gam variable selection
On Wed, 2011-09-28 at 10:44 +0100, Rebecca Ross wrote:
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.
Forward selection/backward elimination should be avoided at all costs. By doing this sort of inclusion/elimination you are introducing selection bias into the "coefficients" for the terms in the models. You are explicitly setting some to zero be excluding them from the model and this biases the other "coefficients". Many quantitative ecologists bemoan the continued use of step-wise feature selection procedures by ecologists. See for example Whittingham et al. (2006). Marra and Wood (2011) look at a backwards elimination strategy as part of their comparison of variable selection methods for GAMs. IIRC, it performs badly.
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.
By restricting the dimension of the basis functions to such low levels, you are making an explicit statement about the forms of model that the GAM can fit. This is fine if you have knowledge to guide this process, say from previous work etc. that suggests such forms for the fitted smooths, but if not, you are forcing a very restrictive set of models that can be fitted.
Also remember to throw out significantly correlated variables once one of your correlates has been selected.
This is an important point - known as concurvity in additive models. mgcv has a function to compute some measures that might indicate the presence of concurvity, but this is more involved than just looking for correlated variables - note that linear correlation is not much use when you are allowing for non-linear relationships between variables.
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.
The idea here is that one can average the predictions from the set of best candidate models - not use it as a means to find the best set of predictors for a single model. The paper by Marra and Wood (2011), whilst being somewhat technical in places, is a excellent resource for comparing the various means available for doing feature selection in GAMs. Whilst theirs is but one study, the general result appears to be that adding an extra penalty to the penalised regression solved by mgcv:::gam(), which allows variables to be shrunk out of the model entirely, is a robust and powerful means of identifying important features. Couple this with fitting via REML or ML (not the default GCV) as GCV can overfit and we now have very good guides as to how to perform feature selection in, and fit, GAMs via the penalised regression approach of Simon Wood as implemented in his mgcv package. G Refs: Marra G., Wood S.N. (2011) Practical variable selection for generalized additive models. Computational Statistics and Data Analysis 55; 2372-2387 Whittingham MJ, Stephens PA, Bradbury RB, Freckleton RP (2006) Why do we still use step-wise modelling in ecology and behaviour? J Animal Ecol 75:1182-1189
All the best, Bex Research Assistant University of Plymouth -----Original Message----- From: r-sig-ecology-bounces at r-project.org [mailto:r-sig-ecology-bounces at r-project.org] On Behalf Of r-sig-ecology-request at r-project.org Sent: 27 September 2011 11:00 To: r-sig-ecology at r-project.org Subject: R-sig-ecology Digest, Vol 42, Issue 16 Send R-sig-ecology mailing list submissions to r-sig-ecology at r-project.org To subscribe or unsubscribe via the World Wide Web, visit
https://stat.ethz.ch/mailman/listinfo/r-sig-ecology or, via email, send a message with subject or body 'help' to r-sig-ecology-request at r-project.org You can reach the person managing the list at r-sig-ecology-owner at r-project.org When replying, please edit your Subject line so it is more specific than "Re: Contents of R-sig-ecology digest..." Today's Topics: 1. gam variable selection (Marco Helbich) 2. Re: gam variable selection (Gavin Simpson) ---------------------------------------------------------------------- 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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