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I use GAMs more and more. When I go to provide references for their various components (smoothing parameter selection, various spline bases, p-values of smooth terms), they are all from one researcher -- Simon Wood, at the University of Bath, in England.

He is also the maintainer of mgcv in R, which implements his body of work. mgcv is enormously complex, but works remarkably well.

There is older stuff, for sure. The original idea is credited to Hastie & Tibshirani, and a great older textbook was written by Ruppert et al in 2003.

As an applied person, I don't have much of a feel for the zeitgeist among academic statisticians. How is his work regarded? Is it a bit strange that one researcher has done so much in one area? Or is there other work that simply isn't noticed as much because it doesn't get put inside of mgcv? I don't see GAMs used that much, though the material is reasonably accessible to people with statistical training, and the software is quite well-developed. Is there much of a "back-story"?

Recommendations of perspectives pieces and other similar stuff from stat journals would be appreciated.

user59828
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  • This questions seems to me to be not well suited to CV. It seems somewhat broad, fuzzy & potentially off-topic. Can you focus it more & try to make it more clearly on-topic? (Asking for references for a specific aspect of GAMs would certainly be on-topic, for example.) – gung - Reinstate Monica Nov 02 '14 at 23:16
  • I'm aware that it's a bit fuzzy. It's sort of a meta-question about the discipline of statistics, and I'm not sure where to go with it. I would appreciate references to commentary and perspectives pieces however, and will amend the question to include that. – user59828 Nov 02 '14 at 23:18
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    Thomas Kneib and Fabian Scheipl are two names that I am familiar with from this field and who promote a somewhat different way of fitting GAMs and related models. I get the impression that there is friendly "competition" between Simon Wood and these guys as I see Wood developing new ideas in papers & features in **mgcv** that are in "response" to the work of Kneib & Schiepl, and others. Knieb for example is one of the developers of BayesX which fits structured additive models & is somewhat different from Wood's penalized regression approach. – Gavin Simpson Nov 02 '14 at 23:25
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    For example, see [Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data](http://ukcatalogue.oup.com/product/9780199533022.do) by Fahrmier & Kneib for a wide ranging coverage of the structure additive model approach. – Gavin Simpson Nov 02 '14 at 23:31
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    I think questions about statistical culture are really useful. This one has already attracted one interesting answer, albeit posted as a pair of comments. – Flounderer Nov 02 '14 at 23:48
  • @Flounderer I don't think Gung was suggesting that such questions weren't useful, just not on topic for [stats.se]. This is a general statement for the family of [se] sites, not something we dreamt up just for [stats.se]. This isn't a discussion site and there really isn't going to be a definitive answer etc. I'm sympathetic as I think this is an interesting question too, but I also know the [se] rules; that's why I threw in a bone in the comments in case the OP didn't focus their question. – Gavin Simpson Nov 03 '14 at 14:36

2 Answers2

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There are many researchers on GAMs: it's just that basically the same model (GLM with linear predictor given by sum of smooth functions) is given lots of different names. You'll find models that you could refer to as GAMs called: semiparametric regression models, smoothing spline ANOVA models, structured additive regression models, generalized linear additive structure models, generalized additive models for location scale and shape, Gaussian latent variable models, etc.

A small selection of researchers on GAM-related topics with a computational angle is:

Ray Carroll, Maria Durban, Paul Eilers, Trevor Hastie, Chong Gu, Sonja Greven, Thomas Kneib, Stephan Lang, Brian Marx, Bob Rigby, David Ruppert, Harvard Rue, Fabian Scheipl, Mikis Stasinopoulus, Matt Wand, Grace Wahba, Thomas Yee.

(and there are a whole lot more people working on boosted GAMs, GAM-related theory and closely related functional data analysis methods). My papers are mostly about developing GAM methods that are efficient and general to compute with, but that's certainly not all there is to say on the subject.

Nick Cox
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Simon Wood
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google scholar gives a lot of hits, in addition to the references above, and in comments, some which looks interesting is:

http://www.sciencedirect.com/science/article/pii/S0304380002002041 GAM's in studies of species distributions, published in "Ecological Modelling"

http://aje.oxfordjournals.org/content/156/3/193.short Use of GAM's in studies of air pollution and health

but the OP seems to care more for statistical theory, so:

http://www.sciencedirect.com/science/article/pii/S0167947398000334 this is about better fitting algorithms

http://onlinelibrary.wiley.com/doi/10.1111/1467-9876.00229/abstract Bayesian inference based on MArkov Random Field priors

http://onlinelibrary.wiley.com/doi/10.1111/1467-9469.00333/abstract?deniedAccessCustomisedMessage=&userIsAuthenticated=false about estimation methods in GAM's ...

all this with many different authors, so the answer to original question seems to be many.

kjetil b halvorsen
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    As an aside, I have found little advantage of GAM's over parametric additive regression spline models, which give simpler formal tests and confidence intervals, and provide formulas for prediction. – Frank Harrell Jan 01 '15 at 22:18