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! -- View this message in context: http://www.nabble.com/A-question-about-using-%E2%80%9Cby%E2%80%9D-in-GAM-model-fitting-of-interaction-between-smooth-terms-and-factor-tp23390342p23390342.html Sent from the R help mailing list archive at Nabble.com. ______________________________________________ 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.