[R-sig-eco] capscale() for PCoA-CDA

[gabriel singer]

Hi everybody,

Anybody has used capscale() in package vegan to compute a PCoA-CDA as 
suggested by Anderson and Willis 2003 (Ecology 84: 511 ff) using one or 
more factors as "predictors"?

Then I wonder about:

*) How to interpret interactions of factors? Why are interactions 
(specified as "~factor1*factor2" in the function call) shown as 
continuous predictors (using arrows) in the plot function? Wouldn´t 
centroids for all cells in the design be more appropriate? Aren´t 
factorial interactions in a CDA setting more or less meaningless?

*) How to get classification statistics? And how to efficiently run a 
"leave 1 out" classification analysis? I thought of manually writing 
code that checks for the closest centroid. Would it be appropriate to 
use Euclidean distance as a criterion for this since it happens in PCo 
space? Probably there are more efficient functions which I do not know 
of, yet,... for example a function that allows extraction of distances 
of all objects to all centroids?

*) Is the application of capscale on a Euclidean distance matrix 
equivalent to a classical DFA aka CDA on the original data - or am I 
completely wrong with this idea?

*) Given only one factor as a "predictor", I guess using permutest() or 
anova() on an object resulting from capscale is completely equivalent to 
a direct application of adonis()? Correct?

These are lots of questions at once and no code to play with, sorry... 
Thanks for any help!

Gabriel