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

[vito muggeo]

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]]
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
> 

-- 
====================================
Vito M.R. Muggeo
Dip.to Sc Statist e Matem `Vianelli'
Università di Palermo
viale delle Scienze, edificio 13
90128 Palermo - ITALY
tel: 091 6626240
fax: 091 485726/485612