[R-sig-eco] troubles with global test of rda from vegan

[Martin Weiser]

claire della vedova píše v So 22. 03. 2014 v 00:30 -0700:
> Hi everybody,
> 
> I’m in troubles with results I obtained using rda function of vegan package
> and I would greatly appreciate some help.
> I did a rda to assess if my  matrix of species abundances (18 sites and 34
> species)  can be explained by my  environmental matrix (18 sites and 5
> variables). Abundances were transformed according hellinger equation
> First I did a rda with all my environmental variables, and then did the
> overall test. It was no significant.
> 
> myrda1<-rda(decostand(abund, "hellinger")~.,VarEnv)
> anova(myrda1)
> Permutation test for rda under reduced model
> 
> Model: rda(formula = decostand(abund, "hellinger") ~ VAR1 + VAR2 + Var3 +
> Var4 + VAR5, data = VarEnv)
>          Df      Var     F N.Perm Pr(>F)
> Model     5 0.062863 1.025     99   0.43
> Residual 12 0.147195         
> 
>  I also did the test by margin (all pvalues were no significant), and by
> axis (first axis significant)
> anova(myrda1, by="axis")
> 
> Model: rda(formula = decostand(abund, "hellinger") ~ VAR1 + VAR2 + Var3 +     
> Var4 + VAR5, data = VarEnv)
>          Df      Var      F N.Perm Pr(>F)   
> RDA1      1 0.030016 2.4470    199   0.01 **
> RDA2      1 0.013816 1.1263     99   0.29   
> RDA3      1 0.009770 0.7965     99   0.68   
> RDA4      1 0.006273 0.5114     99   0.84   
> RDA5      1 0.002989 0.2437     99   1.00   
> Residual 12 0.147195                        
> 
> On the plot, first axis is explained by Var1 and Var4
> 
> 
> Since I was surprised by the results of the global test I tried a forward
> selection. Only the Var4 was kept is the final model, and the test was now
> significant. I also did backward selection ;  it was the Var1 which was kept
> is the final model, and the test was significant too.
> 
> So my question is, why the global test of the rda with all the environmental
> variables is not significant while the test by “axis” is significant for the
> first one (explain by variables Var1 and Var4) and while model selection
> lead to significant test for Var1 or Var4 ?
> 
> I analyzed the VIF of the full model, and all were lower than 3
> vif.cca(myrda1)
>      VAR1       VAR2     Var3       Var4      VAR5 
> 2.573506 2.949139 2.209569 2.023914 1.854133
> 
> Thanks in advance for your help.
> 
> All the best.
> Claire Della Vedova
> 
> 
> 
> 
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Hi,

it is not so easy to answer without the knowledge of data sampling,
whole data itself or complete results, but I will try anyway.(My
apologies if I would not use some terms correctly - I would be happy to
see more proper explanation). I guess that the data do not come from the
experiment that manipulated (somehow) these 5 env. var. you mention.

First of all, you would be quite lucky if you got overall significant
test with five variables and 18 samples in non-experimental dataset.
Moreover, only 1 axis and 2 env. var seem to describe some
species-environment pattern, but they are definitely not great at it. 
As I understand your results, it could be read as: 1st canonical axis
describes something non-random. It seems that it is related to Var1 and
Var4, but not so tightly, as there is no significant marginal term. Both
of the variables seem to be somehow correlated with the data, but not
necessarily with each other. Everything else is just a mess that can be
used to correlate with anything else - therefore the overall
significance of the model is low.
It is like having single (small) gem in the whole mountain: The gem
would not increase the price of the whole mountain too much even if you
know it is there, and an average cubic foot of the mountain is almost
priceless. 

What to do: plot var1 and var4 against each other (and against data) and
try to think what links them together. If you have enough  resources, go
to the field and try to get info about that common link.
If not, present it like this: I have tried to relate my data to these 5
env vars. (Plot envfit). Using my variables, I was able link 0.06/(0.06
+0.14)*100 percent of overall variability in the data to the
environment, which was not a significant portion. None of the env.
variables described significant portion of variability alone, but
(...number)% of variability in the data could be ascribed to linear
combination of Var1 and Var4 (plot: RDA species~Var1+Var4. Besides: Is
not there some interaction here?). Do not forget to discuss link
data-var1-var4.
(Maybe this could be still seen as fishing, so be prepared.)

I both hope this helps and that someone who understands this topic
better will correct me.

Best,
Martin




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