Paolo,

Using GLS seems a good approach for what you want to do.
However, as its names indicates GLS models does not use the OLS approach,
so you can't use the "classic" R square interpretation.

I would follow these steps (but if I am wrong please feel free to correct
me !!).
1) Run your model in GLS without the spatial structure.
2) Make a variogram with your residuals (in order to see what kind of
spatial structure you need)
3) Run your model in GLS with the spatial structure (using corStruct)
4) Compare AICs to see if including the spatial structure improve your
model (you can also use AICs to test several spatial structures and find
the best).

However, I don't know how to evaluate the proportion of the variance
explained by the spatial structure. If someone have the information, I
would be pleased to learn !

Arnaud


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Dear community

I write to pose a question about the best way to incorporate spatial non
independence in a regression model that has multivariate responses and
multiple predictors. I would like to estimate the global R-sq under OLS and
its significance (no problem for that..) and compare it when incorporating
spatial non independence.
My response are PCs (about 6 or 7)  of trait measured (actually coming from
Geometric Morhometrics data) on teeh shape on 16 populations. I will use
population means for my analyses. I'm not interested in exploring single
spatial structure of single responses or single predictors (that could be
different); rather I look for  for a GLOBAL assessment of the model in term
of significance and, POSSIBLY, in term of variance explained by spatial
structure. However, I would prefer to avoid the eigenvector filtering on
the basis of some seminal literature:

(i.e:
Beale, C. M., J. J. Lennon, J. M. Yearsley, M. J. Brewer, and D. A. Elston.
2010. Regression analysis of spatial data. Ecology Letters 13:246
Rob P. Freckleton, Natalie Cooper, Walter Jetz, Associate Editor: Gregory
D. D Comparative Methods as a Statistical Fix: The Dangers of Ignoring an
Evolutionary Model. 2011. The American Naturalist)

My predictors are climatic and soil variables.Multicollinearities are
controlled performing within each block a PCA and retaining all PCs
explaining at least 90% of variance.
So...I thought  to use a gls procedure with a spatial covariance as
corStructure term or to the package spgwr; however, I'm not sure about the
possibility to include multivariate response in spgwr.
Being relatively new in this type of analyses I wrote you in order to have
some useful suggestions about my model.
Thankyou in advance
Paolo Piras

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