Linear and generalized linear mixed models and their applications / / Jiming Jiang and Thuan Nguyen

• Autore: Jiang Jiming
• Pubblicazione: New York, New York ; ; London, England : , : Springer, , [2021]; ©2021
• Edizione: Second edition.
• Descrizione fisica: 1 online resource (352 pages) : illustrations
• Disciplina: 519.5
• Soggetto topico: Mathematical statistics; Linear models (Statistics); Estadística matemàtica; Models lineals (Estadística)
• Soggetto genere / forma: Llibres electrònics
• Persona (resp. second.): NguyenThuan
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- Contents -- List of Notations -- 1 Linear Mixed Models: Part I -- 1.1 Introduction -- 1.1.1 Effect of Air Pollution Episodes on Children -- 1.1.2 Genome-Wide Association Study -- 1.1.3 Small Area Estimation of Income -- 1.2 Types of Linear Mixed Models -- 1.2.1 Gaussian Mixed Models -- 1.2.1.1 Mixed ANOVA Model -- 1.2.1.2 Longitudinal Model -- 1.2.1.3 Marginal Model -- 1.2.1.4 Hierarchical Models -- 1.2.2 Non-Gaussian Linear Mixed Models -- 1.2.2.1 Mixed ANOVA Model -- 1.2.2.2 Longitudinal Model -- 1.2.2.3 Marginal Model -- 1.3 Estimation in Gaussian Mixed Models -- 1.3.1 Maximum Likelihood -- 1.3.1.1 Point Estimation -- 1.3.1.2 Asymptotic Covariance Matrix -- 1.3.2 Restricted Maximum Likelihood (REML) -- 1.3.2.1 Point Estimation -- 1.3.2.2 Historical Note -- 1.3.2.3 Asymptotic Covariance Matrix -- 1.4 Estimation in Non-Gaussian Linear Mixed Models -- 1.4.1 Quasi-Likelihood Method -- 1.4.2 Partially Observed Information -- 1.4.3 Iterative Weighted Least Squares -- 1.4.3.1 Balanced Case -- 1.4.3.2 Unbalanced Case -- 1.4.4 Jackknife Method -- 1.4.5 High-Dimensional Misspecified Mixed Model Analysis -- 1.5 Other Methods of Estimation -- 1.5.1 Analysis of Variance Estimation -- 1.5.1.1 Balanced Data -- 1.5.1.2 Unbalanced Data -- 1.5.2 Minimum Norm Quadratic Unbiased Estimation -- 1.6 Notes on Computation and Software -- 1.6.1 Notes on Computation -- 1.6.1.1 Computation of the ML and REML Estimators -- 1.6.1.2 The EM Algorithm -- 1.6.2 Notes on Software -- 1.7 Real-Life Data Examples -- 1.7.1 Analysis of Birth Weights of Lambs -- 1.7.2 Analysis of Hip Replacements Data -- 1.7.3 Analyses of High-Dimensional GWAS Data -- 1.8 Further Results and Technical Notes -- 1.8.1 A Note on Finding the MLE -- 1.8.2 Note on Matrix X Not Being Full Rank -- 1.8.3 Asymptotic Behavior of ML and REML Estimators in Non-Gaussian Mixed ANOVA Models. ; 1.8.4 Truncated Estimator -- 1.8.5 POQUIM in General -- 1.9 Exercises -- 2 Linear Mixed Models: Part II -- 2.1 Tests in Linear Mixed Models -- 2.1.1 Tests in Gaussian Mixed Models -- 2.1.1.1 Exact Tests -- 2.1.1.2 Optimal Tests -- 2.1.1.3 Likelihood-Ratio Tests -- 2.1.2 Tests in Non-Gaussian Linear Mixed Models -- 2.1.2.1 Empirical Method of Moments -- 2.1.2.2 Partially Observed Information -- 2.1.2.3 Jackknife Method -- 2.1.2.4 Robust Versions of Classical Tests -- 2.2 Confidence Intervals in Linear Mixed Models -- 2.2.1 Confidence Intervals in Gaussian Mixed Models -- 2.2.1.1 Exact Confidence Intervals for Variance Components -- 2.2.1.2 Approximate Confidence Intervals for Variance Components -- 2.2.1.3 Simultaneous