Re: proportionality constraints (fwd)

From: Bruce Southey <southey_at_UIUC.EDU>
Date: Wed, 4 May 2005 10:26:58 -0500

Perhaps the alternative solution is to create a new model to your model so
these are linearly equivalent (mean and variance are the same).

This is wrong as I have not done this type of stuff and I know these
are variances etc. But it should be along the lines that you need.

Since you want the variances to be restricted such that v3 = v1 + 0.5 * v2.
(Thus v1 and v2 are uncorrelated.)
I think this means that u3 = u1 + sqrt(0.5)*u2.

If you expand your model: Y= Xb + Z1u1 + Z2u2 + Z3u3 +e

Y*= Xb + Z1u1 + Z2u2 + a*Z3*u1 + b*Z3*u2 +e

Y*= Xb + (Z1+a*Z3)u1 + (Z2+b*Z3)*u2 +e

Then is a matter of finding a (1) and b (square root of 0.5) so that Var(Y)
equals Var(Y*). This requires the cross products of both Z1 and Z3 and Z2 and
Z3 to be zero to work. (But then I did not expect it to work.)


---- Original message ----
>Date: Wed, 4 May 2005 13:05:38 +1000
>From: Arthur Gilmour <arthur.gilmour_at_AGRIC.NSW.GOV.AU>
>Subject: Re: proportionality constraints (fwd)
>Dear Ian,
>Indeed your email was distributed but apparantly nobody has or is willing
>to offer a solution.
>The relationship matrix stuff in Genstat is, as far as I know, the same as
>is available
>in ASReml. I do not think it helps with your situation.
>While the concept of enabling what you want has been around for years, a
>syntax and procedure has not been implemented.
>The best I could offer, using the beta version, is to extract the
>information matrix and score
>from the unconstrained model after an iteration and derive new constrained
>parameters from that.
>Refit the model with the updated parameters and iterate the process to
>The relevant qualifier is !SCORE.
>Another idea is
> In ASReml, I have to let v2=k*v1,
>v3=(1+0.5*k)*v1, and then calculate a profile likelihood for a range of
>values of k.
>The !VCC qualifier allows you to fix the relationship between v2 and v1 by
>nominating k
>So, for a given k, estimate v1 and v3 (with v2=k*v1).
>Given v1 and v3 estimated, solve k=2(v3/v1 -1)
>and repeat the process until convergence.
>I apologise for not responding earlier.
>with God's love in the Name of Jesus Christ.
>Check out
>Arthur Gilmour PhD
>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;
>The ASReml discussion group
> has reactivated. To join,
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>Date: Thu, 21 Apr 2005 13:00:38 +0100 (BST)
>From: I M S White <>
>Cc: Robin Thompson <>
>Subject: proportionality constraints
>If there are (say) three variance components, v1, v2, and v3, I think
>Genstat REML allows me to set a constraint such as v3 = v1 + 0.5 * v2
>(using VCOMP[RELATIONSHIP=matrix]). In ASReml, I have to let v2=k*v1,
>v3=(1+0.5*k)*v1, and then calculate a profile likelihood for a range of
>values of k.
>(1) Is there a better way? (2) Is there any reason why ASReml cannot
>provide the more general form of constraint?
>University of Edinburgh
>Ashworth Laboratories, West Mains Road
>Edinburgh EH9 3JT
>Tel: 0131 650 5490 Fax: 0131 650 6564
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Received on Tue May 04 2005 - 10:26:58 EST

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