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

[Kari Lintulaakso]

Thank you Jari for quick responce,

> So how close do you need to get?
>
>> 0.78101^2
> [1] 0.6099766
>> 0.69142^2
> [1] 0.4780616

Yes, that one I understood from Anderson's CAP manual.

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

Thank you for pointing this out for me. I was referring to the R
documentation where there was no mention about these objects
(directly). A misunderstanding here.

When using dune.cap$manova$Eigenvalues:
               [,1]     [,2]      [,3]         [,4]          [,5]         [,6]
y[, group] 8.543145 0.825438 0.6292823 1.334105e-16 -5.300794e-17 1.572394e-17

These values are identical to the Eigenvalues in Anderson's CAP manual
and by ^2 I get the delta^2 values like in A&W2003?

Can you tell why
   > sum(dune.cap$manova$Eigenvalues)
  [1] 9.997866
is not same as
  > dune.cap$tot
  [1] 3.850346 ?
Are they measuring different axes? dune.cap2$tot for (sum of all
eigenvalues of PCoA) and dune.cap2$manova$Eigenvalues for the CAP
axes?

Can I compute the proportion of variance explained on each axis by:
> dune.cap$manova$Eigenvalues/sum(dune.cap$manova$Eigenvalues)
                [,1]       [,2]       [,3]         [,4]          [,5] ...
y[, group] 0.8544969 0.08256142 0.06294166  ...

And finally, does the dune.cap$manova give me the similar p as in the A&W2003?

Thank you for answering to my (for you trivial) questions.

-Kari


On Tue, Jun 7, 2011 at 2:54 PM, Jari Oksanen <jari.oksanen at oulu.fi> wrote:
> 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
>
>



-- 
Kari Lintulaakso, M.Sc.(Biosciences)

Doctoral student
Paleontology and Paleoecology
Department of Geosciences and Geography
University of Helsinki

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