Hi Simon, Thanks for this explanation. To make sure I understand, another way of explaining the y axis in my original example is that it is the contribution to snowdepth relative to the other variables (the example only had fsca, but my actual case has a couple others). i.e. a negative s(fsca) of -0.5 simply means snowdepth 0.5 units below the intercept+s(x_i), where s(x_i) could also be negative in the case where total snowdepth is less than the intercept value.
The use of by=fsca is really useful for interpreting the marginal impact of the different variables. With my actual data, the term s(fsca):fsca is never negative, which is much more intuitive. Is it appropriate to compare magnitudes of e.g. s(x2):x2 / mean(x2) and s(x2):x2 / mean(x2) where mean(x_i) are the mean of the actual data? Lastly, how would these two differ: s(x1,by=x2); or s(x1,by=x1)*s(x2,by=x2) since interactions are surely present and i'm not sure if a linear combination is enough. Thanks! Dominik On Wed, May 11, 2016 at 3:11 AM, Simon Wood <simon.w...@bath.edu> wrote: > The spline having a positive value is not the same as a glm coefficient > having a positive value. When you plot a smooth, say s(x), that is > equivalent to plotting the line 'beta * x' in a GLM. It is not equivalent > to plotting 'beta'. The smooths in a gam are (usually) subject to > `sum-to-zero' identifiability constraints to avoid confounding via the > intercept, so they are bound to be negative over some part of the covariate > range. For example, if I have a model y ~ s(x) + s(z), I can't estimate the > mean level for s(x) and the mean level for s(z) as they are completely > confounded, and confounded with the model intercept term. > > I suppose that if you want to interpret the smooths as glm parameters > varying with the covariate they relate to then you can do, by setting the > model up as a varying coefficient model, using the `by' argument to 's'... > > gam(snowdepth~s(fsca,by=fsca),data=dat) > > > this model is `snowdepth_i = f(fsca_i) * fsca_i + e_i' . s(fsca,by=fsca) > is not confounded with the intercept, so no constraint is needed or > applied, and you can now interpret the smooth like a local GLM coefficient. > > best, > Simon > > > > > On 11/05/16 01:30, Dominik Schneider wrote: > >> Hi, >> Just getting into using GAM using the mgcv package. I've generated some >> models and extracted the splines for each of the variables and started >> visualizing them. I'm noticing that one of my variables is physically >> unrealistic. >> >> In the example below, my interpretation of the following plot is that the >> y-axis is basically the equivalent of a "parameter" value of a GLM; in GAM >> this value can change as the functional relationship changes between x and >> y. In my case, I am predicting snowdepth based on the fractional snow >> covered area. In no case will snowdepth realistically decrease for a unit >> increase in fsca so my question is: *Is there a way to constrain the >> spline >> to positive values? * >> >> Thanks >> Dominik >> >> library(mgcv) >> library(dplyr) >> library(ggplot2) >> extract_splines=function(mdl){ >> sterms=predict(mdl,type='terms') >> datplot=cbind(sterms,mdl$model) %>% tbl_df >> datplot$intercept=attr(sterms,'constant') >> datplot$yhat=rowSums(sterms)+attr(sterms,'constant') >> return(datplot) >> } >> dat=data_frame(snowdepth=runif(100,min = >> 0.001,max=6.7),fsca=runif(100,0.01,.99)) >> mdl=gam(snowdepth~s(fsca),data=dat) >> termdF=extract_splines(mdl) >> ggplot(termdF)+ >> geom_line(aes(x=fsca,y=`s(fsca)`)) >> >> [[alternative HTML version deleted]] >> >> ______________________________________________ >> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see >> 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. >> > > > -- > Simon Wood, School of Mathematics, University of Bristol BS8 1TW UK > +44 (0)117 33 18273 http://www.maths.bris.ac.uk/~sw15190 > > [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.