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

[Christian A. Parker]

Based on you output it looks like you are trying to explain the 
variability in MEMS with fish abundance, i.e. it looks like you have 
your x and y switched around. Hope this helps,
-Chris

Andrea Bertolo wrote:
> 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 ?
> Many thanks for your help !
> Best
> Andrea 
> 
> 
> PS: Here's a part of the output, but I can send the full data on demand
> 
> #  The output of the forward.sel function (MEMs are names V1 to V60 here)
> 
> 
>>sel.MEM_north = forward.sel(.........)
>>sel.MEM_north
> 
>    variables order         R2     R2Cum  AdjR2Cum         F  pval
> 1        V10    10 0.17854647 0.1785465 0.1686494 18.040409 0.001
> 2        V30    30 0.15327356 0.3318200 0.3155230 18.809950 0.002
> 3         V1     1 0.14301005 0.4748301 0.4553793 22.057268 0.001
> 4         V5     5 0.06462536 0.5394554 0.5164282 11.225904 0.003
> 5        V44    44 0.04339158 0.5828470 0.5564449  8.217452 0.013
> 6         V8     8 0.04234191 0.6251889 0.5963573  8.811557 0.004
> 7         V2     2 0.03250842 0.6576974 0.6265789  7.312675 0.010
> 8        V82    82 0.02918562 0.6868830 0.6539233  7.083954 0.007
> 9        V58    58 0.02468642 0.7115694 0.6769577  6.419157 0.013
> 10       V15    15 0.02359004 0.7351594 0.6993702  6.591374 0.013
> 11       V24    24 0.02329607 0.7584555 0.7220584  7.040580 0.014
> 12       V31    31 0.01782909 0.7762846 0.7389987  5.738070 0.021
> 13       V60    60 0.01709061 0.7933752 0.7555425  5.872643 0.017
> 14       V26    26 0.01245058 0.8058258 0.7669909  4.488445 0.040
> 
> 
> 
> # I run the rda on VEGAN (I saved the 14 selected MEMs in the file
> selected.MEM_north)
> 
> 
>>MEM.north.rda = rda(fish_abundance,selected.MEM_north)
>>MEM.north.rda
> 
> 
> Call:
> rda(X = fish_abundance, Y = selected.MEM_north) 
> 
>               Inertia Rank
> Total         0.48062     
> Constrained   0.39274    1
> Unconstrained 0.08788    1
> Inertia is variance 
> Some constraints were aliased because they were collinear (redundant)
> 
> Eigenvalues for constrained axes:
>   RDA1 
> 0.3927 
> 
> Eigenvalues for unconstrained axes:
>     PC1 
> 0.08788 
> 
> 
>>vif.cca(MEM.north.rda) 
> 
> V10 V30  V1  V5 V44  V8  V2 V82 V58 V15 V24 V31 V60 V26 V18 
>   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
> 
>>alias.cca(MEM.north.rda) 
> 
> Model :
> NULL
> 
> Complete :
>     [,1]
> V30     
> V1      
> V5      
> V44     
> V8      
> V2      
> V82     
> V58     
> V15     
> V24     
> V31     
> V60     
> V26     
> V18     
> 
>  # ??? 
> 
> 
> 
> Andrea BERTOLO, Ph.D.
> 
> Associate researcher
> Canada Research Chair in Freshwater Ecology
> Université du Québec à Trois-Rivières
> C.P.500, Trois-Rivières (Québec) Canada
> G9A 5H7
> 
> Tel.: (819) 376-5011 #3302
> FAX : (819) 376-5084
> 
> e-mail: andrea.bertolo at uqtr.ca
> http://www2.uqtr.ca/GREA/en/proftechs.php?id=4
> 
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