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**Generalized latent variable modeling. Multilevel, longitudinal, and structural equation models.**
*(English)*
Zbl 1097.62001

Interdisciplinary Statistics. Boca Raton, FL: Chapman & Hall/CRC (ISBN 1-58488-000-7/hbk; 978-0-203-48943-7/ebook). xi, 508 p. (2004).

A major aim of this book is to unify and extend latent variable modeling in the widest sense. The models covered include multilevel, longitudinal and structural equation models as well as relatives and friends such as generalized linear mixed models, random coefficient models, item response models, factor models, panel models, repeated measurement models, latent class models and frailty models. Numerous displays, figures, and graphs make the book vivid and easy to read.

The book consists of two parts: methodology and applications. In Chapter 1 the concept, uses and interpretations of latent variables are discussed. In Chapter 2, a wide range of response processes are introduced and most of the processes can more or less be expressed as generalized linear models, and many as latent response models. The classical latent variable models are surveyed in Chapter 3, and these models are unified and extended in Chapter 4 for all response types surveyed in Chapter 2.

Established and novel methods of model identification, estimation, latent variable prediction and model diagnostics are extensively covered in Chapters 5 to 8.

In applications in Chapters 9 to 14, the methodology developed in the first part is used to address problems from biology, medicine, psychology, education, sociology, political science, economics, marketing and other areas. All applications are based on real data, but the analysis is often simplified for didactic reasons. The STATA program GLLAMM is used for all applications.

This book is an excellent reference book on generalized latent variable modeling. It may also serve as a textbook for a graduate course in generalized latent variable modeling. It is noted that exercises are not provided in this book.

The book consists of two parts: methodology and applications. In Chapter 1 the concept, uses and interpretations of latent variables are discussed. In Chapter 2, a wide range of response processes are introduced and most of the processes can more or less be expressed as generalized linear models, and many as latent response models. The classical latent variable models are surveyed in Chapter 3, and these models are unified and extended in Chapter 4 for all response types surveyed in Chapter 2.

Established and novel methods of model identification, estimation, latent variable prediction and model diagnostics are extensively covered in Chapters 5 to 8.

In applications in Chapters 9 to 14, the methodology developed in the first part is used to address problems from biology, medicine, psychology, education, sociology, political science, economics, marketing and other areas. All applications are based on real data, but the analysis is often simplified for didactic reasons. The STATA program GLLAMM is used for all applications.

This book is an excellent reference book on generalized latent variable modeling. It may also serve as a textbook for a graduate course in generalized latent variable modeling. It is noted that exercises are not provided in this book.

Reviewer: Yuehua Wu (Toronto)

### MSC:

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

62J12 | Generalized linear models (logistic models) |

65C60 | Computational problems in statistics (MSC2010) |

62Pxx | Applications of statistics |