Thanks Joe. That's a very clear way of explaining why models that assume
a fixed & common correlation structure (OLS in lm, contrasts regression,
or gls::corBrownian) are 'symmetric' (i.e., the same P-value is obtained
by fitting y~x vs. x~y); whereas models that do not (e.g., corPagel) are
not. All the best, Liam
Liam J. Revell, Assistant Professor of Biology
University of Massachusetts Boston
web: http://faculty.umb.edu/liam.revell/
email: liam.rev...@umb.edu
blog: http://blog.phytools.org
On 7/11/2013 5:46 PM, Joe Felsenstein wrote:
If the "regressions" are being done in a model which implies
that the two variables are multivariate normal, then we can
simply estimate the parameters of that joint distribution,
which are of course the two means and the three elements of the
covariance matrix.
If we then test whether Cov(X,Y) is different from zero, that
should be equivalent to a test of significance of either
regression.
/* crankiness on */
Note of course that most "phylogenetic" regressions are being
done wrong: if they assume that Y responds to the current value
of X, but when the value of Y may actually be the result of
optimum selection which is affected by past values of X which
we do not observe directly.
I've complained about this here in the past, to no avail,
Thomas Hansen, in a recent paper, made the same point, with
evidence too.
/* crankiness off */
J.F.
----
Joe Felsenstein j...@gs.washington.edu
Department of Genome Sciences and Department of Biology,
University of Washington, Box 355065, Seattle, WA 98195-5065 USA
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