Mixed Models

EUGENE DEMIDENKO, PhD, is Professor of Biostatistics and Epidemiology at the Geisel School of Medicine and Department of Mathematics at Dartmouth College. Dr. Demidenko carries out collaborative work at the Thayer School of Engineering, Dartmouth College, including nanocancer therapy and electrical impedance tomography for breast cancer detection. Dr. Demidenko is recipient of several awards from the American Statistical Association and has been an invited lecturer at several institutes and academies around the world.

• Preface xviiPreface to the Second Edition xixR software and Functions xxData Sets xxiiOpen Problems in Mixed Models xxiii1 Introduction: Why Mixed Models? 11.1 Mixed effects for clustered data 21.2 ANOVA, variance components, and the mixed model 41.3 Other special cases of the mixed effects model 61.4 A compromise between Bayesian and frequentist approaches 71.5 Penalized likelihood and mixed effects 91.6 Healthy Akaike information criterion 111.7 Penalized smoothing 131.8 Penalized polynomial fitting 161.9 Restraining parameters, or what to eat 181.10 Ill-posed problems, Tikhonov regularization, and mixed effects 201.11 Computerized tomography and linear image reconstruction 231.12 GLMM for PET 261.13 Maple shape leaf analysis 291.14 DNA Western blot analysis 311.15 Where does the wind blow? 331.16 Software and books 361.17 Summary points 372 MLE for LME Model 412.1 Example: Weight versus height 422.2 The model and log-likelihood functions 452.3 Balanced random-coefficient model 602.4 LME model with random intercepts 642.5 Criterion for the MLE existence 722.6 Criterion for positive definiteness of matrix D 742.7 Preestimation bounds for variance parameters 772.8 Maximization algorithms 792.9 Derivatives of the log-likelihood function 812.10 Newton—Raphson algorithm 832.11 Fisher scoring algorithm 852.12 EM algorithm 882.13 Starting point 932.14 Algorithms for restricted MLE 962.15 Optimization on nonnegative definite matrices 972.16 lmeFS and lme in R 1082.17 Appendix: Proof of the MLE existence 1122.18 Summary points 1153 Statistical Properties of the LME Model 1193.1 Introduction 1193.2 Identifiability of the LME model 1193.3 Information matrix for variance parameters 1223.4 Profile-likelihood confidence intervals 1333.5 Statistical testing of the presence of random effects 1353.6 Statistical properties of MLE 1393.7 Estimation of random effects 1483.8 Hypothesis and membership testing 1533.9 Ignoring random effects 1573.10 MINQUE for variance parameters 1603.11 Method of moments 1693.12 Variance least squares estimator 1733.13 Projection on D+ space 1783.14 Comparison of the variance parameter estimation 1783.15 Asymptotically efficient estimation for β 1823.16 Summary points 1834 Growth Curve Model and Generalizations 1874.1 Linear growth curve model 1874.2 General linear growth curve model 2034.3 Linear model with linear covariance structure 2214.4 Robust linear mixed effects model 2354.5 Appendix: Derivation of the MM estimator 2434.6 Summary points 2445 Meta-analysis Model 2475.1 Simple meta-analysis model 2485.2 Meta-analysis model with covariates 2755.3 Multivariate meta-analysis model 2805.4 Summary points 2916 Nonlinear Marginal Model 2936.1 Fixed matrix of random effects 2946.2 Varied matrix of random effects 3076.3 Three types of nonlinear marginal models 3186.4 Total generalized estimating equations approach 3236.5 Summary points 3307 Generalized Linear Mixed Models 3337.1 Regression models for binary data 3347.2 Binary model with subject-specific intercept 3577.3 Logistic regression with random intercept 3647.4 Probit model with random intercept 3847.5 Poisson model with random intercept 3887.6 Random intercept model: overview 4037.7 Mixed models with multiple random effects 4047.8 GLMM and simulation methods 4137.9 GEE for clustered marginal GLM 4187.10 Criteria for MLE existence for binary model 4267.11 Summary points 4318 Nonlinear Mixed Effects Model 4358.1 Introduction 4358.2 The model 4368.3 Example: Height of girls and boys 4398.4 Maximum likelihood estimation 4418.5 Two-stage estimator 4448.6 First-order approximation 4508.7 Lindstrom—Bates estimator 4528.8 Likelihood approximations 4578.9 One-parameter exponential model 4608.10 Asymptotic equivalence of the TS and LB estimators 4678.11 Bias-corrected two-stage estimator 4698.12 Distribution misspecification 4718.13 Partially nonlinear marginal mixed model 4748.14 Fixed sample likelihood approach 4758.15 Estimation of random effects and hypothesis testing 4788.16 Example (continued) 4798.17 Practical recommendations 4818.18 Appendix: Proof of theorem on equivalence 4828.19 Summary points 4859 Diagnostics and Influence Analysis 4899.1 Introduction 4899.2 Influence analysis for linear regression 4909.3 The idea of infinitesimal influence 4939.4 Linear regression model 4959.5 Nonlinear regression model 5129.6 Logistic regression for binary outcome 5179.7 Influence of correlation structure 5269.8 Influence of measurement error 5279.9 Influence analysis for the LME model 5309.10 Appendix: MLE derivative with respect to σ2 5369.11 Summary points 53710 Tumor Regrowth Curves 54110.1 Survival curves 54310.2 Double—exponential regrowth curve 54510.3 Exponential growth with fixed regrowth time 55910.4 General regrowth curve 56510.5 Double—exponential transient regrowth curve 56610.6 Gompertz transient regrowth curve 57310.7 Summary points 57611 Statistical Analysis of Shape 57911.1 Introduction 57911.2 Statistical analysis of random triangles 58111.3 Face recognition 58411.4 Scale-irrelevant shape model 58511.5 Gorilla vertebrae analysis 58911.6 Procrustes estimation of the mean shape 59111.7 Fourier descriptor analysis 59811.8 Summary points 60712 Statistical Image Analysis 60912.1 Introduction 60912.2 Testing for uniform lighting 61212.3 Kolmogorov—Smirnov image comparison 61612.4 Multinomial statistical model for images 62012.5 Image entropy 62312.6 Ensemble of unstructured images 62712.7 Image alignment and registration 64012.8 Ensemble of structured images 65212.9 Modeling spatial correlation 65412.10 Summary points 66013 Appendix: Useful Facts and Formulas 66313.1 Basic facts of asymptotic theory 66313.2 Some formulas of matrix algebra 67013.3 Basic facts of optimization theory 674References 683Index 713