On Tue, 2009-08-25 at 10:00 +0100, Corrado wrote: > 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 think you are pushing things a bit with such a complicated smooth. You're unlikely to be able to fit that either due to insufficient data and / or hardware limits on your machine. I see that Simon has responded to this as well, in a far more comprehensive and informed manner than I could manage.... So I'll leave it at that... > > 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. That sounds a bit like data fishing; throw everything into the pot and see what comes out of it. <snip /> > I have also some difficulties in understanding the values you have chosen for > k > in the first example (why 60?). Sorry, that was a complication on my part. The main point was to show that you need to try to get the same bases used in the s(x1) and s(x2) parts of the formula; So if you had this model y ~ s(x1, k = 20) + s(x2, k = 20) You need something like y ~ s(x1, k = 20) + s(x2, k = 20) + s(x2, x2) [If you wanted the bivariate smooth to be more complicated than the default in mgcv, then you might have done: y ~ s(x2, x2, k = 60) ## for example in which case you could fit that model as y ~ s(x1, k = 20) + s(x2, k = 20) + s(x2, x2, k = 60) ] That was where the k = 60 came from, but in simplifying my response I forgot to remove it. Simon has since provided a more thorough response (Thanks Simon). HTH G > > 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 > > > -- %~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~% Dr. Gavin Simpson [t] +44 (0)20 7679 0522 ECRC, UCL Geography, [f] +44 (0)20 7679 0565 Pearson Building, [e] gavin.simpsonATNOSPAMucl.ac.uk Gower Street, London [w] http://www.ucl.ac.uk/~ucfagls/ UK. WC1E 6BT. [w] http://www.freshwaters.org.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.
