R help - Sep 2005 - Estimate predictor contribution in GAM models

hi,

i'm using gam() function from package mgcv. 

if G is my gam object, then 
>SG=summary(G)
Formula:
y ~ +s(x0, k = 5) + s(x1) + s(x2, k = 3)

Parametric coefficients:
              Estimate  std. err.    t ratio    Pr(>|t|)
(Intercept)  3.462e+07  1.965e+05      176.2    < 2.22e-16

Approximate significance of smooth terms:
               edf         chi.sq     p-value
 s(x0)      2.858       70.629     1.3129e-07
 s(x1)      8.922       390.39     2.6545e-13
 s(x2)      1.571        141.6     1.8150e-11

R-sq.(adj) =  0.955   Deviance explained =   97%
GCV score = 2.4081e+12   Scale est. = 1.5441e+12  n = 40
--------------------------------------

I know i can estimate the significance of smooth terms with chi.sq &
p.value. In this example, i now that s(x1) is the most significant
follow by s(x2) and s(x0). also, i know the 3 give a good contribution
in my model and i have a very good model (dev expl = 97%)

=>
But how can i estimate numericaly the contribution of each smooth
against the others. In others words, is there a way to quantify this
significance like a percentage of how the model is improved by each of
my predictors? 

I hope it's ~ clear (i'm french!)

thanks.




	[[alternative HTML version deleted]]

On Tue, 20 Sep 2005, Yves Magliulo wrote:
> hi,
>
> i'm using gam() function from package mgcv.
>
> if G is my gam object, then
> >SG=summary(G)
> Formula:
> y ~ +s(x0, k = 5) + s(x1) + s(x2, k = 3)
>
> Parametric coefficients:
>               Estimate  std. err.    t ratio    Pr(>|t|)
> (Intercept)  3.462e+07  1.965e+05      176.2    < 2.22e-16
>
> Approximate significance of smooth terms:
>                edf         chi.sq     p-value
>  s(x0)      2.858       70.629     1.3129e-07
>  s(x1)      8.922       390.39     2.6545e-13
>  s(x2)      1.571        141.6     1.8150e-11
>
> R-sq.(adj) =  0.955   Deviance explained =   97%
> GCV score = 2.4081e+12   Scale est. = 1.5441e+12  n = 40
> --------------------------------------
>
> =>
> But how can i estimate numericaly the contribution of each smooth
> against the others. In others words, is there a way to quantify this
> significance like a percentage of how the model is improved by each of
> my predictors?
- The easiest thing to do is probably to refit the model without each
predictor, and look at how much the r^2 drops. You might want to fix the
smoothing parameters when you do this: G$sp gives the original smoothing
parameter estimates for the model with all terms, so you can pick out the
appropriate smoothing parameters to send to `gam' via the `sp' argument,
for the 2 term fits.

best,
Simon