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