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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Dr. Gavin Simpson [t] +44 (0)20 7679 0522

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