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

[Nicholas Lewin-Koh]

Hi Carlos,
I think that there are tools in the sp package for dealing with grids.
If I am understanding you correctly and you want to do "zoning" of your
region
than you probably are not looking to do pca, but some sort of
clustering.
Marie Jose Fortin had some nice papers on a technique called wombling,
for finding
regions of abrupt ecological change. There are some other techniques for
spatial partitioning,
but I am not sure if they are implemented in R. It has been a long time
since
I worked on ecological problems.

For more information on the spatial tools in R a good place to start is 
 http://cran.r-project.org/src/contrib/Views/Spatial.html
the CRAN task view for spatial statistics, and 
http://cran.r-project.org/src/contrib/Views/Environmetrics.html
has some more pointers.

Hope this helps,

Nicholas
On Sat, 11 Nov 2006 20:24:59 -0000, "Carlos A. Bastos M.Guerra"
<carlosguerra at esa.ipvc.pt> said:
> 
> Dear Nicholas,
> 
> First of all thanks for the references, I think they will help me with my
> current problem. :)
> The thing is that I am used to work with AcrGIS to do the spatial
> analysis, but the statistical methods in ArcGIS are a bit "dummy", namely
> in spatial PCA. I am used to work with R with the ade4 package :) but
> when I heard that I could do spatial analysis with R I ad to try it...but
> its more difficult that it seams (at first)...
> 
> What I did was: (in ArcGIS) convert the centroids of a grid into a point
> shape file, than I have integrated all the information into different
> columns. I converted the dbf file into a txt an then I imported the file
> into R ... and my problems began... :)
> 
> My objective is to do a PCA and extract the different groups of points in
> order to make an ecological zoning.
> 
> I am still starting with R and "the Geo tools" can you point me some
> reading material that I can use?
> 
> Best regards,
> 
> Carlos
> 
> 
> -----Mensagem original-----
> De: Nicholas Lewin-Koh [mailto:nikko at hailmail.net] 
> Enviada: sábado, 11 de Novembro de 2006 19:06
> Para: r-sig-geo at stat.math.ethz.ch
> Cc: Carlos GUERRA
> Assunto: [R-sig-Geo] RE: how to do a principle component analysis with
> geo-referenced points
> 
> 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