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Anderson and Willis 2003, CAP squared canonical correlations of delta^2

3 messages · Kari Lintulaakso, Jari Oksanen

#
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?
# The only Eigenvalue related value I find is dune.cap$tot

# And later in anderson and Willis 2003:
# "The two canonical test statistics were highly significant (P =
0.0001 for both tests, using 9999 permutations)"
# QUESTION 2: I did only 9 permutations in my example, but do I get
similar results by using  dune.cap$manova => Pr(>F) 0.002224 ?

Instead of CAPdiscrim should I use capscale in some form to achieve
similar results as they did in A&W 2003?
I'm still out of my comfort area here, so any help will be valuable.
Cheers,
-Kari

Kari Lintulaakso, M.Sc.(Biosciences)

Doctoral student
Paleontology and Paleoecology
Department of Geosciences and Geography
University of Helsinki
#
On 7/06/11 06:48 AM, "Kari Lintulaakso" <kari.lintulaakso at gmail.com> wrote:

            
So how close do you need to get?
[1] 0.6099766
[1] 0.4780616

Which are identical in three decimal places to those values that A&W
reported (and they reported squared values).
What about dune.cap$manova$Eigenvalues?

Cheers, Jari Oksanen
#
Thank you Jari for quick responce,
Yes, that one I understood from Anderson's CAP manual.
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:
[,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: