Requesting EM updates


!EMFLAG n !PXEM n request ASReml use Expectation-Maximization (EM) rather than Average Information (AI) updates when the AI updates would make a US structure non-positive definite. This only applies to US structures and is still under development.

When the !GP is associated with a US structure, ASReml checks whether the updated matrix is positive definite (PD). If not, it replaces the AI update with a single round of EM. If the non PD characteristic is transitory, then the Expectation-Maximization (EM) update is only used as necessary. If the converged solution would be non PD, there will be a EM update each iteration even when !EM is omitted. Faster convergence is achieved for G structures in this situation if the !EM or !PXEM qualifiers are used. The arguments define various alternatives which may work better (fewer iterations).     
!EMFLAG 1    EM + 10 local EM steps in current US term
!EMFLAG 2    EM + 10 local PXEM steps in current US term
!EMFLAG 3    EM + 10 local EM steps on all US terms
!EMFLAG 4    EM + 10 local PXEM steps on all US terms
!EMFLAG 5    Standard EM step
!EMFLAG 6    Single local PXEM step
!EMFLAG 7    Standard EM step + 1 local EM in current US term
!EMFLAG 8    Standard EM step + 1 local PXEM step in current US term
The test of whether the AI updated matrix is positive definitite based on inverting the matrix to check it is positive definite. EM updates may bring the matrix closer to being singular. is assessed by checking the product of the diagonal elements before and after If any exceed 1E7, ASReml fixes the matrix at that point estimates any other parameters conditional on these values. preceed with further iterations without fixing the matrix values would ultimately make the matrix such that it would be judged singular the analysis being aborted.

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