Bruce has pointed out what I meant, but better!
With regards to my example, the two correlations I quote are for traits
with heritabilities T1=.32+-.08, T2=.42+-.09, and T3=.45+-.10. The
correlations I reported were between t1 and t3 (0.83+-0.07), and t2 and
t3(.91+-.04). I quoted these correlations because the number of records
used to estimate these correlations and the pedigree are identical. Yes,
trait one has a lower heritability than trait two (but even the
heritabilities are probably of a similar magnitude for t1 and t2 given the
size of the SEs for the heritability estimates). Yes the correlations I
report are not significantly different from each other. The changes in
magnitude of the SEs are in the expected DIRECTION given the trait
heritabilities and the correlations between them. However, their usefulness
(based on the actual magnitude) is probably misleading. This is a fault of
approximation while violating the assumptions under which the approximation
My main point was that the SEs for the high correlations are not very
meaningful for exactly Bruces' reasons. If I want to know whether a
correlation is different from one, for example, I would not use the SEs of
the correlation to prove/disprove this. I would use the likelihood ratio
test (LRT). I should have said this earlier (as Greg Dutkowski reminded
me). I have done several analyses where if I used the SE I would consider
the correlation to be different to one, but this is not supported by the
LRT. Do you prefer to be conservative or not?
Whether Joao chooses to use the information provided by approximate SEs for
correlations close to 1 or -1 (or any value for that matter) depends on
whether he (she? - sorry don't know) feels the SEs are meaningful. I do
not feel they are when approximated for parameters close to the boundary.
As I mentioned earlier, this is an issue of estimation (with approximation
of SEs) rather than an issue related to the use of ASREML itself.
Anyway, I have dribbled on enough. Good luck with your analyses Joao!
>With your estimates Kim, are the correlations actually different (0.91 is 1
>standard deviation of 0.83 +-0.08)? Without knowing the data structure,
>and the estimated variance components, it is hard to draw any conclusions
>about the results. You may have a part-whole relationship between
>Further, you clearly have more statistical information about one of the
>than the others and it probably has a higher heritability as well.
>Bayesian would overcome some (all) of the problems as the posterior would
>you considerable amount of information. But introduce other issues e.g
>proving that you have converged if using MCMC,...
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