> 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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