spatial regression model

Inviato: gioved? 1 novembre 2012 14.58
A: Arnaud Mosnier
Cc: Paolo Piras; r-sig-geo at r-project.org
Oggetto: Re: [R-sig-Geo] spatial regression model

You can evaluate the proportion of the variance explained by spatial
structure by  log-likelihood test-  between spatial model and a model
with intercept:
suppose:

library(lnlme)

M1<-lme(response~ predictots+...., method="REML", correlation=corExp(form=~x+y, nugget=T), data=yourdata) # model with spatial structure
Mo<-gls(response~1,method = "REML",data=yourdata) # model with intercept only
anova(M1, Mo) # Compare two models

a<-logLiklehood value of M1
b<-logLiklehood value of Mo
n<- nrow(yourdata)

R2<- (1 - exp((-2/n)*( -a -b)))   # log-likelihood R^2 for M1


On 11/1/2012 8:48 AM, Arnaud Mosnier wrote:
> 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
>
>
> ------------------------------------------------------
>
> 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
>
>       [[alternative HTML version deleted]]
>
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--
---------------------
Zia Ahmed, PhD
Research Associate
Department of Crop and Soil Sciences
1002 Bradfield Hall, Cornell University
Ithaca, NY 14853-4203
t. 607.255.9387
f. 607.255.3207
email zua3 at cornell.edu