Generalized Linear Models (Chapman & Hall/CRC Monographs on Statistics and Applied Probability)

This was one of two books that were references for a course I took in Generalized Linear Models - GLM. This was an excellent book in explaining the technical (mathematical) details of the GLM, such as the importance of the link function (how covariates/predictors/explanatory variables are related to the response), the importance of moment generating functions and cumulant generating functions, and the contribution of various types of likelihoods (like conditional, quasi, and partial ) in parameter estimation in GLM. It also covers things like geometrical intepretations...which seems to be very important in the multivariate setting. Most of the problems in the book lean towards proofs. For example... problem 4.7 asks you to show that the ratio of a binomial and poisson random variable is asymptotically equivalent to a constant.This book is kinda old, so things like Bayesian regression (which I'm not acquainted with...yet) or high dimensional data analysis are not going to be in this book. I know that the latest edition of Agresti's Categorical Data Analysis (CDA) does cover these topics though. Still, I think that the McCullagh book is more mathematically rigorous than Agresti's book, since it covers things like the geometrical interpretation of least squares estimation.This book was clearly written for researchers who have a quantitative background - those who have a background in at least intermediate statistical theory (Casella & Berger) as well as statistical Linear Modeling. Anybody who only has some of this knowledge would probably find Agresti's Categorical Data Analysis more accessible (this was the other book used in our GLM course), and those don't have any math experience might find Agresti's An Introduction to Categorical Data Analysis a better book.

This book is very well structured and easy to follow. It provides both detail mathematical foundation of each topic and practical examples to showcase their usefulness in application.

A statistitian bible for generalized linear models. Indispensable for students and statisticians.

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I found it difficult to follow this book. It is not meant for dummies like me. However, I don't have any alternative suggestions.

This book is the best theoretical work on Generalized Linear Models I have read. The mathematical foundations are gradually built from basic statistical theory and expanded until one has a good sense of the power and scope of the Generalized Linear Model approach to regression.As a learning text, however, the book has some deficiencies. GLM beginners probably want to know answers to question like: 1) Why should I perform GLM rather than OLS? 2) How do I determine an appropriate variance and link function? 3) How can I test whether my GLM has outperformed OLS?As is, the reader has to read through some 500 pages of theory to find answers to these relatively simple questions. There is real room for a text that could provide an easier approach to mastering this material.Even so, the book succeeds in its aim to provide an authoritative guide to GLM theory and practice. It deserves a place on every applied statistician's bookshelf.