[R] RDA permutest envfit

[Gavin Simpson]

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
> 
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> 
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