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**Mixed-effects models in S and S-Plus.**
*(English)*
Zbl 0953.62065

Statistics and Computing (Cham). New York, NY: Springer. xvi, 528 p. (2000).

This book provides an overview on the theory and applications of linear and nonlinear mixed-effects models in the analysis of grouped data. Examples of grouped data include longitudinal data, repeated measures, blocked designs, and multilevel data. The increasing popularity of mixed-effects models is explained by the flexibility they offer in modeling the within-group correlation often present in grouped data, by the handling of balanced and unbalanced data in a unified framework, and by the availability of reliable and efficient software for fitting them. The class of mixed-effects models considered in this book assumes that both the random effects and the errors follow Gaussian distributions. These models are intended for grouped data in which the response variable is (at least approximately) continuous.

A unified model-building strategy for both linear and nonlinear models is presented and applied to the analysis of over 20 real datasets from a wide variety of areas, including pharmacokinetics, agriculture, and manufacturing. A strong emphasis is placed on the use of graphical displays at the various phases of the model-building process, starting with exploratory plots of the data and concluding with diagnostic plots to assess the adequacy of a fitted model. Over 170 figures are included in the book. The nlme library the authors developed for analyzing mixed-effects models in implementations of the S language, including S-PLUS and R, provides the underlying software for implementing the methods presented in the text, being described and illustrated in detail throughout the book.

The book is divided into two parts. Part I, comprising five chapters, is dedicated to the linear mixed-effects (LME) model and Part II, comprising three chapters, covers the nonlinear mixed-effects (NLME) model. Ch. 1 gives an overview of LME models, introducing some examples of grouped data and the type of analyses that applies to them. The theory and computational methods for LME models are the topics of Ch. 2. Ch. 3 describes the structure of grouped data and the many facilities available in the nlme library to display and summarize such data. The model-building approach is described and illustrated in detail in the context of LME models in Ch. 4. Extensions of the basic LME model to include variance functions and correlation structures for the within-group errors are considered in Ch. 5. Ch. 6 provides an overview of NLME models and some of the analysis tools available for them in nlme. The theory and computational methods for NLME models are described in Ch. 7. The final chapter is dedicated to model building in the context of NLME models and to illustrating in detail the nonlinear modeling facilities available in the nlme library.

Even though the material covered in the book is self-contained, it is assumed that the reader has some familiarity with linear regression models, say at the level of the monograph of N.R. Draper and H. Smith, Applied Regression Analysis; see Zbl 0895.62073 for the review of the 3rd ed. from 1998, and Zbl 0158.17101 for the review of the original edition from 1967. The balanced mix of real data examples, modeling software, and theory makes this book a useful reference for practitioners who use, or intend to use, mixed-effects models in their data analyses. It can also be used as a text for a one-semester graduate-level applied course in mixed-effects models.

A unified model-building strategy for both linear and nonlinear models is presented and applied to the analysis of over 20 real datasets from a wide variety of areas, including pharmacokinetics, agriculture, and manufacturing. A strong emphasis is placed on the use of graphical displays at the various phases of the model-building process, starting with exploratory plots of the data and concluding with diagnostic plots to assess the adequacy of a fitted model. Over 170 figures are included in the book. The nlme library the authors developed for analyzing mixed-effects models in implementations of the S language, including S-PLUS and R, provides the underlying software for implementing the methods presented in the text, being described and illustrated in detail throughout the book.

The book is divided into two parts. Part I, comprising five chapters, is dedicated to the linear mixed-effects (LME) model and Part II, comprising three chapters, covers the nonlinear mixed-effects (NLME) model. Ch. 1 gives an overview of LME models, introducing some examples of grouped data and the type of analyses that applies to them. The theory and computational methods for LME models are the topics of Ch. 2. Ch. 3 describes the structure of grouped data and the many facilities available in the nlme library to display and summarize such data. The model-building approach is described and illustrated in detail in the context of LME models in Ch. 4. Extensions of the basic LME model to include variance functions and correlation structures for the within-group errors are considered in Ch. 5. Ch. 6 provides an overview of NLME models and some of the analysis tools available for them in nlme. The theory and computational methods for NLME models are described in Ch. 7. The final chapter is dedicated to model building in the context of NLME models and to illustrating in detail the nonlinear modeling facilities available in the nlme library.

Even though the material covered in the book is self-contained, it is assumed that the reader has some familiarity with linear regression models, say at the level of the monograph of N.R. Draper and H. Smith, Applied Regression Analysis; see Zbl 0895.62073 for the review of the 3rd ed. from 1998, and Zbl 0158.17101 for the review of the original edition from 1967. The balanced mix of real data examples, modeling software, and theory makes this book a useful reference for practitioners who use, or intend to use, mixed-effects models in their data analyses. It can also be used as a text for a one-semester graduate-level applied course in mixed-effects models.

Reviewer: E.M.Psyadlo (Odessa)

### MSC:

62J10 | Analysis of variance and covariance (ANOVA) |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

62-04 | Software, source code, etc. for problems pertaining to statistics |

62J02 | General nonlinear regression |

62J05 | Linear regression; mixed models |

62J99 | Linear inference, regression |