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(More customer reviews)This is an important book. It is a mature, deep introduction to generalized linear models.
General linear models extend multiple linear models to include cases in which the distribution of the dependent variable is part of the exponential family and the expected value of the dependent variable is a function of the linear predictor. Besides the normal (Gaussian) distribution, the binomial distribution, the Poisson distribution and the Gamma distribution, are just some of the exponential family members most frequently encountered in the scientific literature. Using appropriate functions to join the dependent variable to the linear predictor many classic models of applied statistics are included in the broad frame of generalized linear models: "logistic regression", log-linear models, Cox's proportional hazards models are just some of them.
Further extensions to the "base" family of generalized linear models, such as those based on the use of quasi-likelihood functions, and models in which both the expected value and the dispersion are function of a linear predictor, are well presented in the book.
Examples, and exercises, introduce many non-banal, useful, designs.
There are some minor drawbacks. Some more advanced topics might have been introduced more smoothly (i.e. conditional likelihood). Some other topics are better understood when you are already familiar with the specific object of study (i.e. Cox's proportional hazards models as a generalized linear model). The book does not provide software examples, nor is it related with any specific statistical package. However, the maturity of the reader to whom the book is addressed should be so high that translating the majority of the examples presented in the book in the "language" of a familiar statistical package should not be a problem.
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The success of the first edition of Generalized Linear Models led to the updated Second Edition, which continues to provide a definitive unified, treatment of methods for the analysis of diverse types of data. Today, it remains popular for its clarity, richness of content and direct relevance to agricultural, biological, health, engineering, and other applications.The authors focus on examining the way a response variable depends on a combination of explanatory variables, treatment, and classification variables. They give particular emphasis to the important case where the dependence occurs through some unknown, linear combination of the explanatory variables.The Second Edition includes topics added to the core of the first edition, including conditional and marginal likelihood methods, estimating equations, and models for dispersion effects and components of dispersion. The discussion of other topics-log-linear and related models, log odds-ratio regression models, multinomial response models, inverse linear and related models, quasi-likelihood functions, and model checking-was expanded and incorporates significant revisions.Comprehension of the material requires simply a knowledge of matrix theory and the basic ideas of probability theory, but for the most part, the book is self-contained. Therefore, with its worked examples, plentiful exercises, and topics of direct use to researchers in many disciplines, Generalized Linear Models serves as ideal text, self-study guide, and reference.
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