[R-sig-eco] gam variable selection

Wed Sep 28 12:00:27 CEST 2011

Hi Bex

Did you mean the dredge function from the MuMIn package? I'm not really sure what you mean by "it does not take into account correlates or significance". The point about dredge is that it is part of a family of functions for multi-model inference which specifically avoid concepts of "significance". It must not be used on its own. ANY stepwise procedure, forwards, backwards and including all subsets (dredge) will give BIASED parameter estimates if you just pick the best model. The application of the multi-model inference approach guards against this, and MuMIn provides all the functions to do this properly. I'd recommend anyone thinking of doing stepwise variable selection to learn more about this by reading the book by Burnham and Anderson, who give an excellent description of the pitfalls of dredging and stepwise selection, and explains why a multimodel approach, which completely avoids concepts of significance, is the most appropriate manner to compare alternative models of environmental data (i.e. not designed experiments) and make predictions.

Regards
Mike

-----Original Message-----
From: r-sig-ecology-bounces at r-project.org [mailto:r-sig-ecology-bounces at r-project.org] On Behalf Of Rebecca Ross
Sent: 28 September 2011 10:45
To: r-sig-ecology at r-project.org
Subject: Re: [R-sig-eco] gam variable selection

Hi Marco,
Having recently been working with gams myself I would suggest a procedure whereby you build your model in a forward stepwise approach first, having run individual gams for each of your variables and selecting the significant variable with the best AIC as your first variable, and iteratively trying out the other variables as 2nd in the gam, selecting the combination with the best AIC, and repeating until you get no further AIC improvement.

I found it advisable to always first run each gam with all smooth functions applied (and with number of knots restricted to avoid overfitting the model using the term k=4 for 4 knots e.g. gam(x~s(y,k=4)+s(z,k=4), family=Gaussian)) then check the plots for each of your variables and rerun each model with linear functions applied as advised by the plots.

Also remember to throw out significantly correlated variables once one of your correlates has been selected.

The backwards stepwise model build could then be run to check the forwards build and using a global model that has excluded the thrown out correlates.

Also worth knowing, but not worth relying on, is that there is a function called "dredge" which will run through your global model and list the potential model builds in order of best AIC. This is a variable selection algorithm but it does not take into account correlates or significance so it is best used only as advice and another check for a longhand build.

All the best,
Bex

Research Assistant 
University of Plymouth

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Subject: R-sig-ecology Digest, Vol 42, Issue 16

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Today's Topics:

   1. gam variable selection (Marco Helbich)
   2. Re: gam variable selection (Gavin Simpson)

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Message: 1
Date: Tue, 27 Sep 2011 08:54:52 +0200
From: Marco Helbich <marco.helbich at gmx.at>
To: r-sig-ecology at r-project.org
Subject: [R-sig-eco] gam variable selection
Message-ID: <4E81733C.8090700 at gmx.at>
Content-Type: text/plain; charset=ISO-8859-15; format=flowed

Dear list,

I am studying the influence of several environmental factors (numeric &
dummies) on species densities (= numeric) using the gam() function with a gaussian link function in the mgcv package. As stated in Wood (2006) there is no variable selection algorithm.

Is it an appropriate (iterative) approach to drop the predictor being least significant (eg. p > 0.05), refit the model, compare the GCV/AIC score and so forth. Should I first focus on the smoothing functions or fixed effects? Or is such a distinction not important at all?

Perhaps someone has more experience with GAMs and can give me a helping hand? Thanks in advance!

Best
Marco
--
Marco Helbich
Department of Geography
University of Heidelberg

------------------------------

Message: 2
Date: Tue, 27 Sep 2011 10:40:27 +0100
From: Gavin Simpson <gavin.simpson at ucl.ac.uk>
To: Marco Helbich <marco.helbich at gmx.at>
Cc: r-sig-ecology at r-project.org
Subject: Re: [R-sig-eco] gam variable selection
Message-ID: <1317116427.2714.3.camel at chrysothemis.geog.ucl.ac.uk>
Content-Type: text/plain; charset="UTF-8"

On Tue, 2011-09-27 at 08:54 +0200, Marco Helbich wrote:
> Dear list,
> 
> I am studying the influence of several environmental factors (numeric &
> dummies) on species densities (= numeric) using the gam()
> function with a gaussian link function in the mgcv package. As stated in
> Wood (2006) there is no variable selection algorithm.
> 
> Is it an appropriate (iterative) approach to drop the predictor being
> least significant (eg. p > 0.05), refit the model, compare the GCV/AIC
> score and so forth. Should I first focus on the smoothing functions or 
> fixed effects? Or is such a distinction not important at all?
> 
> Perhaps someone has more experience with GAMs and can give me a helping
> hand? Thanks in advance!

You could do that, but I would be sceptical of the results.

Marra and Wood (2011, Computational Statistics and Data Analysis 55;
2372-2387) compare various approaches for feature selection in GAMs.
IIRC, they concluded that an additional penalty term in the smoothness
selection procedure gave the best results. This can be activated in
mgcv::gam() by using the `select = TRUE` argument/setting.

HTH

G

> Best
> Marco

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