Confidence Intervals -- 2.2.1.4 Confidence Intervals for Fixed Effects -- 2.2.2 Confidence Intervals in Non-Gaussian Linear MixedModels -- 2.2.2.1 ANOVA Models -- 2.2.2.2 Longitudinal Models -- 2.3 Prediction -- 2.3.1 Best Prediction -- 2.3.2 Best Linear Unbiased Prediction -- 2.3.2.1 Empirical BLUP -- 2.3.3 Observed Best Prediction -- 2.3.4 Prediction of Future Observation -- 2.3.4.1 Distribution-Free Prediction Intervals -- 2.3.4.2 Standard Linear Mixed Models -- 2.3.4.3 Nonstandard Linear Mixed Models -- 2.3.4.4 A Simulated Example -- 2.3.5 Classified Mixed Model Prediction -- 2.3.5.1 CMMP of Mixed Effects -- 2.3.5.2 CMMP of Future Observation -- 2.3.5.3 CMMP When the Actual Match Does Not Exist -- 2.3.5.4 Empirical Demonstration -- 2.3.5.5 Incorporating Covariate Information in Matching -- 2.3.5.6 More Empirical Demonstration -- 2.3.5.7 Prediction Interval -- 2.4 Model Checking and Selection -- 2.4.1 Model Diagnostics -- 2.4.1.1 Diagnostic Plots -- 2.4.1.2 Goodness-of-Fit Tests -- 2.4.2 Information Criteria -- 2.4.2.1 Selection with Fixed Random Factors -- 2.4.2.2 Selection with Random Factors -- 2.4.3 The Fence Methods. ; 2.4.3.1 The Effective Sample Size -- 2.4.3.2 The Dimension of a Model -- 2.4.3.3 Unknown Distribution -- 2.4.3.4 Finite-Sample Performance and the Effect of a Constant -- 2.4.3.5 Criterion of Optimality -- 2.4.4 Shrinkage Mixed Model Selection -- 2.5 Bayesian Inference -- 2.5.1 Inference About Variance Components -- 2.5.2 Inference About Fixed and Random Effects -- 2.6 Real-Life Data Examples -- 2.6.1 Reliability of Environmental Sampling -- 2.6.2 Hospital Data -- 2.6.3 Baseball Example -- 2.6.4 Iowa Crops Data -- 2.6.5 Analysis of High-Speed Network Data -- 2.7 Further Results and Technical Notes -- 2.7.1 Robust Versions of Classical Tests -- 2.7.2 Existence of Moments of ML/REML Estimators -- 2.7.3 Existence of Moments of EBLUE and EBLUP -- 2.7.4 The Definition of Σn(θ) in Sect.2.4.1.2 -- 2.8 Exercises -- 3 Generalized Linear Mixed Models: Part I -- 3.1 Introduction -- 3.2 Generalized Linear Mixed Models -- 3.3 Real-Life Data Examples -- 3.3.1 Salamander Mating Experiments -- 3.3.2 A Log-Linear Mixed Model for Seizure Counts -- 3.3.3 Small Area Estimation of Mammography Rates -- 3.4 Likelihood Function Under GLMM -- 3.5 Approximate Inference -- 3.5.1 Laplace Approximation -- 3.5.2 Penalized Quasi-likelihood Estimation -- 3.5.2.1 Derivation of PQL -- 3.5.2.2 Computational Procedures -- 3.5.2.3 Variance Components -- 3.5.2.4 Inconsistency of PQL Estimators -- 3.5.3 Tests of Zero Variance Components -- 3.5.4 Maximum Hierarchical Likelihood -- 3.5.5 Note on Existing Software -- 3.6 GLMM Prediction -- 3.6.1 Joint Estimation of Fixed and Random Effects -- 3.6.1.1 Maximum a Posterior -- 3.6.1.2 Computation of MPE -- 3.6.1.3 Penalized Generalized WLS -- 3.6.1.4 Maximum Conditional Likelihood -- 3.6.1.5 Quadratic Inference Function -- 3.6.2 Empirical Best Prediction -- 3.6.2.1 Empirical Best Prediction Under GLMM -- 3.6.2.2 Model-Assisted EBP. ; 3.6.3 A Simulated Example -- 3.6.4 Classified Mixed Logistic Model Prediction -- 3.6.5 Best Look-Alike Prediction -- 3.6.5.1 BLAP of a Discrete/Categorical Random