[R-sig-eco] orthogonal variables aliased by rda(vegan)

[Jari Oksanen]

Quoting Andrea Bertolo <andrea.bertolo at uqtr.ca>:

> Hi to all,
>
> I am running some RDAs on Vegan using Moran eigenvector Maps (MEM) to
> explain the variation in the abundance of a fish species.
>
> In several occasions I noticed that, despite MEM are othogonal by
> definition, they were aliased by the rda fonction and thus not taken into
> account in the analysis, as if they were collinear !
>
> I cannot understand why, since the MEMs used in the analysis showed not
> only to be orthogonal (I post-verified it by calculating a VIF, in case
> of), but also to add each a significant fraction to the explained variation
> of the dependent variable (MEMs were selected by the forward.sel fonction
> available in the packfor package).
>
> Could anybody tell me if I am doing something wrong or there is a real bug
> here ?

I'll try.

This is something that really may be a problem in vegan, and may  
change in future versions. The problem here is (probably) that the  
number of your PCNMs is higher than min(nrow(x), ncol(y)) in your  
dependent data. There really are two kind of ranks in rda/cca etc. in  
vegan: the rank of the dependent community data, and the rank of the  
constraints. It seems that in your case of spatial filtering the rank  
of the MEM's is higher than the rank of the dependent matrix. The  
current practice in vegan is the take the rank of the solution as the  
min of these two ranks, and the extra constraints are aliased.  
However, these extra constraints are taken into account, but not  
reported in all cases (the aliasing is explicit: there is code to turn  
down displaying the results that were calculated). This will change in  
the future, but I'm not yet quite sure how this should be changed --  
this needs research, and discussion among developers and other  
interested parties. However, the main results will not change. Things  
that will change are the display of the same results, and some derived  
functions (predict, calibrate.cca and perhaps some others, but I don't  
know yet which). This is a change that has wide reaching effects, and  
therefore you cannot expect this before autumn -- or "fall" on that  
side of the pond).

Vegan is not yet ready for the full blown spatial analysis, but we are  
working for that (and here "we" is really plural and implies several  
persons). If you need detailed advice on the possible consequences of  
the upcoming change, you may directly contact me or us at the  
http://vegan.r-forge.r-project.org/.

Best wishes, Jari Oksanen