# Re: Singularity In Average Information Matrix Using Ainverse

From: Arthur <asremlforum_at_VSNI.CO.UK>
Date: Mon, 21 Sep 2009 23:13:14 +0100

Dear Michelle,

You have a vector of observations, y.

In your case, observations that are from relatives are relatively
very similar.

The animal model models the covariance structure as V = aA + bI
where 'a' is the additive genetic variance component scaling the relationship matrix 'A', and b is the error variance component (independent residuals'

Lets take a fery simple example and assume V has a structure
3
2 3

and A has a structure

1
0.5 1

and be have to solve for a and b

The magnitude of 'a' is determined from the size of the covariances
and has to be 4.

The magnitude of b is then obtained by difference and turns out
to be -1.

But ASReml does not handle models with a negative residual variance.
The residual variance goes to the boundary, 0, and the algorithm falls over.

What can be do? Use a different variance parameterization.
e.g. Let V = cJ + dI
where J is
1 1
1 1

The c=2 and d=1
i.e. the residual variance is 1 and ASReml can fit this
parameterization.

So, you can explore what is happening in your data by fitting a
Sire model (using the pedigree maybe on sires)
or a
Sire + MGS model. possibly ignoring sire pedigree.

These models will help you understand what the variance structure is.
I expect you will find a sire component which is greater than a third
of the residual variance under that model.

What that means is that the genetic model (animal model) is inadequate.
Maybe there are non genetic effects confounded with 'sire' variance,
or there are maternal effects that should be separated out.

The problem of the residual going to the variance is particularly
associated with the ANIMAL model and should not occur under
a simple sire model (unless there is no variation within sires).

Now reread the earlier replies.

Then you can estimate

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

Retired Principal Research Scientist (Biometrics)

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Received on Tue Sep 21 2009 - 23:13:14 EST

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