[R-sig-phylo] Detection association between traits

Joe Felsenstein

2018-03-28 11:38:55 UTC

Rafa Braga asked

Post by Rafa Braga
Does anybody know how to detect association between two traits while removing the influence of the third one? I have three traits which are named a b and c. I'm wanting to test the correlation of a and b while controling c as a covariate. In other words, the correlation between trait a and b can be a result of the correlation between b and c and I'm wanting to remove the influence of c on b.

This goes all the way back 100 years.

Once you have inferred the variances and covariances of
the three traits, you can compute the partial correlation
between a and b.

This is defined as the correlation between the residual
of a when predicted by c, and the residual of b when
predicted by c.

When there is only one variable c, and when
r(a,b) is the correlation of a with b, then the
partial correlation is

[ r(a,b) - r(a,c) r(b,c)] / [(sqrt(1 - r(a,c)^2) sqrt(1 - r(b,c)^2)]

For likelihood ratio testing in a linear model,
one could compare the likelihoods of models
that did or did not have direct connection of
a and b. RA Fisher also derived a distribution
of the partial correlation coefficient.

Joe
----
Joe Felsenstein ***@gs.washington.edu
Department of Genome Sciences and Department of Biology,
University of Washington, Box 355065, Seattle, WA 98195-5065 USA

Post by Rafa Braga
Yours,
Rafa
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--
----
Joe Felsenstein ***@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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