hi Andrew.
gam does suppress the intercept, it's just that this doesn't force the
smooth through the intercept in the way that you would like. Basically
for the parameteric component of the model '-1' behaves exactly like it
does in 'lm' (it's using the same code). The smooths are 'added on' to
the parametric component of the model, with sum to zero constraints to
force identifiability.
There is a solution to forcing a spline through a particular point at
http://r.789695.n4.nabble.com/Use-pcls-in-quot-mgcv-quot-package-to-achieve-constrained-cubic-spline-td4660966.html
(i.e. the R help thread "Re: [R] Use pcls in "mgcv" package to achieve
constrained cubic spline")
best,
Simon
On 16/04/13 22:36, Andrew Crane-Droesch wrote:
Dear List,
I've just tried to specify a GAM without an intercept -- I've got one
of the (rare) cases where it is appropriate for E(y) -> 0 as X ->0.
Naively running a GAM with the "-1" appended to the formula and the
calling "predict.gam", I see that the model isn't behaving as expected.
I don't understand why this would be. Google turns up this old R help
thread: http://r.789695.n4.nabble.com/GAM-without-intercept-td4645786.html
Simon writes:
*Smooth terms are constrained to sum to zero over the covariate
values. **
**This is an identifiability constraint designed to avoid
confounding with **
**the intercept (particularly important if you have more than one
smooth). *
If you remove the intercept from you model altogether (m2) then the
smooth will still sum to zero over the covariate values, which in
your
case will mean that the smooth is quite a long way from the data.
When
you include the intercept (m1) then the intercept is effectively
shifting the constrained curve up towards the data, and you get a
nice fit.
Why? I haven't read Simon's book in great detail, though I have read
Ruppert et al.'s Semiparametric Regression. I don't see a reason why
a penalized spline model shouldn't equal the intercept (or zero) when
all of the regressors equals zero.
Is anyone able to help with a bit of intuition? Or relevant passages
from a good description of why this would be the case?
Furthermore, why does the "-1" formula specification work if it
doesn't work "as intended" by for example lm?
Many thanks,
Andrew
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