# Reference Request: Generalized Linear Models

I am looking for an introductory to intermediate level book on Generalized Linear Models. Ideally, in addition to the theory behind the models, I would want it to include applications and examples in R or another programming language - I hear SAS is also a popular choice. I intend to study it on my own and so it would help if it provided the answers to its own exercises.

You can assume I have taken the traditional year-long courses in calculus and probability theory. I am also familiar with the basics of regression analysis.

Gelman, Andrew, and Jennifer Hill. Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, 2007, is not about GLMs per se, but also covers that and has a nice mix of theory, hands-on-advice, implementation in R, and exercises (and, when you websearch for it, you might find an ebook version of it!).

Not a textbook, but freely available is this graduate statistics course from the Harvard Government Department, which also covers the most common GLMs. The section videos cover implementation in R. The textbook is King, Gary. Unifying political methodology: The likelihood theory of statistical inference. University of Michigan Press, 1989.

Disclaimer: Highly subjective personal opinion follows...

For theory and applications I can't recommend Generalized Linear Models and Extensions by Hardin and Hilbe too highly. It uses SPSS Stata, (both of) which I never use and know nothing about, but it covers the theory and has a very rich set of examples. If I had to choose one book to start with, it would be this one.

A more theory-focused book is Generalized, Linear, and Mixed Models by McCulloch, Searle, and Neuhaus. This has fewer examples than Hardin and Hilbe but goes further into random effects for both the linear model and the GLM. This is my favorite GLM book, because it connects a lot of things together, but if you have no interest in random effects it may be overkill.

What I would call a canonical reference for GLMs is Generalized Linear Models by McCullagh and Nelder. It's a little older title but I enjoyed it very much.

Generalized Linear Models with Applications in Engineering and the Sciences by Myers, Montgomery, Vining, and Robinson spends a little more time on the binary/poisson GLMs and also has interesting examples. The new edition has examples in a few languages, including R.

I picked up Faraway's Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models a while back, and it has been very useful for helping me do things in R, though it's not a good "teach yourself GLM" book. But it may be a good companion to some of the other books out there.

• Thanks! I think I'll take a closer look at Hardin and Hilbe as well as McCullagh and Nelder. You must have got very good after studying all these texts. ^^ Apr 20 '14 at 21:14
• The McCullagh & Nelder book is an uber-classic! Apr 20 '14 at 21:14
• Major error: Hardin and Hilbe book is based on Stata, not SPSS. Apr 20 '14 at 23:02
• Hardin & Hilbe is quite good. Apr 21 '14 at 3:23

I really like Frank Harrell's Regression Modeling Strategies.

The text by Dobson and Barnett

http://www.amazon.com/Introduction-Generalized-Edition-Chapman-Statistical/dp/1584889500

is I think aimed in exactly the direction you ask. It does a good job of balancing technical detail and friendly style.

• I am really liking that book. I wish it included R-code as well. Apr 20 '14 at 19:39

This one helped me out a lot:

Springer Linear mixed effect models using R by A. Galecki and T. Burzykowski.

http://www.springer.com/statistics/statistical+theory+and+methods/book/978-1-4614-3899-1

Introduction to Statistical Learning with Applications in R was a really easy to follow introductory text that covers GLM's and as the title suggests comes with problem sets and example code in R. I learned a lot from going through that book.

If you feel comfortable with Linear Algebra Elements of Statistical Learning covers that same material in more detail, and many other topics as well, but it doesn't have the same kind of easy to follow tutorial style R examples in the chapters.

• I am very impressed with the quality of Statistical Learning with Applications in R. I think I will give it a try and possibly buy it. Thank you. Apr 22 '14 at 22:23

The lecture notes for German Rodriguez' Princeton course on GLMs are a thorough introduction, packed with examples of the more common types, & explaining the relationships between them. The more theoretical aspects are separated in two appendices.

Alain Zuur's book "A beginners guide to GLM and GLMM with R" gives some nice examples for GLMs and GLMMs in R.

Here is a good write up on generalized linear regression. The code is done in R and it explains how they work. CRAN also has a package glmnet which does this for you but can be a bit unwieldy to use initially. But once you get a hang of it, its quite flexible. Here is a good write up on glmnet. Hope that helps.

• The first link is not about generalized linear models at all. GLMs doesn't mean use regression with transformations. May 25 '15 at 17:30