7
$\begingroup$

Is there consensus in the field of statistics that one book is the absolute best source and completely covering every aspect of GLM - detailing everything from estimation to inference?

$\endgroup$
  • 3
    $\begingroup$ In my opinion, no book should be considered the first and last word on any topic, and it's often a bad idea to try to have one. Further, it leads to people treating statements in overly comprehensive works as prescriptive -- this often leads to poor practice when such statements are applied too broadly. I'd prefer to see several shorter works than one huge one -- among other things it helps prevent stagnation - e.g. it's easier to replace any of them when a better short work on that aspect comes along (i.e. to keep up to date). ... ctd $\endgroup$ – Glen_b Apr 27 '16 at 9:30
  • 1
    $\begingroup$ ctd ... It also helps to read several different takes on the same topic, which there's a tendency to avoid if one book is seen as "the" reference. $\endgroup$ – Glen_b Apr 27 '16 at 9:30
  • 2
    $\begingroup$ A book covering every aspect is impossible to write and impossible to read. So forget about that. Instead you need to be looking for a book that answers your questions. So it should be appropriate for your background knowledge, and it should deal with questions that are likely to pop up in the kind of applications you are planning. McCullagh and Nelder suggested by @Tim is a great book, and at the time it was a great step forwards, but it may or may not be the right book for you. $\endgroup$ – Maarten Buis Apr 27 '16 at 9:34
  • $\begingroup$ Thank you for the input. I was just curious if any such attempt to make such a "bible" had been made, even though you make very good points why it would be a bad idea. Personally I have not one question needing to be answered, just being curious here :) $\endgroup$ – Erosennin Apr 27 '16 at 10:39
12
$\begingroup$

Is there consensus in the field of statistics that one book is the absolute best source and completely covering every aspect of GLM - detailing everything from estimation to inference?

No, there is not. However the classic reference about GLM's would be:

McCullagh, P., & Nelder, J.A. (1989). Generalized linear models. CRC press.

$\endgroup$
  • $\begingroup$ Be warned that it is quite tough reading. But worth it. $\endgroup$ – mdewey Apr 27 '16 at 10:49
  • $\begingroup$ @mdewey Knowing this, I shall embrace my future frustration $\endgroup$ – Erosennin Apr 27 '16 at 10:55
  • 1
    $\begingroup$ @mdewey it's not that tough :) $\endgroup$ – Tim Apr 27 '16 at 11:05
4
$\begingroup$

It's hard to beat

Generalized Linear Models. P. McCullagh, J. Nelder. CRC Press. 2nd edition, 1989

It is comprehensive.

$\endgroup$
  • $\begingroup$ Does it explain the concepts in a simple matter? I have tried a book from Alan _ Agresti( foundations of linear and generalized linear models. It was hard for me to keep up with. $\endgroup$ – R.Hes Jul 18 '16 at 12:28
  • $\begingroup$ Agresti is a good book. Is there anything in particular you struggled with ? Any book on glms is going to assume a certain level of mathematics. You might benefit from studying some underlying concepts such as matrix algebra and general statistical theory. $\endgroup$ – Robert Long Jul 18 '16 at 12:37
  • $\begingroup$ Yeah. Definitely it's a good book, no doubt. But you know some times it jumps some concepts that it hasn't yet discussed. For example I was trying to figure out the proof for least square function and then right at the middle of the way says" based on pearson product moment formula..." and then everything breaks apart in my mind. How should I have to know about Pearson - product - formula, when I was trying to understand leat squares for simple lines regression in chapter 2 of the book. Pearson distribution is in later chapters. So you know these sort of things bother me. $\endgroup$ – R.Hes Jul 18 '16 at 12:46
  • $\begingroup$ Note that Tim offered this exact reference in an answer posted earlier than this one (April vs July). It appears to be a duplicate of his answer. $\endgroup$ – Glen_b Sep 30 '17 at 0:38
3
$\begingroup$

I don't think there is a single book that will be exactly what you want. From your description, I think the best fit would be:

It is a classic. It does cover the math, but is also more introductory than other books that do so.

$\endgroup$
2
$\begingroup$

The closest thing I've found to a GLM Bible is Applied Linear Statistical Models by Kutner, Nachtsheim, Neter, and Li. It's over 1400 pages and covers linear regression and GLMs. Virtually anything involving GLMs can be found in that book.

$\endgroup$
  • $\begingroup$ Cheers! I'll take a look at it $\endgroup$ – Erosennin Apr 27 '16 at 15:19
  • 1
    $\begingroup$ The question says GLM, but the tag says generalized linear model. Correct me if I am wrong, but I think this is a general linear model book. $\endgroup$ – Nick Cox Apr 27 '16 at 16:05
  • $\begingroup$ No it definitely has generalized. Poisson, logistic regression, negative binomial, probit, etc. $\endgroup$ – Brandon Sherman Apr 27 '16 at 16:06
  • 1
    $\begingroup$ From top reviewer on Amazon: "My only disappointment regarding content was the rather slim coverage of random and mixed effects models and GLM's". But it has the size of a bible, at least :-) $\endgroup$ – Erosennin Apr 29 '16 at 14:03
  • $\begingroup$ Random and mixed effect models are so complex, you pretty much need a book entirely on them. For a 1400-page book that covers literally everything else, you'd need some kind of a crazy binding to fit that! For random and mixed effects, Gelman & Hill is the gold standard. $\endgroup$ – Brandon Sherman Apr 29 '16 at 14:04
2
$\begingroup$

The Nelder book already mentioned is a good one.

Just for more consideration I would recommend Elements of Statistical Learning Second Edition by Trevor Hastie, Robert Tibshirani, Jerome Friedman. I Like ESL because it covers such a breadth of statistical and machine learning topics. It shows how GLMs fit in with other techniques (and it's free).

And as seen in this question, I'd recommend the Simon Wood text Generalised Additive Models: an introduction with R. I really believe the Wood text is worth considering because, while it says it covers GAMs, it really covers LMs, GLMs, and GAMs in detail and introduces some mixed modeling techniques as well. Wood's approach is to introduce each topic with a theoretical background, but then the text is very practical and has examples already in an R package that can be downloaded to accompany the book.

$\endgroup$
1
$\begingroup$

Introductory books:

  • An introduction to generalized linear models, by George Dunteman and Moon-Ho Ho (2006). Only 72 pages.

  • Generalized linear models : a unified approach, by Jeff Gill (2001) This is also short (101 pages).

Then you have more textbook-like, longer books like the one you mention (444 pages), or the one in the other answer (511 pages).

$\endgroup$
1
$\begingroup$

A good book is the one by Fahrmeir et al https://www.amazon.com/Multivariate-Statistical-Modelling-Generalized-Statistics/dp/0387951873/ref=sr_1_1?s=books&ie=UTF8&qid=1506715879&sr=1-1 "Multivariate Statistical Modelling Based on Generalized Linear Models (second edition)", maybe not for a first treatment, but for various extensions of the basic model and coverage of computational algorithms. As the title says, multivariate extensions, semiparametric approaches (splines) and extensions to time series, and more.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.