Re: constraining correlation = 1

Dear Professor Gilmour,
I have obtained ASReml2 and the factor analytic model seems to work
fine, i.e. without any error messages, but I'm not sure if I'm really
getting it right.
Please find the model definitions and excerpts of the output below. I
was a bit surprised by the rather large changes in the parameter
estimates, and this becomes especially evident when I run .pin-files
calculating e.g. heritabilities as 4 over 1+4+7 for the first and as 6
over 1+6+8 for the second model.
Of course, this is of little relevance for hypothesis testing
regarding the genetic correlation, but I am jsut a bit suspicious that
I'm still doing something wrong or misunderstanding something.
Any help would be highly appreciated and I thank you very much for any advice.

Kind regards-
Lutz
==
US model

hkwPre hkwPst ~ Trait !r Trait.id Trait.hh
1 2 2

0
Trait 0 US 0.8 !GUFU
0.0 0.8

Trait.id 2
Trait 0 US
3*0
id

Trait.hh 2
Trait 0 US
3*0
hh

Source Model terms Gamma Component Comp/SE % C
 Residual UnStructured 1 1 0.542215 0.542215 14.46 0 U
 Residual UnStructured 2 1 0.00000 0.00000 0.00 0 F
 Residual UnStructured 2 2 0.191281 0.191281 9.36 0 U
 Trait.id UnStructured 1 1 0.113742 0.113742 2.44 0 U
 Trait.id UnStructured 2 1 0.243217E-01 0.243217E-01 1.18 0 U
 Trait.id UnStructured 2 2 0.546860E-01 0.546860E-01 2.09 0 U
 Trait.hh UnStructured 1 1 0.783119E-01 0.783119E-01 2.87 0 U
 Trait.hh UnStructured 2 1 0.484309E-01 0.484309E-01 3.10 0 U
 Trait.hh UnStructured 2 2 0.193302E-01 0.193302E-01 1.24 0 U
 Covariance/Variance/Correlation Matrix UnStructured Residual
  0.5422 0.000
   0.000 0.1913
 Covariance/Variance/Correlation Matrix UnStructured Trait.id
  0.1137 0.3084
  0.2432E-01 0.5469E-01
 Covariance/Variance/Correlation Matrix UnStructured Trait.hh
  0.7831E-01 1.245
  0.4843E-01 0.1933E-01

XFA model

hkwPre hkwPst ~ Trait !r xfa(Trait,1).id Trait.hh
1 2 2

0
Trait 0 US 0.8 !GUFU
0.0 0.8

xfa(Trait,1).id 2
xfa(Trait,1) 0 XFA1
0 0 0.45 0.26
id 0 AINV

Trait.hh 2
Trait 0 US
3*0
hh

Source Model terms Gamma Component Comp/SE % C
 Residual UnStructured 1 1 0.555071 0.555071 15.09 0 U
 Residual UnStructured 2 1 0.00000 0.00000 0.00 0 F
 Residual UnStructured 2 2 0.214141 0.214141 12.60 0 U
 xfa(Trait,1).id XFA 0 1 0.00000 0.00000 0.00 0 F
 xfa(Trait,1).id XFA 0 2 0.00000 0.00000 0.00 0 F
 xfa(Trait,1).id XFA 1 1 0.306827 0.306827 4.32 0 U
 xfa(Trait,1).id XFA 1 2 0.124747 0.124747 2.31 0 U
 Trait.hh UnStructured 1 1 0.835373E-01 0.835373E-01 3.07 0 U
 Trait.hh UnStructured 2 1 0.414336E-01 0.414336E-01 2.67 0 U
 Trait.hh UnStructured 2 2 0.366873E-01 0.366873E-01 2.57 0 U
 Covariance/Variance/Correlation Matrix UnStructured Residual
  0.5551 0.000
   0.000 0.2141
 Covariance/Variance/Correlation Matrix XFA xfa(Trait,1).id
  0.9417E-01 1.000 1.000
  0.3826E-01 0.1554E-01 1.000
  0.3069 0.1247 1.000
 Covariance/Variance/Correlation Matrix UnStructured Trait.hh
  0.8354E-01 0.7484
  0.4143E-01 0.3669E-01

On 11/28/06, arthur.gilmour_at_dpi.nsw.gov.au
<arthur.gilmour_at_dpi.nsw.gov.au> wrote:
> Dear Lutz,
>
> re:
> I am trying to test the hypothesis that the additive genetic
> correlation in my bivariate trait animal model is different from 1.
>
> For the significance of its difference from 0, I can simply specify a
> starting value of 0.0 for the covariance term in the variance
> structure specification and use a qualifier like !GUFU to keep it
> fixed at 0.
>
> But I don't find a way to fix the correlation = 1. Constraining the
> two variances and their covariance to be equal (using a VCC line
> -depending on the exact model- like 13 14 15) won't converge in any
> case. Essentially, this is also asking too much, since for cor12=1, it
> is not really necessary to have var1=var2, right?
>
> Are there any options that I'm not aware of, or does my approach look
> simply wrong altogether? Any comments would be highly appreciated.
>
>
> Further to Ari's response
>
> The way to fit a model with correlation of 1 is to use XFA with zero PSI's
>
> Thus, replace the model term Tr.animal with xfa(Tr,1).animal
>
> and define its G structure as
>
>
> xfa(Tr,1).animal 2
> xfa(Tr,1) 0 XFA1
> 0 0 a b # replace a and b with SQRT of the respective genetic
> variances
> animal 0 AINV
>
> Qualifications:
> 1) XFA crossed with relationship matrix does not work in ASReml 1
> 2) There was a bug in the LogL calculation for XFA with zero PSI crossed
> with NRM
> which is fixed in ASReml 2.00 build am ; this will affect any LogL tests
> you might make.
>
>
>
>
> Grace, mercy and peace to you from God our Saviour Jesus Christ
>
> Arthur Gilmour PhD
> mailto:Arthur.Gilmour_at_dpi.nsw.gov.au
> 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
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>
> http://www.dpi.nsw.gov.au/reader/17263
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>
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--
Dr. med. Lutz Ph. Breitling, Marie Curie EST Research Fellow
Integrative & Comparative Biology (Irene Manton 8.93e)
University of Leeds, LS2 9JT Leeds/UK
--
permanent address: Brunirode 18
30880 Laatzen/Germany