Envelope constraints

Nicholas,

May I ask why you want to construct a "global" p-value in the manner you 
indicate?  What hypothesis are you wanting to test?

Look at the equation for the Bray-Curtis dissimilarity.  It, like most 
of the common dissimilarity measures, is a SUM (over species) of a 
function of the difference between two species.  Different dissimilarity 
measures have different functions.

Your approach is to regress the sum on each of the underlying 
differences.  What would this tell you?

One possible answer is a measure of the "importance" of each species to 
the dissimilarity of one sample to all others.  At best, that's a 
summary statistic, not a test of some hypothesis.

However, the function defining the dissimilarity directly tells you when 
a pair of densities contributes a large amount to the dissimilarity.  So 
I don't see the purpose of the regression.

Best wishes,
Philip Dixon