[R-sig-Geo] Comparing abundances at fixed locations in space - Syrjala test

[jiho]

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
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