Following up Arthur's comments, what is the log likelihood with and
without the additive genetic variance? The difference is probably very
small. Note that the difference is not distributed Chi-squared but
probably a mixture of Chi-squared.
With a variance component on the boundary condition, I doubt that SE are
valid. But, I don't remember my math stats about this and relates to
the conditions required.
Given your comments, it does not sound that you should be fitting this
model. Basically, you don't have sufficient information to make any
conclusion about additive genetic variance. What would be informative
is to profile the likelihood with respect to the additive and permanent
variance components. I think that you would see that this is rather
flat with respect to the additive genetic variance. If so, then you are
best to just to fit animal as a random effect. This causes a bias and,
if I recall correctly, John James gave a paper about ignoring repeated
records in an animal model at one of the AAABG meeting around 1990.
If you have a suitable pedigree structure, you could try a
parent-offspring regression or sire-dam model etc.
Best of luck,
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