# [R] Smooth terms significance in GAM models

From: Yves Magliulo <ym_at_climpact.com>
Date: Fri 23 Sep 2005 - 19:33:33 EST

hi,

i'm using gam() function from package mgcv with default option (edf estimated by GCV).

>G=gam(y ~ s(x0, k = 5) + s(x1) + s(x2, k = 3))
>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.

With GCV, p-value are obtained by comparing the statistic to an F distribution,isn't it?
help(summary.gam) says "use at your own risk!".Does it mean i should only estimated signifiance of smooth terms by chi.sq?.Is there a way to link both information (p.value and chi.sq)?

I have read an article where chi.sq was interpreted like residual deviance (reduction in deviance by each smooth). Can i do something like that in my case?
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 smooth?

Last question, using GAM with default, should i look at R-sq rather than Deviance explain, or both?

I hope it's ~ clear

thanks.

Yves

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