gam()

2. John Fox has modified anova.glm() into anova.gam() 
(http://www.socsci.mcmaster.ca/jfox/Books/Companion/nonparametric-regression.txt) 
for comparison of two or more fitted models based on the difference 
between residual deviances. Indiscriminate use of such a procedure 
shouldn't perhaps be encouraged, but I think that many users expect it to 
be part of the mgcv package since this model selection idea is covered in 
several texts and also implemented in S-plus (and may be OK for truly 
nested models). And even if it's been decided that this functionality is 
not wanted in mgcv, perhaps another function comparing several models by 
the GCV/UBRE score and other useful statistics can be implemented?

The problem with comparing two gams in R fit with mgcv is that, by 
default, the degree of smoothing for terms is selected independently for 
each model. Simon Wood previously posted a message to the R-help list 
discussing this issue and making some suggestions. The issue doesn't arise 
in the same way with models fit by the gam function in S-PLUS because the 
degree of smoothing there is instead selected by the user. I should update 
my appendix on nonparametric regression to discuss this question -- the 
current presentation isn't really adequate.

I'm aware of this difference between gam() in R and S-Plus, which is why I 
proposed a function listing relevant statistics for every fitted model so 
the analyst can use these to judge, without hypothesis testing, which model 
to prefer. Still, for models where the analyst has made sure that the 
models are truly nested, the use of your anova.gam can be justified by the 
simulation results reported by Hastie & Tibshirani (1990, p. 155); maybe I 
just want it for purely nostalgic reasons?! ;-)

Admittedly, I like the more attractive way of chosing the degrees of 
freedom that mgcv provides. However, I must admit that since most text 
books covering GAMs are more or less Splus based, and the possibilities 
that mgcv offers are so vast, I'm feeling a bit lost at times; it's great 
to have to new more flexible tools, but on the downside that means more 
choices to be made. So, anyone got any essential literature tips? I've read 
(and re-read, and read again) Simon Wood's articles in JRSS, R News and 
Ecological Modelling, and, of course, the mgcv manual.

//Henric

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