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
Anderson and Willis 2003, CAP squared canonical correlations of delta^2
3 messages · Kari Lintulaakso, 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$Eigenvalues? Cheers, Jari Oksanen
Thank you Jari for quick responce,
So how close do you need to get?
0.78101^2
[1] 0.6099766
0.69142^2
[1] 0.4780616
Yes, that one I understood from Anderson's CAP manual.
# The only Eigenvalue related value I find is dune.cap$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 * Mobile: +358 50 40 33391 * Office:? +358 9 191 50842 * Email: kari.lintulaakso at helsinki.fi * Post: Department of Geology, Gustaf H?llstr?min katu 2a (P.O Box 64), 00014 University of Helsinki * Web page: http://blogs.helsinki.fi/lintulaa/