Generalized Linear Models, Second Edition

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Summary: first great treatment of generalized linear models
Review: Nelder and Wedderburn wrote the seminal paper on generalized linear models in the 1970s. Since then John Nelder has pioneered the research and software development of the methods. This is the first of several excellent texts on generalized linear models. It illustrates how through the use of a link function many classical statistical models can be unified into one general form of model. This unification is helpful both theoretically and computationally. Various applications are presented in a clear manner.

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Summary: Very comprehensive, very helpful.
Review: The first edition is already a well-known text and reference, this expanded version is even better. Very comprehensive and very helpful.

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Summary: One of the best books on modelling
Review: 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.