Re: [R] how to use the basis matrix of "ns" in R? really confused by multi-dim spline filtering?

From: vito muggeo <vmuggeo_at_dssm.unipa.it>
Date: Mon 27 Feb 2006 - 23:17:59 EST

Dear Micheal,

 > the output of the "ns" function in R is "basis matrix", but then Yes you are right, the output of the ns(x, df) is the basis matrix of a natural cubic spline with df degrees of freedom. See ?ns (in package splines) on how to specify df or knots or ..

Fitting y~ns(x,df) yields a smooth curve given by a linear combination of the basis functions (the single colums of the basis matrix) by the estimated coefficients (returned by the fitted model).

As far as I know, a tensor product is usually employed to multidimensional smoothing and the multidimensional basis is formed via the kronecker product of the marginal bases.

Finally, last but not least: Probably you need some statistical backaground on spline fitting..
Please, read some statistical papers/books on such topic (for instance see references in packages splines, mgcv)

best,
vito

Michael wrote:
> Hi all,
>
> Could anybody recommend some easy-to-understand and example based
> notes/tutorials on how to use cubic splines to do filtering on
> multi-dimension data?
>
> I am confused by the 1-dimensional case, and more confused by
> multi-dimensional case.
>
> I found all the books suddenly become very abstract when it comes to this
> subject.
>
> They don't provide examples in R or Splus at all.
>
> Specifically, I don't know how to provide data "x" to the "ns" function in
> R,
>
> and I don't understand what should be the output matrix, and how to use the
> output matrix to "filter" data?
>
> Books mention about basis matrix, design matrix, model matrix, data matrix,
> etc. I got lost.
>
> I presume the output of the "ns" function in R is "basis matrix", but then
> how do I use it? How to form tensor-product?
>
> I don't understand it at all.
>
> Please help me!
>
> Thank you very much!
>
> [[alternative HTML version deleted]]
>
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-- 
====================================
Vito M.R. Muggeo
Dip.to Sc Statist e Matem `Vianelli'
UniversitÓ di Palermo
viale delle Scienze, edificio 13
90128 Palermo - ITALY
tel: 091 6626240
fax: 091 485726/485612

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Received on Mon Feb 27 23:29:04 2006

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