Hi, I have collected data on trees from 5 forest plots located within the same landscape. Data within the plots are spatially autocorrelated (calculated using Moran's I). I would like to do a ANCOVA type of analysis combining these five plots, but the assumption that there is no autocorrelation in the residuals is obviously violated. Does anyone have any ideas how to incorporate these spatial effects in my analysis? I have been reading up on autoregressive techniques, but I am not sure if it works with more than one plot. All help is greatly appreciated! Many thanks, Geertje van der Heijden [[alternative HTML version deleted]]
Geertje Van der Heijden wrote:>Hi, > >I have collected data on trees from 5 forest plots located within the >same landscape. Data within the plots are spatially autocorrelated >(calculated using Moran's I). I would like to do a ANCOVA type of >analysis combining these five plots, but the assumption that there is no >autocorrelation in the residuals is obviously violated. Does anyone have >any ideas how to incorporate these spatial effects in my analysis? I >have been reading up on autoregressive techniques, but I am not sure if >it works with more than one plot. > >All help is greatly appreciated! > >Many thanks, >Geertje van der Heijden > > >Hi, one way to remove spatial autocorrelation is to use Moran's Eigenvectors as predictors in multiple regression. But as there are always n-1 vectors for n points, you will have to choose the predictors to be retained (using standard model selection procedures). Here is an example of how to get the eigenvectors using the ade4 and spdep packages. library(ade4) library(spdep) library(adegenet) xy = matrix(rnorm(100),ncol=2) plot(xy) # get a connection network (here, Delaunay triangulation) cn = chooseCN(xy,ask=FALSE,res="listw")$cn # get Moran's Eigenvectors U = orthobasis.listw(cn) # visualize the first 9 vectors par(mfrow=c(3,3)) for(i in 1:9) s.value(xy,U[,i],addaxes=FALSE, include.ori=FALSE) And then you can use the columns of U as spatial predictors in your model. A few vectors should be able to remove the autocorrelation among residuals. Regards, Thibaut. -- ###################################### Thibaut JOMBART CNRS UMR 5558 - Laboratoire de Biom?trie et Biologie Evolutive Universite Lyon 1 43 bd du 11 novembre 1918 69622 Villeurbanne Cedex T?l. : 04.72.43.29.35 Fax : 04.72.43.13.88 jombart at biomserv.univ-lyon1.fr http://lbbe.univ-lyon1.fr/-Jombart-Thibault-.html?lang=en http://pbil.univ-lyon1.fr/software/adegenet/
Hi Geertje, You should look into linear mixed-effects models. In these you can incorporate spatial correlation explicitly. The basic function to use is lme(), but you should do some reading about this type of models before jumping into it. An excellent resource is the book "Mixed Effects Models in S and S-Plus" by Jose Pinheiro and Douglas Bates. Good Luck! Julian Geertje Van der Heijden wrote:> Hi, > > I have collected data on trees from 5 forest plots located within the > same landscape. Data within the plots are spatially autocorrelated > (calculated using Moran's I). I would like to do a ANCOVA type of > analysis combining these five plots, but the assumption that there is no > autocorrelation in the residuals is obviously violated. Does anyone have > any ideas how to incorporate these spatial effects in my analysis? I > have been reading up on autoregressive techniques, but I am not sure if > it works with more than one plot. > > All help is greatly appreciated! > > Many thanks, > Geertje van der Heijden > > > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code.
Hi, On the online Early articles of the Ecography Journal you can find this paper: Dormann et al. 2007: Methods to account for spatial autocorrelation in the analysis of species distributional data: a review. – Ecography in press (Online Early). This article describe several methods to account for spatial autocorrelation and include an online appendix with R commands! victor On 10/22/07, Geertje Van der Heijden <g.m.f.vanderheijden04@leeds.ac.uk> wrote:> > Hi, > > I have collected data on trees from 5 forest plots located within the > same landscape. Data within the plots are spatially autocorrelated > (calculated using Moran's I). I would like to do a ANCOVA type of > analysis combining these five plots, but the assumption that there is no > autocorrelation in the residuals is obviously violated. Does anyone have > any ideas how to incorporate these spatial effects in my analysis? I > have been reading up on autoregressive techniques, but I am not sure if > it works with more than one plot. > > All help is greatly appreciated! > > Many thanks, > Geertje van der Heijden > > > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. >-- Victor Lemes Landeiro Instituto Nacional de Pesquisas da Amazônia - INPA Manaus, Amazonas, Brasil Skype: landeiro (Bloqueado no INPA) Homo notsosapiens (Colin Townsend) [[alternative HTML version deleted]]