variance modelling
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# variance modelling

```G'day Asreml

I am trying to model some g2 data using a mixed model

y = XB + Zu + e

where u is (2*numg1 + numg2) vector, numg1 is the number of generation
1 animals and numg2 is the number of generation 2 animals.  Generation 1
animals are comprised of sires and dams, numg1 = numsg1 + numdg1.

u can be partitioned into u = [ ua | ub | a ]T, a is a random animal effect
derived from the numerator relationship matrix.

ua can be partitioned into ua = [ uas | uad ] and ub can be partitioned
ub = [ ubs | ubd ], here a or b distinguish between two types of effects
and s or d distinguish between sire or dam origin of the effect.

where

ua ~ (0, &#61555;2aGa) and ub ~ (0, &#61555;2bGb)

this means that sire and dam a effects are coming from the same variance
&#61555;2a with a known correlation structure Ga as sires and dams from g1
are
correlated with each other. Sire and dam b effects are similar.

I am fitting the asreml model

Traitname ~ mu  !r  sire.sirea  dam.dama  sire.sireb  dam.damb animal

Here sire and dam are factors with a level for each sire and dam while
Sirea, dama sireb and damb are the respective a or b coefficients for
each g2 animal.

Initially I want to set &#61555;2a = &#61555;2b so that all ua and ub
effects are coming
From one variance, all the u's are now grouped.

How do I get asreml to model traitname this way knowing that sirea, dama,
sireb and damb are all from the one variance and relationships exist between
sirea and dama and sireb and damb. I want to get a blup estimate
for each level of sire and dam for both a and b effects and overlay the
predetermined correlation matrices Ga and Gb.

Secondly I want to repeat this without the constraint  &#61555;2a =
&#61555;2b , unequal
Variances.

Any help is appreciated.

Cheers
Joe Daley
PhD researcher
Central Queensland University

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```