Dear Gavin / Rlings, thanks for your kind answer and sorry for posting to the dev mailing list.
Concerning the specific of your answer: I am working with 6 to 36 covariates, and they are all centred and scaled. I represented the problem with two variables to simplify the question. So ideally, the situation is: 1) y ~ s(x1) + .... + s(x36) vs. 2) y~s(x1, .... ,x36) I am trying to build a predictive model. Since the the variables are centred and scaled, I think I need an isotropic smooth. I am also interested in having the interactions between the variables included, that is not a purely additive model. It is not clear to me when should I give preference to tensor smooths, possibly because I have not understood well how they work. I am reading Wood(2003) as recommended and I have also read rather extensively Simon N. Wood. Generalized Additive Models: An Introduction, 2006, but still I am stuck. Any additional suggestion or reading recommendation would be greatly appreciated. I have also some difficulties in understanding the values you have chosen for k in the first example (why 60?). Thanks Best, On Monday 24 August 2009 17:33:55 Gavin Simpson wrote: > [Note R-Devel is the wrong list for such questions. R-Help is where this > should have been directed - redirected there now] > > On Mon, 2009-08-24 at 17:02 +0100, Corrado wrote: > > Dear R-experts, > > > > I have a question on the formulas used in the gam function of the mgcv > > package. > > > > I am trying to understand the relationships between: > > > > y~s(x1)+s(x2)+s(x3)+s(x4) > > > > and > > > > y~s(x1,x2,x3,x4) > > > > Does the latter contain the former? what about the smoothers of all > > interaction terms? > > I'm not 100% certain how this scales to smooths of more than 2 > variables, but Sections 4.10.2 and 5.2.2 of Simon Wood's book GAM: An > Introduction with R (2006, Chapman Hall/CRC) discuss this for smooths of > 2 variables. > > Strictly y ~ s(x1) + s(x2) is not nested in y ~ s(x1, x2) as the bases > used to produce the smoothers in the two models may not be the same in > both models. One option to ensure nestedness is to fit the more > complicated model as something like this: > > ## if simpler model were: y ~ s(x1, k=20) + s(x2, k = 20) > y ~ s(x1, k=20) + s(x2, k = 20) + s(x1, x2, k = 60) > ^^^^^^^^^^^^^^^^^ > where the last term (^^^ above) has the same k as used in s(x1, x2) > > Note that these are isotropic smooths; are x1 and x2 measured in the > same units etc.? Tensor product smooths may be more appropriate if not, > and if we specify the bases when fitting models s(x1) + s(x2) *is* > strictly nested in te(x1, x2), eg. > > y ~ s(x1, bs = "cr", k = 10) + s(x2, bs = "cr", k = 10) > > is strictly nested within > > y ~ te(x1, x2, k = 10) > ## is the same as y ~ te(x1, x2, bs = "cr", k = 10) > > [Note that bs = "cr" is the default basis in te() smooths, hence we > don't need to specify it, and k = 10 refers to each individual smooth in > the te().] > > HTH > > G > > > I have (tried to) read the manual pages of gam, formula.gam, > > smooth.terms, linear.functional.terms but could not understand properly. > > > > Regards -- Corrado Topi Global Climate Change & Biodiversity Indicators Area 18,Department of Biology University of York, York, YO10 5YW, UK Phone: + 44 (0) 1904 328645, E-mail: ct...@york.ac.uk ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
