[R] variance explained by each term in a GAM

[Pierre Kleiber]

Picking up an ancient thread (from Oct 2007), I have a somewhat more complex 
problem than given in Simon Wood's example below. My full model has more than 
two smooths as well as factor variables as in this simplified example:

b <- gam(y~fv1+s(x1)+s(x2)+s(x3))

Judging from Simon's example, my guess is to fit reduced models to get 
components of deviance as follows:

b1 <- gam(y~s(x1)+s(x2)+s(x3),sp=b$sp)
b2 <- gam(y~fv1+s(x2)+s(x3),sp=b$sp[-1])
b3 <- gam(y~fv1+s(x1)+s(x3),sp=b$sp[-2])
b4 <- gam(y~fv1+s(x1)+s(x2),sp=b$sp[-3])
b0 <- gam(y~1)

And then proceed as in Simon's example, i.e.
   (deviance(b1)-deviance(b))/deviance(b0) ## prop explained by fv1
   (deviance(b2)-deviance(b))/deviance(b0) ## prop explained by x1
   etc.

Am I more or less on the right track?

Thanks,  Pierre


  On Tue Oct 9 20:25:24 CEST 2007, Simon Wood wrote:
 > I think that your approach is reasonable, except that you should use the same
 > smoothing parameters throughout. i.e the reduced models should use the same
 > smoothing parameters as the full model. Otherwise you get in trouble if x1
 > and x2 are correlated, since the smoothing parameters will then tend to
 > change alot when terms are dropped as one smooth tries to `do the work' of
 > the other. Here's an example, (which is modifiable to illustrate the problem
 > with not fixing the sp's)
 >
 >  ## simulate some data
 > set.seed(0)
 > n<-400
 > x1 <- runif(n, 0, 1)
 > ## to see problem with not fixing smoothing parameters
 > ## remove the `##' from the next line, and the `sp'
 > ## arguments from the `gam' calls generating b1 and b2.
 > x2 <- runif(n, 0, 1) ## *.1 + x1
 > f1 <- function(x) exp(2 * x)
 > f2 <- function(x) 0.2*x^11*(10*(1-x))^6+10*(10*x)^3*(1-x)^10
 > f <- f1(x1) + f2(x2)
 > e <- rnorm(n, 0, 2)
 > y <- f + e
 > ## fit full and reduced models...
 > b <- gam(y~s(x1)+s(x2))
 > b1 <- gam(y~s(x1),sp=b$sp[1])
 > b2 <- gam(y~s(x2),sp=b$sp[2])
 > b0 <- gam(y~1)
 > ## calculate proportions deviance explained...
 > (deviance(b1)-deviance(b))/deviance(b0) ## prop explained by s(x2)
 > (deviance(b2)-deviance(b))/deviance(b0) ## prop explained by s(x1)
 >
 >
 >
 >
 >
 > On Monday 08 October 2007 20:19, Julian M Burgos wrote:
 >> Hello fellow R's,
 >>
 >> I do apologize if this is a basic question.  I'm doing some GAMs using the
 >> mgcv package, and I am wondering what is the most appropriate way to
 >> determine how much of the variability in the dependent variable is
 >> explained by each term in the model.  The information provided by
 >> summary.gam() relates to the significance of each term (F, p-value) and to
 >> the "wiggliness" of the fitted smooth (edf), but (as  far as I understand)
 >> there is no information on the proportion of variance explained.
 >>
 >> One alternative may be to fit alternative models without each term, and
 >> calculate the reduction in deviance.  For example:
 >>
 >> m1=gam(y~s(x1) + s(x2)) # Full model
 >> m2=gam(y~s(x2))
 >> m3=gam(y~s(x1))
 >>
 >> ddev1=deviance(m1)-deviance(m2)
 >> ddev2=deviance(m1)-deviance(m3)
 >>
 >> Here, ddev1 would measure the relative proportion of the variability in y
 >> explained by x1, and ddev2 would do the same for x2.  Does this sound like
 >> an appropriate approach?
 >>
 >> Julian
 >>
 >> Julian Burgos
 >> FAR lab
 >> University of Washington
 >>
 >> ______________________________________________
 >> R-help at 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.
 >
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Pierre Kleiber, Ph.D                  Email: pierre.kleiber at noaa.gov
Pacific Island Fisheries Science Center        Tel. wk: 808 983-5399
NOAA Fisheries                                      hm: 808 737-7544
2570 Dole St., Honolulu, HI 96822-2396
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