[R] GAM Penalised Splines - Intercept

[Gavin Simpson]

On Tue, 2013-04-23 at 17:51 +0200, Lucas Holland wrote:
> Hey all,
> 
> I'm using the gam() function inside the mgcv package to fit a
> penalised spline to some data. However, I don't quite understand what
> exactly the intercept it includes by default is / how to interpret
> it. 
> 
> Ideally I'd like to understand what the intercept is in terms of the
> B-Spline and/or truncated power series basis representation. 

It is the mean of the response:

library(mgcv)
set.seed(2) ## simulate some data... 
dat <- gamSim(1, n=400, dist="normal", scale=2)
#Gu & Wahba 4 term additive model

> b <- gam(y ~ s(x2), data = dat)
> coef(b)[1]
(Intercept) 
   7.833279 
> with(dat, mean(y))
[1] 7.833279
> b2 <- gam(y ~ s(x0) + s(x1) + s(x2) + s(x3), data = dat)
> coef(b2)[1]
(Intercept) 
   7.833279

In models with parametric factor terms what the intercept is depends on
the contrasts used - the default in R would represent the mean of the
response for the reference level(s) of factor terms in the model.

The intercept is separates from the penalised spline terms in the model.

HTH

G

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