# Textbooks on GLMs outside of Bernoulli, Binomial, and Poisson?

Edit: The question What is the best book about generalized linear models for novices? does not answer my question. For one thing, I have essentially all of the books mentioned in the answers to that question. They do not cover this material. I've bolded the parts that need particular emphasis in my question. These "novice" textbooks don't cover the topics that I am looking for.

Every textbook I've seen on linear models or generalized linear models covers the usual Bernoulli, binomial, and poisson GLMs (generalized linear models).

I am looking for a textbook which covers the theory behind other types of GLMs that I've read about: e.g., normal, inverse-Gaussian, and Gamma (and I think I've heard of Tweedie GLMs as well from someone; can't remember where).

Does anyone know where this material is covered in a textbook?

• Possible duplicate of What is the best book about generalized linear models for novices? Jun 7 '18 at 3:14
• @Xi'an I hate to tell you this, but I have all of those textbooks mentioned in the answers of that question, so I don't see how my question is resolved by the question you linked. Jun 7 '18 at 4:41
• The Extending the Linear Model with R by Faraway has a chapter on "other GLM", and the count regression also has a Negative Binomial discussion. Jun 7 '18 at 11:44
• @Greenparker That's a really good recommendation, thank you! Please feel free to put that as an answer. Jun 7 '18 at 11:44

I don't know why the book Generalized Linear Models by McCullagh and Nelder shouldn't be a top contender. It's considered the founding work on GLMs. It is a highly technical book, focused on interpretation, asymptotic theory, and general framework. A GLM is nothing more than a link function and a mean-variance relationship. Speaking as a mathematician, all the "second-generation" GLMs you mention are just special cases of the framework; and so with a good understanding and some confidence, you could derive, implement, fit, interpret, and test any of those models.

In the book, you can find many applied data analysis examples of interesting problems and inference such as cumulative link models (like proportional odds), the Cox model (which is a GLM interestingly), the cloglog link for discrete survival, and so on.

This book is not a comprehensive dictionary of named GLMs (that would be a waste of time) nor is it a detailed step-by-step implementation guide for fitting GLMs in R (it assumes the reader has the know-how). However, it dovetails excellently with R's glm. The help file even demonstrates fitting models with custom link functions.

• (+1) I agree with this as 2018 Matt, but when I was first getting into statistics (from a math background) this book was completely impenetrable to me. I think it's a really good second book, or a good first book for someone that knows the jargon of the field pretty well already. Just a heads up for anyone that is feeling discouraged. Jun 7 '18 at 20:50
• I agree that it's good but highly technical. It's "McCullagh", by the way ... Jun 7 '18 at 21:06

The book Extending the Linear Model with R by Faraway has a chapter on "other GLM", and the count regression chapter also has a Negative Binomial discussion.

Generalized Linear Modeling with H20 has something on Gamma GLMs and Tweedie GLMs. Note that Tweedie GLMs are used often by insurance companies, so you may be able to find more literature with key words from there.

Hardin and Hilbe cover a bit more than the typical basic book (Dobson and Barnett, etc.); the table of contents shows that they have chapters covering Gamma, inverse Gaussian, etc.. As I recall they also have some other useful extensions for count data (like the NB1, i.e. a negative binomial with variance proportional to the mean rather than a quadratic function of the mean).