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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