On 12/05/16 02:29, Dominik Schneider wrote: > Hi again, > I'm looking for some clarification on 2 things. > 1. On that last note, I realize that s(x1,x2) would be the other > obvious interaction to compare with - and I see that you recommend > te(x1,x2) if they are not on the same scale. - yes that's right, s(x1,x2) gives an isotropic smooth, which is usually only appropriate if x1 and x2 are naturally on the same scale.
> 2. If s(x1,by=x1) gives you a "parameter" value similar to a GLM when > you plot s(x1):x1, why does my function above return the same yhat as > predict(mdl,type='response') ? Shouldn't each of the terms need to be > multiplied by the variable value before applying > rowSums()+attr(sterms,'constant') ?? predict returns s(x1)*x1 (plot.gam just plots s(x1), because in general s(x1,by=x2) is not smooth). If you want to get s(x1) on its own you need to do something like this: x2 <- x1 ## copy x1 m <- gam(y~s(x1,by=x2)) ## model implementing s(x1,by=x1) using copy of x1 predict(m,data.frame(x1=x1,x2=rep(1,length(x2))),type="terms") ## now predicted s(x1)*x2 = s(x1) best, Simon > Thanks again > Dominik > > On Wed, May 11, 2016 at 10:11 AM, Dominik Schneider > <dominik.schnei...@colorado.edu > <mailto:dominik.schnei...@colorado.edu>> wrote: > > 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 > <mailto: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 <mailto: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 <tel:%2B44%20%280%29117%2033%2018273> > http://www.maths.bris.ac.uk/~sw15190 > <http://www.maths.bris.ac.uk/%7Esw15190> > > > -- 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.
