[R-sig-Geo] RE: how to do a principle component analysis with geo-referenced points

[Nicholas Lewin-Koh]

Hi Carlos,
There are a couple of ways to do this, but you have to be a little more
specific
about what your goals/intentions are. I assume you have points p(x1,y1),
...., p(xn,yn), where p
is a vector of observations.

If the goal is interpolation than you have to model the spatial
covariance
of the orthognal factors, and you should look at waekernagel's book.
if your goal is to extract principal components and account for the
variance induced by a spatial
process, a quick and dirty approach is to include polynomials of the xy
coordinates in the data and 
do pca on the augmented matrix. Take a look at

Borcard, D., P. Legendre & P. Drapeau. 1992. Partialling out the spatial
component of ecological variation. Ecology 73: 1045-1055

Méot, A., P. Legendre & D. Borcard. 1998. Partialling out the spatial
component of ecological variation: questions and propositions in the
linear modeling framework. Environmental and Ecological Statistics 5
(1): 1-27.

Another approach is spatial factor analysis

Christensen, WF, and Amemiya, Y (2001).  "Generalized shifted-factor
analysis method for multivariate geo-referenced data," Mathematical
Geology, 33, 801-824.

Christensen, WF, and Amemiya, Y (2002).  "Latent variable analysis of
multivariate spatial data," Journal of the American Statistical
Association, 97, 302-317

If your question is there R code to do this, I think the ade4 package
can to the spatial variance partitioning,
but for factor analysis, you are on your own.

Nicholas

> Message: 1
> Date: Fri, 10 Nov 2006 12:19:42 -0000
> From: "Carlos GUERRA" <carlosguerra at esa.ipvc.pt>
> Subject: [R-sig-Geo] how to do a principle component analysis with
> 	geo-referenced points
> To: <r-sig-geo at stat.math.ethz.ch>
> Message-ID:
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> 
> Dear friends,
> 
> I wanted to know how to do a principle component analysis (PCA) from
> geo-referenced points.
> 
> I have a list like:
> 
> geo$xy with coordinates,
> 
> and geo$data with the data that I want to do the analysis
> 
> 
is this right?
> 
>  
> 
>  
> 
> +++++++++++++++++++++++++++++++
> 
> Carlos GUERRA
> 
>  
> 
> Instituto Politécnico de Viana do Castelo
> 
> Escola Superior Agrária de Ponte de Lima
> 
>  
> 
> Mosteiro de Refóios do Lima
> 
> 4990-706 Ponte de Lima
> 
> PORTUGAL
> 
>  
> 
> MAIL: carlosguerra at esa.ipvc.pt
> 
> TEL: +351 912 407 109
> 
> +++++++++++++++++++++++++++++++
> 
>  
> 
> 
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