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**Random coefficient models.**
*(English)*
Zbl 0859.62064

Oxford Statistical Science Series. 11. Oxford: Clarendon Press. xiv, 270 p. (1993).

Random coefficient models have applications in animal breeding experiments, longitudinal analysis, small area estimation and astronomy. The starting point of the book is ordinary linear regression. Chapter 1 gives a brief summary of notations and of the prerequisities for the rest of the book, and motivates the development by two examples. Chapter 2 covers the simplest models that incorporate within-group correlation. Chapter 3 contains five illustrative examples. Chapter 4 presents a generalization of random-effects models which allows for a richer pattern of between-cluster variation. In Chapter 6, these models are extended to designs with multiple layers of nesting, such as individuals within families, families within towns, and so on.

While Chapters 2-6 present extensions of ordinary linear regression to correlated observations, Chapter 7 deals with extensions of the factor analysis and measurement errors models for multilevel data. Chapter 8 describes a generalization of the random coefficients models to the class of generalized linear models.

This book is suitable as a reference book for researchers wanting to use random coefficients models.

While Chapters 2-6 present extensions of ordinary linear regression to correlated observations, Chapter 7 deals with extensions of the factor analysis and measurement errors models for multilevel data. Chapter 8 describes a generalization of the random coefficients models to the class of generalized linear models.

This book is suitable as a reference book for researchers wanting to use random coefficients models.

Reviewer: V.P.Gupta (Jaipur)

### MSC:

62J05 | Linear regression; mixed models |

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

62J12 | Generalized linear models (logistic models) |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

62P99 | Applications of statistics |