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Multivariate statistical modelling based on generalized linear models. With contributions by Wolfgang Hennevogl. (English) Zbl 0809.62064

Springer Series in Statistics. New York, NY: Springer-Verlag. xxiv, 425 p. (1994).
In the last decade there are various extensions of generalized linear models (GLM) in various directions such as multivariate and multicategorical models, longitudinal data analysis, random effects and nonparametric predictors. The aim of this book is to bring together and to review a large part of the recent advances in this area. Although the continuous case is sketched sometimes, throughout the book the focus is on categorical data.
The book is aimed at applied statisticians, graduate students of statistics and researchers with a strong interest in statistics and data analysis from areas like econometrics, biometrics and social sciences. It is written on an intermediate level with emphasis on basic ideas. For rigorous proofs the reader is referred to the literature.
The book contains 9 chapters the titles of which are as follows: Ch. 1: Introduction. Ch. 2: Modelling and analysis of cross-sectional data: a review of univariate generalized linear models. Ch. 3: Models for multicategorical responses: multivariate extensions of generalized linear models. Ch. 4: Selecting and checking models. Ch. 5: Semi- and nonparametric approaches to regression analysis. Ch. 6: Fixed parameter models for time series and longitudinal data. Ch. 7: Random effects models. Ch. 8: State space models. Ch. 9: Survival models. The book also contains 63 examples, 45 figures and 48 tables.
There are two appendices. Appendix A provides some material which is necessary to study this book, e.g., exponential families, basic ideas for asymptotics, EM-algorithm and Monte Carlo methods. In Appendix B, some software is described that can be used for fitting GLM and extensions.
In summary, this book gives a fairly helpful picture of recent advances in categorical data based generalized linear models.

MSC:

62J12 Generalized linear models (logistic models)
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62H99 Multivariate analysis
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics

Software:

Fahrmeir
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