Re: Symmetric covariances in asreml

# Re: Symmetric covariances in asreml

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> From: bsouthey@iastate.edu
> To: Arthur Gilmour <gilmoua@ornsun.agric.nsw.gov.au>
> Subject: Re: Symmetric covariances in asreml
> Mime-Version: 1.0
> Date: Mon, 08 Mar 1999 08:29:13 CST
>
> Hi,
> Thanks, I understand that now and I found a comment in the manual saying that
> for the .res file.  But I consider unstructured matrices to be different than
> symmetric ones.  Non-symmetric situations do occasionally appear as Larry
> Schaeffer presented at  Arimdale with his 'Lush equations'.

I acknowledge that.  ASREML however cannot handle the non-symmetric case.
In my context UnStructured is symmetric and should normally
be positive definite.
>
> Also, I have two further questions:
> 1) How to do multiple traits.  I thought I had figured it but can not get a
> third trait to work.  I need to go to 8 traits at least.  I have tried
> different variations.  For Example, when I use the following, I get an error
> of no residual variation.
> w1 w2  w3 ~ Trait Tr.breed Tr.sex Tr.yearb Tr.aod  !r Tr.tag
> 1 2 1
> 0
> Trait 0 US 1.79 1.73 1.58 2.5 2.1 3.0
> Tr.tag 2
> Trait 0 US 0.86 1.29 1.53 2.29 2.77 3.35
> tag 0 0
>

In this context  No residual variation
probably means the Y sums of squares is negative which may happen
when the R matrix is not positive definite so that R inverse has
negative values on the diagonal.

Neither of the initial matrices you have supplied is positve definite (see
below)
so I am not surprised at the outcome.
You need to specify the  !GP  qualifier to constrain the matrices to
be positve definite.  Howvwe, in the version you have, it
was not successfully forcing the matrix to be Positive definite
so adding  !GP will probably result in
'Unable to Unverst R or G US structure.

I have attempted to overcome this in the latest version [March]
which is less likely to fail - although it still will fail if
the matrix is singular.

You may have an additional problem

Note that my matrices are lower triangle rowwise  so the matrices you have
specified above  are

1.79                 and   0.86
1.73 1.58                  1.29 1.53
2.5  2.1  3.0              2.29 2.77 3.35
giving correlations of

1.00                       1.00
1.03 1.00                  1.12 1.00
1.08 0.96 1.00             1.35 1.22 1.00

neither of which are positve definite.

However, if you meant to specify

1.79 1.73 2.5 1.58 2.1 3.0  ==> 1.79      which has correlation 1.00
1.73 2.50                       0.82 1.00
1.58 2.10 3.00                  0.68 0.77 1.00
it is positive definite.

Similarly    0.86 1.29 2.29 1.53 2.77 3.35  is

0.86            giving correlations   1.00
1.29 2.29                             0.92 1.00
1.53 2.77 3.35                        0.90 1.00 1.00

This is not quite positive definite.

Nevertheless, I expect you would get a solution in the latest version
if you specify  !GP on both the
Trait 0 US lines.

Concerning your 8 trait example, there is a reasonable chance
with the new version that given you have reasonable univariate
results you could go straight to the 8 trait model with code like

1 2 1
0
Trait 0 US !+36 !+GP
1.79
1.73 2.50
1.58 2.10 3.00
1.40 2.00 2.50 3.50
1.40 2.00 2.50 3.50 4.00
1.40 2.00 2.50 3.50 4.00 4.5
1.40 2.00 2.50 3.50 4.00 4.5 5.0
1.40 2.00 2.50 3.50 4.00 4.5 5.0 5.5

Trait 0 US !+36 !+GP
0.86
1.29 2.29
1.53 2.77 3.35
1.40 2.00 2.50 3.50
1.40 2.00 2.50 3.50 4.00
1.40 2.00 2.50 3.50 4.00 4.5
1.40 2.00 2.50 3.50 4.00 4.5 5.0
1.40 2.00 2.50 3.50 4.00 4.5 5.0 5.5
tag

where I have just quessed some values for the last 5 traits
but you should try and get atleast univariate
solutions for the variances as starting values.

Sometimes it works better to use the CORR structure for the genetic
variance matrix.

> 2) Which solutions are associated with which trait?
> trait_1 trait_2 ~ Trait Tr.effect_1 Tr.effect_2
> For each effect, do they go trait 1 level 1, trait 1 level 2,  ... trait 1
> level (m-1), trait 2 level 1, trait 2 level 2, ..., trait n level (m-1)?  Or
> start at trait n?
>

Hopefully the solutions in the .sln file are reasonably labelled.

The convention is that the first named factor in an interaction
is the outer factor.  So    for  Trait.treatment

trait 1 level 1, trait 1 level 2,  ... trait 1 level (m-1),
trait 2 level 1, trait 2 level 2, ..., trait n level (m-1)

is correct.

is correct.

> Thanks Bruce
>
>
>

<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>
Arthur Gilmour PhD                    mailto:Arthur.Gilmour@agric.nsw.gov.au
Senior Research Scientist (Biometrics)                 fax: <61> 2 6391 3899
NSW Agriculture                                             <61> 2 6391 3922
Orange Agricultural Institute               telephone work: <61> 2 6391 3815
Forest Rd, ORANGE, 2800, AUSTRALIA                    home: <61> 2 6362 0046

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