Re: multivariate analysis - use of !GP and lost SE

From: Arthur <asremlforum_at_VSNI.CO.UK>
Date: Tue, 24 Mar 2009 20:56:00 +0000

ASReml is based on using the Average information algorithm to locate the maximum of the REML likelihood. However, sometimes the maximum is outside the 'parameter space' and so the problem is redefined as trying to locate the maximum REML likelihood inside the boundary of the parameter space.

The AI algorithm cannot handle that more complex optimization so ASReml reverts to other strategies, depending on the particular problem.

In the case of an Unstructure matrix with !GP constraint, it reverts to some form of EM step (see !EMFLAG for some details of options). The procedure is :
1) perform the AI update
2) check US mattttrix is positive definite
  If not
  3) use the SCORE (or whatever) to update the matrix
       and update all other parameters (by AI) conditional on the new values
      for the US matrix.

The consequence of this is that the AI matrix used for the update is modified
so that the lines relating to the elements of the US matrix are zeroed.
Hence, when it comes time to report variances of variance parameters,
(based on the inverse of the AI matrix), values are not available for the US
matrix, and the other values are conditional on the US matrix being fixed
at the updated values.

Thats the state of play.

In a bivariate case, you could change to the CORUH model, fix the correlation at 0.999, (!GFPP) and then you would be able to get variances (SE) for the variances (the correlation has none being fixed).

Arthur Gilmour

Principal Research Scientist (Biometrics)
NSW Dept Primary Industries

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Received on Wed Mar 24 2009 - 20:56:00 EST

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