عنوان

Mixed models :theory and applications with R

Mixed models :theory and applications with R

pages cm

Wiley series in probability and statistics ;398

Includes bibliographical references and index

Eugene Demidenko

1

Machine generated contents note: 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 12.2 ANOVA, variance components, and the mixed model 14.3 Other special cases of the mixed effects model 16.4 A compromise between Bayesian and frequentist approaches 17.5 Penalized likelihood and mixed effects 19.6 Healthy Akaike information criterion 111.7 Penalized smoothing 131.8 Penalized polynomial fitting 161.9 Restraining parameters, or what to eat 181.01 Ill-posed problems, Tikhonov regularization, and mixed effects 102.11 Computerized tomography and linear image reconstruction 132.21 GLMM for PET 162.31 Maple shape leaf analysis 192.41 DNA Western blot analysis 113.51 Where does the wind blow? 133.61 Software and books163.71 Summary points 273 MLE for LME Model 214.1 Example: Weight versus height 224.2 The model and log-likelihood functions 254.3 Balanced random-coefficient model 206.4 LME model with random intercepts 246.5 Criterion for the MLE existence 227.6 Criterion for positive definiteness of matrix D247.7 Preestimation bounds for variance parameters 277.8 Maximization algorithms297.9 Derivatives of the log-likelihood function 218.01 Newton--Raphson algorithm 238.11 Fisher scoring algorithm258.21 EM algorithm 288.31 Starting point 239.41 Algorithms for restricted MLE 269.51 Optimization on nonnegative definite matrices 279.61 lmeFS and lme in R 2801.71 Appendix: Proof of the MLE existence 2211.81 Summary points 3511 Statistical Properties of the LME Model 3911.1 Introduction 3911.2 Identifiability of the LMEmodel 3911.3 Information matrix for variance parameters 3221.4 Profile-likelihood confidence intervals 3331.5 Statistical testing of the presence of random effects 3531.6 Statistical properties of MLE 3931.7 Estimation of random effects 3841.8 Hypothesis and membership testing 3351.9 Ignoring random effects 3751.01 MINQUE for variance parameters 3061.11 Method of moments 3961.21 Variance least squares estimator 3371.31 Projection on D+ space 3871.41 Comparison of the variance parameter estimation 3871.51 Asymptotically efficient estimation for ]beta[ 3281.61 Summary points 4381 Growth Curve Model and Generalizations 4781.1 Linear growth curve model 4781.2 General linear growth curve model 4302.3 Linear model with linear covariance structure 4122.4 Robust linear mixed effects model 4532.5 Appendix: Derivation of the MM estimator 4342.6 Summary points 5442 Meta-analysis Model 5742.1 Simple meta-analysis model 5842.2 Meta-analysis model with covariates 5572.3 Multivariate meta-analysis model 5082.4 Summary points 6192 Nonlinear Marginal Model 6392.1 Fixed matrix of random effects 6492.2 Varied matrix of random effects 6703.3 Three types of nonlinear marginal models 6813.4 Total generalized estimating equations approach 6323.5 Summary points 7033 Generalized Linear Mixed Models 7333.1 Regression models for binary data 7433.2 Binary model with subject-specific intercept 7753.3 Logistic regression with random intercept 7463.4 Probit model with random intercept 7483.5 Poisson model with random intercept 7883.6 Random intercept model: overview 7304.7 Mixed models with multiple random effects 7404.8 GLMM and simulation methods 7314.9 GEE for clustered marginal GLM 7814.01 Criteria for MLE existence for binary model 7624.11 Summary points 8134 Nonlinear Mixed Effects Model 8534.1 Introduction 8534.2 The model 8634.3 Example: Height of girls and boys 8934.4 Maximum likelihood estimation 8144.5 Two-stage estimator 8444.6 First-order approximation 8054.7 Lindstrom--Bates estimator 8254.8 Likelihood approximations 8754.9 One-parameter exponential model 8064.01 Asymptotic equivalence of the TS and LB estimators 8764.11 Bias-corrected two-stage estimator 8964.21 Distribution misspecification 8174.31 Partially nonlinear marginal mixed model 8474.41 Fixed sample likelihood approach8574.51 Estimation of random effects and hypothesis testing 8874.61 Example )continued( 8974.71 Practical recommendations 8184.81 Appendix: Proof of theorem on equivalence 8284.91 Summary points 9584 Diagnostics and Influence Analysis 9984.1 Introduction 9984.2 Influence analysis for linear regression 9094.3 The idea of infinitesimal influence 9394.4 Linear regression model 9594.5 Nonlinear regression model 9215.6 Logistic regression for binary outcome 9715.7 Influence of correlation structure 9625.8 Influence of measurement error 9725.9 Influence analysis for the LME model 9035.01 Appendix: MLE derivative with respect to σ2 9635.11 Summary points 01735 Tumor Regrowth Curves 01145.1 Survival curves 01345.2 Double--exponential regrowth curve 01545.3 Exponential growth with fixed regrowth time 01955.4 General regrowth curve 01565.5 Double--exponential transient regrowth curve 01665.6 Gompertz transient regrowth curve 01375.7 Summary points 11675 Statistical Analysis of Shape 11975.1 Introduction 11975.2 Statistical analysis of random triangles 11185.3 Face recognition 11485.4 Scale-irrelevant shape model 11585.5 Gorilla vertebrae analysis 11985.6 Procrustes estimation of the mean shape 11195.7 Fourier descriptor analysis 11895.8 Summary points 21706 Statistical Image Analysis 21906.1 Introduction 21906.2 Testing for uniform lighting 21216.3 Kolmogorov--Smirnov image comparison 21616.4 Multinomial statistical model for images 21026.5 Image entropy 21326.6 Ensemble of unstructured images 21726.7 Image alignment and registration 21046.8 Ensemble of structured images 21256.9 Modeling spatial correlation 21456.01 Summary points 31066 Appendix: Useful Facts and Formulas 31366.1 Basic facts of asymptotic theory 31366.2 Some formulas of matrix algebra 31076.3 Basic facts of optimization theory 476References 386Index 317

، Analysis of variance

، MATHEMATICS / Probability & Statistics / General

8491-

Demidenko, Eugene

AU

TI

SE