[R] variance explained by each term in a GAM

[Simon Wood]

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
>
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-- 
> Simon Wood, Mathematical Sciences, University of Bath, Bath, BA2 7AY UK
> +44 1225 386603  www.maths.bath.ac.uk/~sw283