Comparing abundances at fixed locations in space - Syrjala test
Hello,
On 2008-February-11 , at 11:46 , Barry Rowlingson wrote:
[...] Now, you could fit a non-spatial generalised linear model to your data using glm() in R and then map the residuals. If the residual map shows structure, then there's something else going on that your model hasn't accounted for. Perhaps there is an obvious trend due to a covariate you've not included, such as elevation above sea level. You could then add this to your model. If the residual surface looks like random noise then you can use standard linear model theory to make conclusions about your covariate parameters. If the residual surface doesn't look like random noise then that's when you get into geoRglm functions which (I think) fit a GLM where the error surface (that's your residuals) is defined by a gaussian random field with a fitted covariance structure. Once that's done, the geoRglm code will tell you about your covariate parameter significance (I think! It's been a while since I've used it. Maybe Paulo and Ole can expand on this). So what I'd do is: * fit a simple GLM using glm. * Look at parameter estimates and significance. * Draw a map of residuals. * Then worry about spatial correlation.
Just to let you know how all this turned out. I started by fitting a regular glm (with poisson errors since I'm dealing with counts) trying to explain the abundances with environmental variables (wich are not spatial in essence but vary spatially). It did not explain much of the variability. I then added some explicitly spatial variables (location/ distance with respect to a point, latitude, longitude etc.) and after adding one of those most of the spatial variability is explained and the residuals don't show spatial patterns[1]. Of course the data does not show much spatial structure even at start and is highly variable but given the results of the model and the look of the residuals, I am still quite confident in saying that there was a spatial effect, and I can even interprete it biologically[2]. So thanks a lot for your detailed advice. The original question remains though: https://stat.ethz.ch/pipermail/r-sig-geo/2008-February/003138.html I've explained some of the variability for the total abundance or for an assemblage of abundant species (a multivariate glm shows the same thing) but I would like to explicitly test wether the distribution of two species differ. Syrjala's test really looks like what I want to do. But either my implementation[3] is faulty (even two completely disjointed distributions are not significantly different) or it is meant to work on a much larger number of points to be efficient (Syrjala has 360 in the exemple presented in the paper). I think that, given that I have replicates of the same sampling, I should be able to gain some statistical power from this. Any advice would be welcome. Thanks in advance. [1] http://jo.irisson.free.fr/dropbox/spatial-residuals.pdf The four columns represent data for the four successive sampling events. The first line shows the raw counts. There's not much spatial structure at the end but there are patterns of high abundance in rotation 1 and 2. The second line shows the residuals of the glm with only environmental factors which leaves much of the patterns in place. The third line is the residuals from a similar model with an added "location" factor which codes the windward/downwind situation of each point. It explains much of the spatial distribution of abundance, expect maybe for some points of rotation 1. [2] For those interested in the details, the longitude or location with respect to the island both have an important and significant effect and show that the organisms are more abundant on the western or downwind side of the island, which is expected since water in enriched in nutrients at these locations. [3] https://stat.ethz.ch/pipermail/r-sig-geo/2008-February/003143.html Jean-Olivier Irisson --- UMR 5244 CNRS-EPHE-UPVD, 52 av Paul Alduy, 66860 Perpignan Cedex, France +336 21 05 19 90 http://jo.irisson.free.fr/work/