[R] RDA permutest envfit

[Gavin Simpson]

On Wed, 2013-04-24 at 13:13 -0700, Rémi Lesmerises wrote:
> Thank you!
> 
> A last question: Is it still the same explanation if I remove the
> condition "first=TRUE" (and then testing for all axis) and permutest
> gives the same result?

No; again `permutest(...., first = FALSE)` and `envfit()` are testing
different models/fits but how they are different is not the same as with
your previous question.

`permutest(...., first = FALSE)` is testing whether the variance
explained by the k environmental variable (k = 4 I believe in your case)
is sufficiently large as to be unusual when compared to the variance
explained under a null model (achieved by permuting residuals,
propagating those residuals plus fitted values to give new data and
refitting the model on those new data). `envfit()` is doing what it
always did; assessing whether the correlation between the vector and the
2-d configuration is unusually large.

In the `permutest(...., first = FALSE)` case, you have a model with 4df.
In the `envfit()` case you have 4 models each with 1 degree of freedom.

The two methods also differ in terms of the role played by the
environmental data. In the `permutest` case, the environmental data are
the predictors. In the `envfit` case the env data are the responses and
the axis scores in the 2 dimensions chosen are the predictors.

HTH

G

> Rémi Lesmerises, biol. M.Sc.,
> Candidat Ph.D. en Biologie
> Université du Québec à Rimouski
> remilesmerises at yahoo.ca
> 
> 
> 
> On Wed, 2013-04-24 at 10:38 -0700, Rémi Lesmerises wrote:
> > Dear all,
> > 
> > I did a RDA and when I looked to the signification of the test with
> > permutest, the output was non-significant. But when I used the envfit
> > function, some of the vectors are significant. All the test's
> > conditions are respected. What it means? Is it an error in the script?
> 
> The two functions are testing two fundamentally different things.
> `permutest` (as you invoked it --- `first = TRUE`) is testing the first
> axis of the RDA. That axis is a linear combination of the constraints.
> 
> The `envfit` procedure is testing the individual correlations between
> the 2-d configuration of samples in the RDA space and the direction of
> maximal variance of the environmental data. Each variable is considered
> separately.
> 
> I can easily imagine a case, where the variance explained on the first
> axis is not significant but variance over 2 axes is significant, as one
> where the vectors do not point solely along the first RDA axis but also
> point along the 2nd axis. By looking only at their contributions to the
> first axis and summing them you don't explain a whole lot, but when you
> look at the directions in 2D space each variable explains a significant
> amount of variance.
> 
> HTH
> 
> G
> 
> > Commands and output:
> > 
> > > permutest(rda.ind, perm=999, first=TRUE)
> > 
> > Permutation test for rda 
> > 
> > Call: rda(formula = x ~ ARH_frs + CON_frs + PRP_frs + RUI_frs +
> > VAM_frs, data = z)
> > Permutation test for first constrained eigenvalue
> > Pseudo-F:        4.093568 (with 1, 10 Degrees of Freedom)
> > Significance:    0.413 
> > Based on 999 permutations under reduced model.
> > 
> > > fit <- envfit(rda.ind, z, perm = 999, display = "lc")
> > > fit
> > 
> > ***VECTORS
> > 
> >              RDA1      RDA2     r2 Pr(>r)    
> > VAM_frs  0.145281 -0.989390 0.2388  0.147    
> > 
> > ARH_frs -0.876494 -0.481413 0.6127  0.002 ** 
> > CON_frs  0.904278  0.426944 0.4846  0.013 *  
> > PRP_frs -0.997634  0.068755 0.9433  0.001 ***
> > RUI_frs -0.648512 -0.761204 0.6243  0.004 ** 
> > ---
> > Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> > P values based on 999 permutations.
> > 
> >  
> > Rémi Lesmerises, biol. M.Sc.,
> > Candidat Ph.D. en Biologie
> > Université du Québec à Rimouski
> > remilesmerises at yahoo.ca
> > 
> >     [[alternative HTML version deleted]]
> > 
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> 

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