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< ASReml ~ Understanding of a warning message as output
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| nicobardol |
 Posted: Tue May 31, 2011 2:22 pm |
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Joined: 13 Jan 2010
Posts: 7
Location: INRA Gif sur Yvette
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Hi there!
I've got an error message, which I don't understand!!
Someone could help me?
Thanks a lot.
Regards,
Nicolas.
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> modelRABLUP_dose.asr = asreml(fixed = Pheno ~ 1, random=~ ped(Ind, var=T), ginverse=list(Ind=ColInvSimil), na.method.Y="include", data=dataAsremlRA)
asreml(): 3.0.1 Library: 3.01gl X86_64 Run: Tue May 31 16:11:40 2011
1 negative pivots treated as singularities
Warning: GIV matrix not positive definite: Negative pivots
LogLik S2 DF
-997.3779 262.6546 300 16:11:42
1 negative pivots treated as singularities
-998.9560 261.4760 300 16:11:42
1 negative pivots treated as singularities
-1000.9106 254.9338 300 16:11:43 (1 component(s) restrained)
1 negative pivots treated as singularities
Logliklihood decreased to -1180.49 - trying again with reduced updates
1 negative pivots treated as singularities
-1000.6261 256.4508 300 16:11:45
1 singularities inAverage Information Matrix
Exit status: -1 - Singularity in Average Information Matrix
Finished on: Tue May 31 16:11:45 2011
Message d'avis :
Abnormal termination
Singularity in Average Information Matrix
Results may be erroneous
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| Arthur |
| Posted: Thu Jun 02, 2011 2:13 am |
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Joined: 05 Aug 2008
Posts: 277
Location: Orange, NSW
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Dear Nicholas,
There are three messages which are probably related.
Warning: GIV matrix not positive definite: Negative pivots
is reporting that the G inverse matrix you have provided is not positive definite, but has 1 negative pivot. While ASReml proceeds with the arithmetic, a non positive definite G matrix can lead to the mixed model equations failing - depending on the magnitude of the variance component. So you should validate the matrix, identify which rows are associated resulting in the negative pivot. You may have an error, or you may need to reduce some covariances or increase some variances.
1 negative pivots treated as singularities
reports that the mixed model equations and not positive semidefinite. A negative pivit in the G matrix means a possibly large negative element on the diagonal of the G inverse. When this is then added to the Z'Z matrix, the result is a negative value on the diagonal of the (adjusted) mixed model coefficient matrix. Again ASReml pushes on with the arithmetic.
1 singularities inAverage Information Matrix
After 3 iterations, the variance componet for the G matrix is such that the AI matrix has become singular. So, fix the first problem and the rest should go away. |
_________________
Arthur Gilmour
Retired Principal Research Scientist (Biometrics) |
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| Yves Rousselle |
| Posted: Fri Mar 23, 2012 12:52 pm |
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Joined: 05 Mar 2012
Posts: 9
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Dear all,
I've got the same problem as Nicolas about the "singularities inAverage Information Matrix" message but I haven't the other ones about the G-inverse matrix.
I already post a message with all the details here :
http://www.vsni.co.uk/forum/viewtopic.php?p=2830#2830
Do you know does the error could come from in my case ?
Regards,
Yves |
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| Arthur |
| Posted: Sat Mar 24, 2012 8:37 pm |
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Joined: 05 Aug 2008
Posts: 277
Location: Orange, NSW
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Dear Yves,
The problem is that the residual variance has reachedthe boundary.
The Algorithm in ASReml assumes the residual variance is positive.
So this is a problem of the model, and arises because the residual variance in these kinds of models is not a simple residual. By analogy:
It is widely known that a sire model estimates 1/4 of the aditive genetic variance. However, it is possible that the intrclass correlation from a sire model exceeds 0.25 leading to a heritability > 1.0. This could happen
if progeny from sires were raised independently, or the sires represented different breeds. If the equivalent animal model was fitted in this situation, the 'residual' would logically be negative, but ASReml would fail when it approached zero.
