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

[Jari Oksanen]

On 4 Jun 2008, at 21:28, Andrea Bertolo wrote:

> Dear Jari,
>
> this is exactly the structure of my data.
> I in fact forgot to mention that I was using the rda fonction as a
> regression here (thanks to Karl Cottenie to let me see it...), i.e. to
> explain the abundance of a single fish species with 14 MEMs.
>
In this case there is no reason to use rda in R: simply use lm.

All independent variables are used in calculations, but not displayed  
in ordination diagrams. If you only have one dependent variable, you  
could not see much, though. The biplot arrows are defined to be of  
unit length  in full constrained space, so that they only can be +1 or  
-1 in one dimension. However, the regression coefficients should be  
available for all: just use coef() on the result to get the  
coefficients.

I cannot find a reason to use a Euclidean multivariate method (rda)  
for univariate data when you can use univariate methods like the  
standard lm() -- and lm indeed is the natural choice in this case.

> There is only one thing that I don't understant.
> What do you mean exactly when you say that "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)." ?
> Does this mean that the rda is calculated with all the 14 contraints  
> (in
> this case), but only the first constraint is plotted ? I ran the rda  
> with
> the only "un-aliased" MEM and I obtained the same results, showing  
> that the
> aliased constraints are effectively eliminated.

I just tried this, and could not confirm this. The result were  
different for eigenvalues, configuration, coefficients or anything I  
looked at. There was this aliasing thing, but that does not mean that  
the results are similar. The only similar thing is that in when  
ordinating a single species you get only one axis (but it's a  
different axis depending on your constraints). So do not ordinate: use  
lm.

> Also, If I remeber well,
> when I run the same rda with Canoco I can keep the all 14  
> constraints in
> the analysis, getting a different result. Are these differences only a
> graphic matter or there are more substantial differeces ?

Perhaps somebody knows Canoco and can tell you.

cheers, jari oksanen

> many thanks
> andrea
>
>
>
>
> At 20:51 2008-06-04 +0300, you wrote:
>> 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
>>
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