R help - Apr 2003 - piece wise functions

Hello,

Apologies if this question has already arised, hope you can
help me to the find the solution to this or point the place to look at.

I have a multidimensional piece-wise regression linear problem, i.e.
to find not only the regression coefficients for each "interval" but
also the beginning and ends of the intervals.

To simplify it to the one dimensional case and
two intervals, the problem is to find A_0, A_1, ... A_p and "C"
from the given sample, assuming the curve is like this:

A_0*f_0(x)+A_1*f_1(x)+ ... + A_p*f_p(x) with x < C

A_0'*f_0(x)+A_1'*f_1(x)+ ... + A_p'*f_p(x) with x >= C

Functions f_1, f_2, ... f_p are known.

Is there anything in R for that?

I have tried to use nonlinear (nls package)
regression, "forcing" with the "nls" function the shape of
the surface,
but it does not work.

By the way, the cofficients A_i have to be positive, but I suppose this is
another question.

Thanks

Casiano
casiano at ull.es

In a message dated 4/21/03 9:00:22 AM Eastern Daylight Time, casiano@ull.es 
writes:
> Hello,
> 
> Apologies if this question has already arised, hope you can
> help me to the find the solution to this or point the place to look at.
> 
> I have a multidimensional piece-wise regression linear problem, i.e.
> to find not only the regression coefficients for each "interval"
but
> also the beginning and ends of the intervals.
> 
Look at "polspline" and "splines" packages, and
"polymars" in "polspline"
package.

	[[alternate HTML version deleted]]

Casiano  -

A practical approach would be to use  gam() and its friends
in package mgcv.  This implements Generalized Additive Models
(Hastie & Tibshirani, 1990).  The fit will be smoother than
you would get with an explicit piece-wise linear regression,
but it's already implemented.

If you really care about estimating the boundaries between
distinct regions of the fit, that's a research question, in
my humble opinion, and you are cast onto the stormy sea of
statistical literature for that.  That's a difficult problem.
Start with  gam() and eyeball the boundaries ?

Others will have better ideas.  Maybe packages "GRASS",
"grasper" or "geoR" have something to offer ?

-  tom blackwell  -  u michigan medical school  -  ann arbor  -

On Mon, 21 Apr 2003, Casiano Rodriguez Leon wrote:
> Hello,
>
> I have a multidimensional piece-wise regression linear problem, i.e.
> to find not only the regression coefficients for each "interval"
but
> also the beginning and ends of the intervals.
>
> To simplify it to the one dimensional case and
> two intervals, the problem is to find A_0, A_1, ... A_p and "C"
> from the given sample, assuming the curve is like this:
>
> A_0*f_0(x)+A_1*f_1(x)+ ... + A_p*f_p(x) with x < C
>
> A_0'*f_0(x)+A_1'*f_1(x)+ ... + A_p'*f_p(x) with x >= C
>
> Functions f_1, f_2, ... f_p are known.
>
> Is there anything in R for that?
>
> I have tried to use nonlinear (nls package) regression, "forcing"
with
> the "nls" function the shape of the surface, but it does not
work.
>
> By the way, the cofficients A_i have to be positive, but I suppose this is
> another question.
>
> Thanks
>
> Casiano
> casiano at ull.es