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

[Andrea Bertolo]

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