Variable -- 3.6.5.2 BLAP of a Zero-Inflated Random Variable -- 3.7 Real-Life Data Example Follow-Ups and More -- 3.7.1 Salamander Mating Data -- 3.7.2 Seizure Count Data -- 3.7.3 Mammography Rates -- 3.7.4 Analysis of ECMO Data -- 3.7.4.1 Prediction of Mixed Effects of Interest -- 3.8 Further Results and Technical Notes -- 3.8.1 More on NLGSA -- 3.8.2 Asymptotic Properties of PQWLS Estimators -- 3.8.3 MSPE of EBP -- 3.8.4 MSPE of the Model-Assisted EBP -- 3.9 Exercises -- 4 Generalized Linear Mixed Models: Part II -- 4.1 Likelihood-Based Inference -- 4.1.1 A Monte Carlo EM Algorithm for Binary Data -- 4.1.1.1 The EM Algorithm -- 4.1.1.2 Monte Carlo EM via Gibbs Sampler -- 4.1.2 Extensions -- 4.1.2.1 MCEM with Metropolis-Hastings Algorithm -- 4.1.2.2 Monte Carlo Newton-Raphson Procedure -- 4.1.2.3 Simulated ML -- 4.1.3 MCEM with i.i.d. Sampling -- 4.1.3.1 Importance Sampling -- 4.1.3.2 Rejection Sampling -- 4.1.4 Automation -- 4.1.5 Data Cloning -- 4.1.6 Maximization by Parts -- 4.1.7 Bayesian Inference -- 4.2 Estimating Equations -- 4.2.1 Generalized Estimating Equations (GEE) -- 4.2.2 Iterative Estimating Equations -- 4.2.3 Method of Simulated Moments -- 4.2.4 Robust Estimation in GLMM -- 4.3 GLMM Diagnostics and Selection -- 4.3.1 A Goodness-of-Fit Test for GLMM Diagnostics -- 4.3.1.1 Tailoring -- 4.3.1.2 χ2-Test -- 4.3.1.3 Application to GLMM -- 4.3.2 Fence Methods for GLMM Selection -- 4.3.2.1 Maximum Likelihood (ML) Model Selection -- 4.3.2.2 Mean and Variance/Covariance (MVC) Model Selection -- 4.3.2.3 Extended GLMM Selection -- 4.3.3 Two Examples with Simulation -- 4.3.3.1 A Simulated Example of GLMM Diagnostics -- 4.3.3.2 A Simulated Example of GLMM Selection. ; 4.4 Real-Life Data Examples -- 4.4.1 Fetal Mortality in Mouse Litters -- 4.4.2 Analysis of Gc Genotype Data -- 4.4.3 Salamander Mating Experiments Revisited -- 4.4.4 The National Health Interview Survey -- 4.5 Further Results and Technical Notes -- 4.5.1 Proof of Theorem 4.3 -- 4.5.2 Linear Convergence and Asymptotic Properties of IEE -- 4.5.2.1 Linear Convergence -- 4.5.2.2 Asymptotic Behavior of IEEE -- 4.5.3 Incorporating Informative Missing Data in IEE -- 4.5.4 Consistency of MSM Estimator -- 4.5.5 Asymptotic Properties of First- and Second-StepEstimators -- 4.5.6 Further Details Regarding the Fence Methods -- 4.5.6.1 Estimation of σM,M* in Case of Clustered Observations -- 4.5.6.2 Consistency of the Fence -- 4.5.7 Consistency of MLE in GLMM with Crossed Random Effects -- 4.6 Exercises -- A Matrix Algebra -- A.1 Kronecker Products -- A.2 Matrix Differentiation -- A.3 Projection and Related Results -- A.4 Inverse and Generalized Inverse -- A.5 Decompositions of Matrices -- A.6 The Eigenvalue Perturbation Theory -- B Some Results in Statistics -- B.1 Multivariate Normal Distribution -- B.2 Quadratic Forms -- B.3 OP and oP -- B.4 Convolution -- B.5 Exponential Family and Generalized Linear Models -- References -- Index.
• Titolo autorizzato: Linear and generalized linear mixed models and their applications
• ISBN: 1-0716-1282-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466561103316
• Lo trovi qui: Univ. di Salerno
• Serie: Springer Series in Statistics