Re: ASReml: Enquiry for problem solving

From: <arthur.gilmour_at_DPI.NSW.GOV.AU>
Date: Tue, 18 Mar 2008 14:13:45 +1100

Dear Hooi Ling,

 Since you sent the original query to the list,
 I'll distribute this response in case it is helpful to others.
 Your query was whether we can fit a binomial/threshold plus two
 normal traits in a trivariate analysis.

 I have previously only fitted a binomial/threshold plus one
 normal traits in a bivariate analysis but on reflection do
 not think there is a fundamental reason why the trivariate model
 should not work.
 So you sent your data and these are my observations.
 We had 9267 records for individuals.
 7482 have an initial weight. 4170 survive to give
 a final weight. That is, survival indicates the presence
 of the final weight. As well as fixed effects, the model
 fitted 'animal' and 'dam' so univariate analyses gaave variance
                surv iw fw
 animal 0.122586 1.39358 99.8385
 dam 0.389605 4.12747 495.651
 residual 1.00000 1.93063 644.766
 Since both animal and dam have pedigree, the next step here
 would be to estimate the genetic covariance but I leave that to you.

You had analysed log of iw and fw.
For iw, there appear to be only 5 extra heavy individuals (> 18.4)
ranging from 32 to 66). My inclination is to drop these.

The case for log transformation is reasonable for iw but excessive for fw.
The residual diagnostic slope for iw reduces from 0.9 to 0.0 with log
The residual diagnostic slope for fw reduces from 0.86 to -0.66 with log
The residual diagnostic slope for fw reduces from 0.86 to 0.54 with sqrt

 So log is good for iw but excessive for fw which has high kurtosis (long
 on both sides).

 Univariate analysis transformed scale

                surv log(iw) sqrt(fw)
 animal 0.122586 0.049758 0.473805
 dam 0.389605 0.344194 1.61442
 residual 1.00000 0.104068 1.82541

For what follows, lets just fit the corresponding sire model.
                surv log(iw) sqrt(fw)
 sire 0.131563 0.087999 0.390122
 dam 0.317624 0.254614 1.38775
 residual 1.00000 0.128877 2.05974

 Notice that the sire variance IS NOT a quater of the animal variance.
 This suggests that there could be management effects associated with
 else the pedigree model is not appropriate. Is this
because animals are raised in 'sire' groups early in life and so
the sire variance is inflated? Alternatively, it could be related
to the reason why so many have missing initial weights. Overall 45%
survived, but only 41% of those with initial weights survived cf
100% of those with final weights survived). I.e. is there a selection
That issue is beyond this report.

 I have also revised the fixed model but that is cosmetic.

 Now, there is a structural problem with including surv and fw
 together in a bivariate analysis to estimate the covariance
 because fw is only ever defined when surv is 1.

 Lets try the bivariate analyses.

 First, because of the missing values in iw and fw and the use of !ASUV
 we MUST include mv in the model.

 So surv and log(iw)
Since average survival for all fixed effects is not far from 0.5,
not much is lost be treating surv as normal, so try that first.

With the !EM5 qualifier this converged to
  Residual Tr.animal Tr.dam
  0.2046 0.9719E-01 0.2755E-01 0.1242 0.1113E-01 0.1755
  0.1408E-01 0.1026 0.4737E-02 0.5284E-01 0.1085E-01 0.3435
 which is consistent

The 'iterated EM' options are designed for uncorrelated random effects
but 'dam' and 'animal' represent correlated random effects.

However, trying surv on the underlying scale, the model fails.
I believe this is because the threshold model is not well behaved
under an animal model, although sometimes it seems to work OK.

  Residual Tr.sire Tr.dam
  0.2185 0.9774E-01 0.6485E-02 0.6834E-01 0.1614E-01 0.1439
  0.1640E-01 0.1289 0.1645E-02 0.8941E-01 0.9215E-02 0.2540

This is consistent for surv; .00648 is about 1/4 of .0275
and dam variance increased about .0065 from .0111 to .0161

The log(iw) components agree with the siremodel results above.

Anyway, what happens in threshold model?

It also converges to
  Residual Tr.sire Tr.dam
  0.9652 0.9597E-01 0.1356 0.7835E-01 0.3279 0.1514
  0.3382E-01 0.1287 0.8620E-02 0.8924E-01 0.4369E-01 0.2540

 This is on the Logit scale for surv so taking the residual as
 sire/res = .0427 which is comparable to 0065/2185 .0297.

 So, there are lots of issues.

 Now if we consider sqrt(fw) and surv; we can't estimate an error
 covariance because fw is only measured when surv=1. Can we do anything?
 ASReml didn't detect a singularity in the AI matrix and converged,
 on the observed scale to

   Residual Tr.sire Tr.dam
  0.2184 0.1810E-01 0.6174E-02 0.3227 0.1657E-01 0.3060
  0.1214E-01 2.059 0.1543E-01 0.3701 0.4694E-01 1.420

The surv results agree with the bivariate analysis involving log(iw)
For sqrt(fw) cf residual 2.059 with 1.825,
                 sire .37 with animal .47
                 dam 1.42 with dam 1.82
Again, sire variance agrees with univariate sire models for sqrt(fw).

Sire model, 3 traits, surv on normal scale

  Residual Tr.sire Tr.dam
   .2185 0.0983 0.1105 0.0060 0.1732 0.4658 .01668 0.1050
  0.0164 0.1272 0.5457 0.0038 0.8054E-01 0.4937 0.00694 0.2618
  0.0756 0.2849 2.143 0.0227 0.8825E-01 0.3967 0.04111 0.5685 1.781

 Sire model, 3 traits, surv on underlying scale
  Residual Tr.sire Tr.dam
   1.000 0.0995 0.0400 0.1240 0.1847 0.4715 0.3300 0.1114 0.2230
  0.0355 0.1271 0.5427 0.0184 0.0800 0.4909 0.0327 0.2622 0.8347
  0.0583 0.2818 2.122 0.1023 0.0855 0.3795 0.1706 0.5693 1.774

So, after all this, my conclusion is that ASReml can fit a trivariate
model with the first trait on an underlying scale but there are many
issues to consider.

1) The model must include 'mv' if there are missing responses.
2) 'animal' models often give trouble on the underlying scale
    and that seems to be the case here.
I trust this has been useful.

May Jesus Christ be gracious to you in 2008,

Arthur Gilmour, His servant .
Mixed model regression mapping for QTL detection in experimental crosses.
Computational Statistics and Data Analysis 51:3749-3764 at

Personal website:
Skype: arthur.gilmour,
Principal Research Scientist (Biometrics)
NSW Department of Primary Industries
Orange Agricultural Institute, Forest Rd, ORANGE, 2800, AUSTRALIA
fax: 02 6391 3899; 02 6391 3922 Australia +61
telephone work: 02 6391 3815; home: 02 6364 3288; mobile: 0438 251 426

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Received on Thu Mar 18 2008 - 14:13:45 EST

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