The problem here is that the help page you are looking at appears to be from an earlier version of `mgcv' than you are using (it's from a version that did not support factor `by' variables). Take a look at ?gam.models for the version that you are actually using.
The reason that your models give the same fit is because ~z and ~z-1 differ only in the identifiability constraints used, when `z' is a factor (for all linear type models). As far as model reasonableness is concerned: it's a bit difficult to say without knowing the context. The only thing that stands out is that you are using an isotropic `s' term for the interaction --- this is fine if `byear' and `FAFR' are really naturally on the same scale, but if not tensor product smooths (`te') may be preferable, as the are independent of the relative scaling of the variables. For plot interpretability, I'd drop the `main effect' smooths and just leave in the interaction. best, Simon On Tuesday 05 May 2009 16:53, willow1980 wrote: > I am a little bit confusing about the following help message on how to fit > a GAM model with interaction between factor and smooth terms from > http://rss.acs.unt.edu/Rdoc/library/mgcv/html/gam.models.html: > “Sometimes models of the form: > E(y)=b0+f(x)z > need to be estimated (where f is a smooth function, as usual.) The > appropriate formula is: > y~z+s(x,by=z) > - the by argument ensures that the smooth function gets multiplied by > covariate z, but GAM smooths are centred (average value zero), so the z+ > term is needed as well (f is being represented by a constant plus a centred > smooth). If we'd wanted: > E(y)=f(x)z > then the appropriate formula would be: y~z+s(x,by=z)-1.” > When I tried two scripts, I found they gave the same results. That is, the > codes “y~z+s(x,by=z)” and “y~z+s(x,by=z)-1” gave the same results. The > following is my result: > ########################################################################### > “anova(model1,model2,test="Chisq") > Analysis of Deviance Table > > Model 1: FLBS ~ SES + s(FAFR, by = SES) + s(byear, by = SES) + s(FAFR, > byear, by = SES) > Model 2: FLBS ~ SES + s(FAFR, by = SES) + s(byear, by = SES) + s(FAFR, > byear, by = SES) - 1 > Resid. Df Resid. Dev Df Deviance P(>|Chi|) > 1 1.2076e+03 1458.4 > 2 1.2076e+03 1458.4 1.9099e-11 5.030e-10 2.074e-10” > ########################################################################### > Is this in conflict with above statement that “If we'd wanted: E(y)=f(x)z > then the appropriate formula would be: y~z+s(x,by=z)-1.”? Also, if you are > familiar with GAM modelling, please have a look at my modelling process. > That is, I want to study how one factor together with two smooth terms will > influence the response. In model2, I also fitted the interaction between > two smooth terms, together with the interaction of this interaction with > factor. Is model 2 reasonable? I find it is rather complicated to interpret > the plot of model 2. > Thank you very much for helping! -- > Simon Wood, Mathematical Sciences, University of Bath, Bath, BA2 7AY UK > +44 1225 386603 www.maths.bath.ac.uk/~sw283 ______________________________________________ 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.
