Reducing spatial autocorrelation
My apologies to Carsten for misspelling his name, but I still see its paper appropriate in the multivariate case. I was thinking on something like computing your favourite ordination or NMDS on the species or environmental or both (i.e RDA), and then compute a correlogram on your ordination scores. This would let you select the minimum distance between sites to minimize autocorrelation (this could also be obtained from a multivariate Mantel correlogram). And /or you could also generate autocovariates from your ordination score(s) and include them as predictors in that "some statistical analyses" to account for the autocorrelation. Marcelino
At 15:41 14/10/2009, Matthew Landis wrote:
That's a really great paper, but if memory serves, it focuses on univariate regression models. Useful in this context for exploring the responses of a single species at a time, instead of a multivariate approach considering multiple species simultaneously. By the way, I have the author as Dormann. M Marcelino de la Cruz wrote:
I would recomend the paper of Dortman et al. (Ecography 30: 609628, 2007). This reviews many available spatial statistical methods to take spatial autocorrelation into account in tests of statistical significance. From their abstract: "Here, we describe six different statistical approaches to infer correlates of species? distributions, for both presence/absence (binary response) and species abundance data (poisson or normally distributed response), while accounting for spatial autocorrelation in model residuals: autocovariate regression; spatial eigenvector mapping; generalised least squares; (conditional and simultaneous) autoregressive models and generalised estimating equations." The suplementary material includes R scripts to run all the methods. HTH Marcelino At 14:49 14/10/2009, Martin Alejandro Piazzon de Haro wrote:
Content-Type: text/plain Content-Disposition: inline Content-length: 3518 Dear friends, I found this thread very useful, so I wanted to apport something, Corrado, you asked for some references about PCNM, here is what i found: Borcard, D. and Legendre, P. 2002. All-scale spatial analysis of ecological data by means of principal coordinates of neighbour matrices. Ecological Modelling 153: 51-68. Borcard, D., P. Legendre, Avois-Jacquet, C. & Tuomisto, H. 2004. Dissecting the spatial structures of ecologial data at all scales. Ecology 85(7): 1826-1832. I hope will help you. 2009/10/14 Corrado <ct529 at york.ac.uk>
Dear Matthew, thanks for your kind answer! The first approach you describe is the one I have been looking at until now. I am puzzled about the second one: I do not really understand it. What model are you talking about, when you say "incorporate the spatial variation in the model"? At the moment I have no model, just the data and I am trying to reduce autocorrelation before analysing the data. Do you have any good reference (articles or books) about the approach you mention? Thanks in advance On Wednesday 14 October 2009 13:11:04 Matthew Landis wrote:
Corrado: The simplest way would be to take a subset of sites to maximize the distance between them. Say, choose 400 sites evenly spread over the study area. That would minimize autocorrelation to the greatest extent possible, but you would be throwing away data. The second thing you could try would be to incorporate the spatial variation in the model to control for it. This way you can also study the autocorrelation, see what spatial scales it is operating and what it looks like and try to learn something from it. Legendre, Borcard, Dray and colleagues have developed some really interesting ways of dealing with multivariate data and decomposing the variance into spatial component vs. explanatory variables. I believe it is called PCNM and can be found in the spacemakeR package (don't think it is on CRAN - have to do a google search). Good luck! Matthew Landis Corrado wrote:
Dear friends, I have a large matrix of species (first 1100 columns) and environmental variables (last 36 columns) for approx 2000 sites. The distance between sites varies. Some sites are near to each other, others are far. I would like to select a subset of N sites (for example: 400 sites)
with
the minimum spatial autocorrelation. The aim is to obtain a significant number of sites to carry out some statistical analysis, but with
spatial
autocorrelation significantly reduced. Is there a procedure to do so in R? How would you approach the problem? The aim of the "reduction" is to then work on dissimilarities between sites that have the lowest possible spatial autocorrelation. Thanks
-- Corrado Topi Global Climate Change & Biodiversity Indicators Area 18,Department of Biology University of York, York, YO10 5YW, UK Phone: + 44 (0) 1904 328645, E-mail: ct529 at york.ac.uk
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________________________________ Marcelino de la Cruz Rot Departamento de Biolog?a Vegetal E.U.T.I. Agr?cola Universidad Polit?cnica de Madrid 28040-Madrid Tel.: 91 336 54 35 Fax: 91 336 56 56 marcelino.delacruz at upm.es _________________________________