What important ideas came since Nelder and McCullagh's book Generalized Linear Models (a 40 year old book)? I read not too long ago Nelder and McCullagh's book Generalized Linear Models and thought the book was fantastic and I consider it a useful manual on the subject. Not surprising that's the case, considering Nelder's one of the authors.
However, the book is 40 years old, and surely things have changed since when the book came out. Simon Wood's book, Generalized Additive Models, is very good, but the book focuses on GAMs, not GLMs. (Yes, GAMs generalize GLMs, but I do think focusing on GLMs specifically is worthwhile.)
Hence, what would be the most important developments since Nelder and McCullagh's book came out regarding GLM theory and application? What am I missing from just reading that book? How should I supplement my knowledge?


Hence, what would be the most important developments since Nelder and McCullagh's book came out regarding GLM theory and application? What am I missing from just reading that book? How should I supplement my knowledge?

Numerical methods if you want to implement the theory on your own.
Computers are now more powerful and computational methods have advanced.
For specific examples,
Firebug mentioned this in their answer about Bayesian methods.
Bolker et al. (2009) include a high-level overview of different methods in their article about GLMMs.
Personally, I would look at two specific areas for numerical methods:

*

*The approach used for speed and larger datasets. For example, Stan is much faster than JAGS for Bayesian methods under most situations. Likewise, Julia can be quicker than R. Both Stan and Julia were created as response to people wanted quicker languages.

*The assumptions of different GLM methods for ideas such as degrees for freedom and treatment of variance structures.

My own experience with Stan has shown me that mathematical ideas can be sped up in computer languages using methods that seem strange to me and not counter intuitively. Browse the Stan forum for discussion and examples such as the "folk theorem".
