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**Multivariate statistical modelling based on generalized linear models.
2nd ed.**
*(English)*
Zbl 0980.62052

Springer Series in Statistics. New York, NY: Springer. xxvi, 517 p. (2001).

The first edition from 1994, see the review Zbl 0809.62064, provided an extension of generalized linear models (GLM) for multivariate and multicategorical models, longitudinal data analysis, random effects and nonparametric predictors. The aim of the new edition is to reflect the major new developments over the past years. The book is clearly written, with emphasis on basic ideas. The authors illustrate concepts with numerous examples, using real data from biological sciences, economics and social sciences.

The organization parallels that of the first edition. Ch. 8 is now called “State space models and hidden Markov models”, and the other titles remain the same. In this second edition, Bayesian concepts are considered more comprehensively. In Ch. 3, marginal models are treated, and marginal means of correlated binary and categorical data are estimated. Ch. 5, on nonparametric and semiparametric generalized regression, has been totally rewritten, it contains new sections on local smoothing and Bayesian inference. Ch. 6 now covers both time series and longitudinal data.

Ch. 7 contains a new subsection on a nonparametric approach based on finite mixtures, and a new section on a fully Bayesian approach, where all parameters are regarded as random. MCMC techniques are described in greater detail in Ch. 8 and in the appendix. Ch. 8 also extends the main ideas from state space models to models with spatial and spatio-temporal data.

In summary, this book gives a thorough exposition of recent developments in categorical data based on GLMs.

The organization parallels that of the first edition. Ch. 8 is now called “State space models and hidden Markov models”, and the other titles remain the same. In this second edition, Bayesian concepts are considered more comprehensively. In Ch. 3, marginal models are treated, and marginal means of correlated binary and categorical data are estimated. Ch. 5, on nonparametric and semiparametric generalized regression, has been totally rewritten, it contains new sections on local smoothing and Bayesian inference. Ch. 6 now covers both time series and longitudinal data.

Ch. 7 contains a new subsection on a nonparametric approach based on finite mixtures, and a new section on a fully Bayesian approach, where all parameters are regarded as random. MCMC techniques are described in greater detail in Ch. 8 and in the appendix. Ch. 8 also extends the main ideas from state space models to models with spatial and spatio-temporal data.

In summary, this book gives a thorough exposition of recent developments in categorical data based on GLMs.

Reviewer: Oleksandr Kukush (Kiev)

### MSC:

62J12 | Generalized linear models (logistic models) |

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

62G08 | Nonparametric regression and quantile regression |

62F15 | Bayesian inference |

62H99 | Multivariate analysis |

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