# Re: bivariate model with some complications

From: Arthur <asremlforum_at_VSNI.CO.UK>
Date: Sun, 2 Aug 2009 00:29:29 +0100

Dear Alistair,

re bivariate analysis where first trait has repeated measures.

The parameters we can estimate are:
Var(Y1) Cov(Y1,Y2) Var(Y2)
AnimalError yes yes no
SamplError yes no no
A+S Error --- no yes

model term Trait.animal with US structure on Trait fits Direct additive

Residual for trait 1 is sampling error
Residual for trait 2 is A+S Error

We can estimate AnimalError with the term at(Trait,1).ide(animal)
and the A+S covariance with a model term ide(animal)

So this suggest

!r Trait.animal ide(animal) !GU at(Trait,1).ide(animal) !GU
1 2 1
0
Trait 0 US !GPZP
.1 0 .1

Trait.animal 2
Trait 0 US !GP
3*0
animal 0 AINV

But there could be a problem if the traits are not on conformable scales
because we need to do some sums.

Under this model, the error covariance is estimated directly
as a G structure, but the residual from trait 2
will need to have the error covariance added back.

Similarly, the animal error for trait 1 will need to have

The potential computational problem is that if the scale of
trait 1 is large relative to trait 2, the error covariance will be large
relative to the residual for trait 2, so that the estimated error may
want to go negative in which case the algorithm will fail.

=================
Now concerning analysing dom on the binomial scale.
Since you want to allow for dominance, you would use
the same model but start the dom variance at 1.0. This variance
is actually the dispersion parameter; it is the scaling applied to the
calculated GLM weight. So in this case, you would not specify !DISP.

Use !GFZP as the constraints if you want to fix the disperion parametr

I hope tha all makes enough sense.

------------------------
Arthur Gilmour

Retired Principal Research Scientist (Biometrics)

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