Mixed Models

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."--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 subr...

Auteur
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.

Texte du rabat
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 Association Mixed 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 dissertations Ideal 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.

Contenu
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 App…