |
| |
| |
| Penalized Quasi-Likelihood Estimation | |
| |
| |
| |
| Tests of Zero Variance Components | |
| |
| |
| |
| Maximum Hierarchical Likelihood | |
| |
| |
| |
| Prediction of Random Effects | |
| |
| |
| |
| Joint Estimation of Fixed and Random Effects | |
| |
| |
| |
| Empirical Best Prediction | |
| |
| |
| |
| A Simulated Example | |
| |
| |
| |
| Further Results and Technical Notes | |
| |
| |
| |
| More on NLGSA | |
| |
| |
| |
| Asymptotic Properties of PQWLS Estimators | |
| |
| |
| |
| MSE of EBP | |
| |
| |
| |
| MSPE of the Model-Assisted EBP | |
| |
| |
| |
| Exercises | |
| |
| |
| |
| Generalized Linear Mixed Models: Part II | |
| |
| |
| |
| Likelihood-Based Inference | |
| |
| |
| |
| A Monte Carlo EM Algorithm for Binary Data | |
| |
| |
| |
| Extensions | |
| |
| |
| |
| MCEM with I.I.D. Sampling | |
| |
| |
| |
| Automation | |
| |
| |
| |
| Maximization by Parts | |
| |
| |
| |
| Bayesian Inference | |
| |
| |
| |
| Estimating Equations | |
| |
| |
| |
| Generalized Estimating Equations (GEE) | |
| |
| |
| |
| Iterative Estimating Equations | |
| |
| |
| |
| Method of Simulated Moments | |
| |
| |
| |
| Robust Estimation in GLMM | |
| |
| |
| |
| GLMM Selection | |
| |
| |
| |
| A General Principle for Model Selection | |
| |
| |
| |
| A Simulated Example | |
| |
| |
| |
| Real-Life Data Examples | |
| |
| |
| |
| Fetal Mortality in Mouse Litters | |
| |
| |
| |
| Analysis of Ge Genotype Data: An Application of the Fence Method | |
| |
| |
| |
| The Salamander-Mating Experiments: Various Applications of GLMM | |
| |
| |
| |
| Further Results and Technical Notes | |
| |
| |
| |
| Proof of Theorem 4.3 | |
| |
| |
| |
| Linear Convergence and Asymptotic Properties of IEE | |
| |
| |
| |
| Incorporating Informative Missing Data in IEE | |
| |
| |
| |
| Consistency of MSM Estimator | |
| |
| |
| |
| Asymptotic Properties of First and Second-Step Estimators | |
| |
| |
| |
| Further Results of the Fence Method | |
| |
| |
| |
| Exercises | |
| |
| |
| |
| List of Notations | |
| |
| |
| |
| Matrix Algebra | |
| |
| |
| |
| Kronecker Products | |
| |
| |
| |
| Matrix Differentiation | |
| |
| |
| |
| Projection | |
| |
| |
| |
| Generalized Inverse | |
| |
| |
| |
| Decompositions of Matrices | |
| |
| |
| |
| The Eigenvalue Perturbation Theory | |
| |
| |
| |
| Some Results in Statistics | |
| |
| |
| |
| Multivariate Normal Distribution | |
| |
| |
| |
| Quadratic Forms | |
| |
| |
| |
| Op and op | |
| |
| |
| |
| Convolution | |
| |
| |
| |
| Exponential Family and Generalized Linear Models | |
| |
| |
| References | |
| |
| |
| Index | |