Mixed models. Theory and applications with R (Q2846470)

[For the review of the first edition from 2004 see Zbl 1055.62086.]NEWLINENEWLINE This edition presents on a total of 717 pages an in-depth and comprehensible examination of mixed model theory. Compared to the first edition, each section has been supplemented with regular and more sophisticated problems providing an active understanding for graduate and Ph.D. students in statistics. In addition, this edition switched to the R language instead of S-Plus used in the first edition.NEWLINENEWLINE There are thirteen chapters in the book which are organized into three principal parts dealing with the theory of mixed models in chapters 1--8 (linear mixed models, generalized linear mixed model and nonlinear mixed model), methods of model diagnostics and influential analysis in chapter 9 and applications in tumour growth, shapes and images in chapter 10-12. The volume ends with an appendix providing useful facts and formulas.NEWLINENEWLINE In chapter 1 the author motivates and reviews the main aspects of the theory of mixed models and shows a variety of applications. After the presentation of numerical algorithms for the likelihood maximization of linear mixed models in chapter 2, their statistical properties are described in chapter 3. Chapter 4 deals with several special cases and generalizations of linear mixed models, like the growth curve model and models with linear covariance structure. Chapter 5 introduces the reader to the theoretical background of simple meta-analysis models, meta-analysis models with covariates and general multivariate meta-analysis models. The generalization of the linear mixed models to a nonlinear mixed model with random effects either being constant, parameter dependent or a function of parameter vector is provided in chapter 6. Further generalizations of nonlinear mixed models are introduced in chapter 7 (nonlinear random effects) and in chapter 8 (nonlinear mixed effect models). Chapter 9 aimed at presenting infinitesimal influence analysis for linear, nonlinear and logistic regression models. The following three chapters illustrate various applications of mixed models: statistical modelling of tumour response (chapter 10), and statistical analysis of shapes (chapter 11) and by statistical image analysis (chapter 12). The volume ends with an appendix on basic facts on asymptotic theory, matrix algebra and optimization theory.NEWLINENEWLINE In summary, the book under review is recommended to graduate and Ph.D. students in statistics just like the first edition. It offers numerous self-study problems and supportive summary points at the end of each chapter summing up the major results and points of discussion.