Something similar is apparently happening in your case. |
_________________
Arthur Gilmour
Retired Principal Research Scientist (Biometrics) |
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| Yves Rousselle |
| Posted: Mon Mar 26, 2012 12:15 pm |
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Joined: 05 Mar 2012
Posts: 9
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Dear Arthur,
Thank you very much for your quick answer, it's quite impressive that one of the people that have created ASREML takes time to answer to users' questions like that.
I had guessed that it was a problem linked to a residual variance story but I wasn't sure of that. Now that you have confirmed this, the real question is What do I do with my analysis ?
My aim is to find if some markers have an effect on some quantitative traits (association mapping in brief). So I try to explain genotypes' BLUP I get from others models with a genotypic random effect with a molecular kinship variance/covariance matrix and a marker fixed effect. I have got as much observations in my data as there are genotypes so the genotype effect has the same levels number as the residual but I know that this should be possible because I specify a variance/covariance matrix.
When I try my model with all the traits, it works fine for some and is doesn't converge for others. In one hand, for every non-convergent cases, the S2 value showed during the iteration details reaches 0 and the gamma value for genetic effect in the varcomp table is very high (like 100018, 397152 or 90282 for example). On the other hand, for every convergent cases, the genetic effect gamma values is quite low (like 3, 6...) but for two traits, S2 reaches 0 at the first iteration.
What does the fact that the model doesn't converge for some traits mean ? It's perhaps more a genetic question by the way...
What are the meaning of these parameters S2 and gamma ?
Thank you for your help,
Yves |
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| Arthur |
| Posted: Tue Mar 27, 2012 4:47 pm |
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Joined: 05 Aug 2008
Posts: 277
Location: Orange, NSW
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Dear Yves,
Without looking at your data, (marker and trait), I cannot comment on why this is happening. I do not expect it.
But a gamma value of 3,6 is not 'quite low'. Most traits have a heritability less than 0.5 which for a sire model implies a gamma value of less than 1/7
In your case, there is a potential issue of scaling of the G matrix but if the
average of its diagonal is about 1, then I would expect gamma < 1/7
Is there a pattern of which traits fail; are these traits you expect to have high heritability? Indeed are you analysing deregressed blups or something
which is not a simple measurement on the individual whose marker data you have?
In matrix notation, the Variance matrix used in ASReml is V=R+ZGZ'
and so the mixed model equations are formally written in terms of R G X and Z
But in a univariate case with with a simple residual term R= \sigma^2 I,
we can factor the \sigma^2 out of the mixed model equations,
that is V = \sigma^2 (I+ ZG^*Z') where G = \sigma^2 G^*
S2 is sigma^2
GAMMA is the variance ratio parameter in G^* which is
gamma=\sigma^2_g / \sigma^2
The variance componet report in the .asr file reports GAMMA and the Components. These columns are the same if the analysis is done
on the variance scale. |
_________________
Arthur Gilmour
Retired Principal Research Scientist (Biometrics) |
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| Yves Rousselle |
| Posted: Wed Mar 28, 2012 2:15 pm |
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Joined: 05 Mar 2012
Posts: 9
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Dear Arthur,
Thanks for your answer. As I guessed, my question is more a quantitative genetic related question than a pure statistical one. I will ask to other colleagues if they have some ideas about my results.
Thanks also for the parameters explanation. It helps me to understand the ASREML outputs. However, I don't understand what you called "G^*".
Concerning the gamma values I find, there are all greater than 1. I think it's what we expect because I try to explain BLUP predicted for each variety in an other model by the same variety random effect with a kinship matrix. It's only a preliminary step before the introduction of a marker fixed effect in order to test for the marker association with the quantitative trait. By the way, I try to explain variety BLUP by a variety effect so I suppose that finding that all the variance is in the variety effect is not so surprising. Am I right ?
If I understand well, one solution could be to introduce a marker effect directly in the full model without doing the BLUP estimation step. If I did that, the residual variance won't reach 0 and therefore, the model would converge. Do you think that could be a good idea ?
Yves |
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