R help - Apr 2013 - Understanding why a GAM can't have an intercept

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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>  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
>
>
>

	[[alternative HTML version deleted]]

please deleter this thread -- wrong title
On 04/16/2013 02:35 PM, 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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