Re: Convergence

Dear Tore,

The effect of !GP on
CORGH
is two fold.

First, the ASReml inverts the implied G matrix,
it checks that it is Positive Definite. If not,
it BENDS the matrix (shrinks its eigen values) to make it
positive definite and then proceeds with the modified matrix.

Second, when ASReml updates the parameters, it checks that all
correlations are within [-1,1]. However it does nto check the whole
matrix.

It is the first of these that is happening in your run.
The values reported in the .asr file will represent the matrix
as updated by the AI algorithm, but without checking the matrix.
The % change shows the change ASReml made in doing the AI update.

However, since these values represent a NPD matrix, they are BENT before
being reused. The bending effectively undoes the AI update.
Consequently it can never converge because it keeps jumping over the
fence, only to be pulled back again.

The parameter values in the .res file are the ones used to calculate the
likelihood, except the very last column which is the result from the
last iteration.

When !GU is used, the non positive definite matrix is allowed to stand.

So, if you require a POSITIVE DEFINITE matrix, use the 'stable' values
from the .res file. Otherwise use the !GU results.

Alternatives are
1) to use !GP with US, starting with the 'stable' result
and ASReml will do EM updates
2) use an XFA1 structure and see if you can get a likelihood almost as
hood.

On Tue, 2009-11-17 at 12:14 +0100, Ericsson Tore wrote:
> This is such a case when convergence is obscure, and also some result presentations that confuses (at least me).
>
> Problem set-up for Asreml 2:
> ----------------------------
> ! Two-site, two-trait. Sites = F34
> ! V = vitality, H = height (standardized to s2a near 1.0)
> ! Tree model with pedigree, two of four sites filtered (factor, 2)
> !FILTER F34 # 264 265
> !DDF -1 !MAXIT 100 !CONTINUE
> V_30 H_30 ~ Trait Trait.F34,
> Trait.at(F34,1).Block,
> Trait.at(F34,2).Block mv !r,
> Trait.F34.Genotype_id
> 2 2 1
> 7949 0 IDEN # 264 Vindeln
> Trait 0 US 16.4 0 3.17 !GU
> 7864 0 IDEN # 265 Villvattnet
> Trait 0 US 15.0 0 2.79 !GU
>
> Trait.F34.Genotype_id 2
> Trait.F34 0 CORGH !GP #or !GU
> 0.6
> 0.2 0
> 0 0.2 0.7
> 1 1 1 1
> Genotype_id 0 AINV
>
> When run with !GP the components and the likelihood stabilize soon and do not change,
> but the iterations do not stop until the iteration limit is reached.
> Then, the result is presented as in 1. below. In the RES file, the
> last column added differs from the stable values, see "Finish res" below.
> In the ASR file, still another component vector is presented, see "Finish ASR" below.
>
> When run with !GU the behaviour is like expected with convergence (before
> getting as fixed as in the !GP case) with a slightly non-positive definite
> correlation matrix. The last RES column equals the ASR column.
> Excerpts from the RES/ASR files:
>
> 1. With CORGH !GP 2. With CORGH !GU
> ---------------------------------------- -----------------
> Stable res Finish res % Finish asr % Finish res/asr %
> ---------------------------------------- -----------------
> 16.4689 16.4689 0 16.4689 0 16.4685 0
> 0.298326 0.298326 0 0.298795 0 0.309826 0
> 3.18372 3.18372 0 3.18374 0 3.183937 0
> 15.068 15.068 0 15.068 0 15.0677 0
> 5.569687 5.569687 0 5.57104 0 5.602113 0
> 4.769561 4.769561 0 4.77056 0 4.79493 0
> 0.916608 0.925867 1 0.925867 15 0.925305 0
> 0.128836 0.130137 1 0.130162 0 0.130485 0
> -0.100716 -0.101733 1 -0.101709 0 -0.100732 0
> 0.37568 0.379475 1 0.379534 2 0.381465 0
> 0.351437 0.354987 1 0.355053 2 0.357152 0
> 0.780453 0.788337 1 0.788312 9 0.787729 0
> 1.027617 1.027617 0 1.02762 0 1.028345 0
> 1.062174 1.062174 0 1.06217 0 1.062729 0
> 0.986806 0.986806 0 0.986812 0 0.987396 0
> 1.16522 1.16522 0 1.16529 0 1.164835 0
>
> Questions: What happened in the !GP run? Please explain!

> Would it be a good idea to rather use the component estimates in the "Stable res"

> column than any result from those ASR files?
>
> Tore Ericsson
> Skogforsk, Sweden
>
> This message is intended for the addressee named and may contain confidential information. If you are not the intended recipient, please delete it and notify the sender. Views expressed in this message are those of the individual sender, and are not necessarily the views of their organisation.
>

-- 
Best Wishes,
Arthur Gilmour
Adjunct Professor
School of Computing and Mathematics
Charles Sturt University
Jesus went to the synagogue in every town in Galilee to preach and drive
out demons.
A leper came, knelt down and said, "If you will, you can make me clean".
Jesus was moved. He reached out and touched him and said 
"I am willing.  Be clean." He was cleansed immediately.
Mobile Number +61 427 227 468
Home phone +61 2 6364 3288  Skype: Arthur.Gilmour
http://www.CargoVale.com.au/asreml
By the way: listen to Alan Jones (2GB Radio) interview 
with Lord Mockton on the Copenhagen Summit 
http://2gb.com.au/index2.php?option=com_newsmanager&task=view&id=4998 
Travel:
Brisbane Probe 29Nov to 6 Dec
Bangladesh Proshikkon 31Dec - 6 Feb