Variance Models
Context: Variance Structure Definition
One G structures for more than one random term
The usual case is that a variance structure applies to a
particular term in the linear model and that there is no
covariance between model terms. Sometimes it is appropriate to
include a covariance. Then, it is essential that the model terms
be listed together and that the variance structure defined for the
first term be the structure required for both terms. When the
terms are of different size, the terms must be linked together
with the
!{ and !} qualifiers.
While ASReml will check the overall size, it does not check that the
order of effects matches the structure definition so the user must
be careful to get this right. Check that the terms are conformable
by considering the order of the fitted effects and ensuring the
first term of the direct product corresponds to the outer factor
in the nesting of the effects.
Two examples are
random regressions, where we want a covariance between intercept and slope
...
!r !{ animal animal.time !}
...
animal 2
2 0 US 3 -.5 2
animal
is equivalent (though not identical because of the scaling differences) to
...
!r pol(time,1).animal
...
pol(time,1).animal 2
pol(time,1) 0 US 1 -.1 .2
animal
maternal/direct genetic covariance
lambid !P
sireid !P
damid !P
...
wwt ywt ~ Trait Trait.sex !r !{ Trait.lambid at(Trait,2).damid !}
...
Trait.lambid 2
3 0 US
1.3 # Var(wwtD
1.0 2.2 # Cov(wwtDywtD Var(ywtD
-.1 -.2 0.8 # Cov(wwtDwwtM Cov(ywtDwwtM Var(wwtM
lambid 0 AINV # AINV explicitly requests to use A inverse
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