[R-sig-eco] Mantel test with skew-symmetric matrices?

[Sarah Goslee]

On Thu, Oct 1, 2009 at 1:46 PM, Jari Oksanen <jari.oksanen at oulu.fi> wrote:
>
>
> Sarah & Steve,
>
> This was the design I had on my mind. However, I was not sure how
> skew-symmetry actually was defined, and therefore I didn't know if free
> permutation of rows and columns (even when done correctly like above) will
> retain the skew-symmetry. The free permutation would be OK for non-symmetric
> matrices, but what about skew-symmetric? (Little thinking and pen & paper
> probably would give a quick answer, but I won't do that for a while).

Exactly. It would need some thinking through, and I don't have a quick answer.

Steve asked elsewhere what I thought about using just the symmetric component.
It depends on whether directionality is important: if the distance
from A to B is
not the same as the distance from B to A, then discarding that information
would not give the same results. But then you're out of Mantel test
territory, and
into network analysis or something similar.

That directional component could be problematic, especially if as Jari mentions,
the permutation must preserve that skew-symmetry (mine doesn't). You
could instead
permute the matrix by reordering the rows and columns, then forcing
the lower triangle
to be positive and the upper to be negative.

Sarah

-- 
Sarah Goslee
http://www.functionaldiversity.org