R help - Sep 2003 - gam and concurvity

Hello, 

in the paper "Avoiding the effects of concurvity in GAM's .." of
Figueiras et
al. (2003) it is mentioned that in GLM collinearity is taken into account in 
the calc of se but not in GAM (-> results in confidence interval too narrow, 
p-value understated,  GAM S-Plus version). I haven't found any references to
GAM and concurvity or collinearity on the R page. And I wonder if the R 
version of Gam differ in this point.
Another question would be, what the best manual way of a variable selection 
is, due to the lack of a stepwise procedure for GAM. Including the first 
variables, add var1, if GCV improves (what would be considered as 
improvement?) or P-value signif., keep it, otherwise drop it - add var 2, and 
so on?

thanks in advance, cheers Martin

As someone (Simon Wood, for instance) could explain much better and as it is
stressed in the help files of the mgcv pakage (the package  including the
gam() function)
gam in R is not a clone of gam in S+.
S+ uses backfitting while R uses penalized splines (see the references
inside gam() function). The approaches are quite different and can lead to
substantial differences in particular cases, for instance with concurvity.

best,
vito

PS Can you point out the exact reference for "Figueiras et al.
(2003)"?


----- Original Message -----
From: Martin Wegmann <mailinglist.wegmann at gmx.net>
To: R-list <r-help at stat.math.ethz.ch>
Sent: Tuesday, September 16, 2003 3:47 PM
Subject: [R] gam and concurvity

> Hello,
>
> in the paper "Avoiding the effects of concurvity in GAM's .."
of Figueiras
et
> al. (2003) it is mentioned that in GLM collinearity is taken into account
in
> the calc of se but not in GAM (-> results in confidence interval too
narrow,
> p-value understated,  GAM S-Plus version). I haven't found any
references
to
> GAM and concurvity or collinearity on the R page. And I wonder if the R
> version of Gam differ in this point.
> Another question would be, what the best manual way of a variable
selection
> is, due to the lack of a stepwise procedure for GAM. Including the first
> variables, add var1, if GCV improves (what would be considered as
> improvement?) or P-value signif., keep it, otherwise drop it - add var 2,
and
> so on?
>
> thanks in advance, cheers Martin
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help

On Tue, 16 Sep 2003, Martin Wegmann wrote:
> Hello,
>
> in the paper "Avoiding the effects of concurvity in GAM's .."
of Figueiras et
> al. (2003) it is mentioned that in GLM collinearity is taken into account
in
> the calc of se but not in GAM (-> results in confidence interval too
narrow,
> p-value understated,  GAM S-Plus version). I haven't found any
references to
> GAM and concurvity or collinearity on the R page. And I wonder if the R
> version of Gam differ in this point.
They do.

R gam() uses penalised splines, resulting in an easily managed design
matrix.  S-PLUS gam() uses smoothing splines, and (until recently) there
wasn't any known feasible formula for the standard errors.

However:

1/ `Concurvity' is a serious problem only for a few extreme uses of gam.
Even in the air pollution time series studies that provoked the recent
fuss, there impact is really important only in studies that very
aggressively removed seasonal patterns or in data with huge seasonal
variations (eg inland Canada).

2/  These two cases are precisely the cases where the results are
sensitive to the choice of time scale at which seasonal variation
confounds the association, a choice that is not identifiable from the
data.

3/  Neither S-PLUS or R gam() standard errors incorporate the uncertainty
in an automatically chosen smoothing parameter.

4/ Trevor Hastie and colleagues have written software for calculating
correct standard errors for S-PLUS gam.

	-thomas

Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle