[R] Estimate predictor contribution in GAM models

[Simon Wood]

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