This is an interesting point for discussion, re standard errors calculated
where correlations are close to the boundary space. I personally don't
think that they are that meaningful because in the constrained situation
there is no belief that the estimated parameter+-SE will go outside the
parameter space. This implies that we are using an SE (symmetric about the
parameter estimate) to estimate an effectively non-symmetric (likely)
distribution for the parameter estimated. Consequently the SE seems to
become ridiculously small at the boundaries of the parameter space,
especially when you consider the number of records used.
In some of my data I have three traits of similar heritability, and
measured on the same animals. Consequently I have the same/similar
information content in the data to estimate the genetic correlations.
However, when the genetic correlation is 0.83, the SE is +-0.08, but when
the genetic correlation is 0.91, the SE is +-0.04. I find it difficult to
believe that the SE is halved simply because in the second case the
correlation is closer to one!
SEs for parameter estimates appear to behave in a much more realistic
fashion when the parameters estimated are not close to the boundary.
Incidentally, this problem is certainly not restricted to ASREML (and any
Bayesians are welcome to talk about posteriors here if they like). Several
packages will give you the same phenomena. I'm not sure how to get around
>> 4) In the unconstrained multi-site analysis, the calculated standard error
>> of the additive genetic correlation estimate was 0.253. Does the standard
>> error tend to be smaller when the estimate of the correlation parameter
>> approaches (or exceeds) the limits of -1 or +1? In this case, is the
>> estimated standard error a meaningful measure of the precision of the
>> additive genetic correlation parameter?
>The formula used in ASREML for the variance of the genetic correlation
>is given in section 5.2.3 of the manual and is a general formula
>for the variance of a ratio. I do not expect it will have any odd behaviour
>with respect to the value of 1. The se is proportional to the correlation.
>The estimate shows that the correlation is not different from 1.
Animal Genetics and Breeding Unit
University of New England
Armidale, NSW, 2351
Ph: (02) 6773 3788
Fax: (02) 6773 3266
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