Mixed Models - Theory and Applications With R

Informationen zum Autor 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. Klappentext Praise for the First Edition"This book will serve to greatly complement the growing number of texts dealing with mixed models, and I highly recommend including it in one's personal library."-Journal of the American Statistical AssociationMixed modeling is a crucial area of statistics, enabling the analysis of clustered and longitudinal data. Mixed Models: Theory and Applications with R, Second Edition fills a gap in existing literature between mathematical and applied statistical books by presenting a powerful examination of mixed model theory and application with special attention given to the implementation in R.The new edition provides in-depth mathematical coverage of mixed models' statistical properties and numerical algorithms, as well as nontraditional applications, such as regrowth curves, shapes, and images. The book features the latest topics in statistics including modeling of complex clustered or longitudinal data, modeling data with multiple sources of variation, modeling biological variety and heterogeneity, Healthy Akaike Information Criterion (HAIC), parameter multidimensionality, and statistics of image processing.Mixed Models: Theory and Applications with R, Second Edition features unique applications of mixed model methodology, as well as:* Comprehensive theoretical discussions illustrated by examples and figures* Over 300 exercises, end-of-section problems, updated data sets, and R subroutines* Problems and extended projects requiring simulations in R intended to reinforce material* Summaries of major results and general points of discussion at the end of each chapter* Open problems in mixed modeling methodology, which can be used as the basis for research or PhD dissertationsIdeal for graduate-level courses in mixed statistical modeling, the book is also an excellent reference for professionals in a range of fields, including cancer research, computer science, and engineering. Zusammenfassung Praise for the First Edition This book will serve to greatly complement the growing number of texts dealing with mixed models, and I highly recommend including it in one s personal library. Inhaltsverzeichnis 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 books361.17 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 D742.7 Preestimation bounds for varian...

List of contents

Preface xvii
 
Preface to the Second Edition xix
 
R software and functions xx
 
Data Sets xxii
 
Open Problems in Mixed Models xxiii
 
1 Introduction: Why Mixed Models? 1
 
1.1 Mixed effects for clustered data 2
 
1.2 ANOVA, variance components, and the mixed model 4
 
1.3 Other special cases of the mixed effects model 6
 
1.4 A compromise between Bayesian and frequentist approaches 7
 
1.5 Penalized likelihood and mixed effects 9
 
1.6 Healthy Akaike information criterion 11
 
1.7 Penalized smoothing 13
 
1.8 Penalized polynomial fitting 16
 
1.9 Restraining parameters, or what to eat 18
 
1.10 Ill-posed problems, Tikhonov regularization, and mixed effects 20
 
1.11 Computerized tomography and linear image reconstruction 23
 
1.12 GLMM for PET 26
 
1.13 Maple shape leaf analysis 29
 
1.14 DNA Western blot analysis 31
 
1.15 Where does the wind blow? 33
 
1.16 Software and books36
 
1.17 Summary points 37
 
2 MLE for LME Model 41
 
2.1 Example: Weight versus height 42
 
2.2 The model and log-likelihood functions 45
 
2.3 Balanced random-coefficient model 60
 
2.4 LME model with random intercepts 64
 
2.5 Criterion for the MLE existence 72
 
2.6 Criterion for positive definiteness of matrix D74
 
2.7 Preestimation bounds for variance parameters 77
 
2.8 Maximization algorithms79
 
2.9 Derivatives of the log-likelihood function 81
 
2.10 Newton--Raphson algorithm 83
 
2.11 Fisher scoring algorithm85
 
2.12 EM algorithm 88
 
2.13 Starting point 93
 
2.14 Algorithms for restricted MLE 96
 
2.15 Optimization on nonnegative definite matrices 97
 
2.16 lmeFS and lme in R 108
 
2.17 Appendix: Proof of the MLE existence 112
 
2.18 Summary points 115
 
3 Statistical Properties of the LME Model 119
 
3.1 Introduction 119
 
3.2 Identifiability of the LMEmodel 119
 
3.3 Information matrix for variance parameters 122
 
3.4 Profile-likelihood confidence intervals 133
 
3.5 Statistical testing of the presence of random effects 135
 
3.6 Statistical properties of MLE 139
 
3.7 Estimation of random effects 148
 
3.8 Hypothesis and membership testing 153
 
3.9 Ignoring random effects 157
 
3.10 MINQUE for variance parameters 160
 
3.11 Method of moments 169
 
3.12 Variance least squares estimator 173
 
3.13 Projection on D+ space 178
 
3.14 Comparison of the variance parameter estimation 178
 
3.15 Asymptotically efficient estimation for ß 182
 
3.16 Summary points 183
 
4 Growth Curve Model and Generalizations 187
 
4.1 Linear growth curve model 187
 
4.2 General linear growth curve model 203
 
4.3 Linear model with linear covariance structure 221
 
4.4 Robust linear mixed effects model 235
 
4.5 Appendix: Derivation of the MM estimator 243
 
4.6 Summary points 244
 
5 Meta-analysis Model 247
 
5.1 Simple meta-analysis model 248
 
5.2 Meta-analysis model with covariates 275
 
5.3 Multivariate meta-analysis model 280
 
5.4 Summary points 291
 
6 Nonlinear Marginal Model 293
 
6.1 Fixed matrix of random effects 294
 
6.2 Varied matrix of random effects 307
 
6.3 Three types of nonlinear marginal models 318
 
6.4 Total generalized estimating equations approach 323
 
6.5 Summary points 330
 
7 Generalized Linear Mixe

Product details

• Authors: Demidenko, E Demidenko, Eugene Demidenko, Eugene (Dartmouth Medical School Demidenko, Demidenko Eugene
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 27.09.2013
• EAN: 9781118091579
• ISBN: 978-1-118-09157-9
• No. of pages: 768
• Series: Wiley Series in Probability and Statistics; Wiley Series in Probability an; Wiley Series in Probability and Statistics; Wiley Series in Probability an
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Statistik, Medizin, Statistics, MATHEMATICS / Probability & Statistics / General, Biostatistik, Biostatistics, Medical Science, Angew. Wahrscheinlichkeitsrechn. u. Statistik / Modelle, Applied Probability & Statistics - Models, Medical Sciences Special Topics, Spezialthemen Medizin