[R-sig-eco] Anderson and Willis 2003, CAP squared canonical correlations of delta^2

[Jari Oksanen]

On 7/06/11 06:48 AM, "Kari Lintulaakso" <kari.lintulaakso at gmail.com> wrote:

> Dear list,
> 
> I'm trying to follow the CAP analysis described in Anderson and Willis
> 2003: Canonical Analysis of Principal Coordinates: A Useful Method of
> Constrained Ordination for Ecology
> For this I'm using CAPdiscrim (instead of capscale) as it seems to
> follow the original description.
> I'm using a data set with n different biomes. Each biome has several
> sites and each site has species counts listed.
> 
> I use the dune data set to describe my questions which are in the comments.
> 
> require(BiodiversityR)
> require(vegan)
> data(dune)
> data(dune.env)
> # Transform variables
> dune.trs <- decostand(dune,"log")
> 
> # Calculate dissimilarities between each pair of observations, Bray-Curtis
> dune.bray <- vegdist(dune.trs, method = "bray")
> 
> # Canonical Analysis of Principal Coordinates (CAP):
> # This is done for Management which acts like class data
> dune.cap <- CAPdiscrim(dune.bray ~ Management, dune.env
> ,dist="bray",axes=4,m=0,permutations=9)
> 
> # In Anderson and Willis 2003, page 518:
> # "... The canonical analysis (CAP) yielded two canonical axes,
> # with squared canonical correlations of delta1^2 = 0.610 and delta1^2
> = 0.478..."
> #
> # It seems that those values come from Eigenvalues (Correlations) of
> 0.78101 and 0.69142
> http://www.stat.auckland.ac.nz/~mja/prog/CAP_UserNotes.pdf
> # QUESTION 1: How do I get similar values using CAPdiscrim?
So how close do you need to get?

> 0.78101^2
[1] 0.6099766
> 0.69142^2
[1] 0.4780616

Which are identical in three decimal places to those values that A&W
reported (and they reported squared values).

> # The only Eigenvalue related value I find is dune.cap$tot
What about dune.cap$manova$Eigenvalues?

Cheers, Jari Oksanen