Variance Structure Qualifiers

Context: Variance Structure definition

Variance Structure qualifiers

There are several qualifiers that directly relate to variance model parameters. These are usually specified as additional areguments in the variance wrapper function. For example, to fix the correlation in an AR1 process for Row to 0.33, write 
 ar1(Row 0.33 !GF)
instead of 
 ar1(Row)

ASReml extracts the qualifiers from the function and applies them after the model has been parsed via a MODIFY statement (which you might see if ASReml fails to parse the qualifiers).

Initial values

ASReml has some basic rules by which it will create initial values for parameters, but these are not always effective.
!INIT list supplies initial values for the parameters. The string !INIT may be omitted if the list appears ahead of all other qualifiers.

Initial values may also be retrieved from the TSV/RSV files.

Fixing/Bounding Variance parameters

  • !=s
    is used to constrain parameters within variance structures.
  • !Fr supplies an argument for the OWN variance model.
  • !Gs
    is used to modify the updating of the variance parameters. The exact action of these codes in setting bounds for parameters depends on the particular model and the value of s.
  • !GP
    (the default in most cases) attempts to keep the parameter in the theoretical parameter space and is activated when the update of a parameter would take it outside its space. For example, if an update would make a variance negative, the negative value is replaced by a small positive value. Under the !GP condition, repeated attempts to make a variance negative are detected and the value is then fixed at a small positive value. This is shown in the output in that the parameter will have the code B rather than P appended to the value in the variance component table.

    !GU (unrestricted) does not limit the updates to the parameter. This allows variance parameters to go negative and correlation parameters to exceed [-1,1]. Negative variance components may lead to problems; the mixed model coefficient matrix may become non-positive definite. In this case the sequence of REML log-likelihoods may be erratic and you may need to experiment with starting values.

    !GF fixes the parameter at its starting value,

    !GZ only applies to FA and FACV models and fixes the corresponding parameter in to zero (0.00).

    For multiple parameters, the form !GXXXX can be used to specify F, P, U or Z for the parameters individually. A shorthand notation allows a repeat count before a code letter. Thus !GPPPPPPPPPPPPPPZPPPZP could be written as !G14PZ3PZP.

    For a US model, !GP makes ASReml attempt to keep the matrix positive definite. After each AI update, it extracts the eigenvalues of the updated matrix. If any are negative or zero, the AI update is discarded and an EM update is performed. Notice that the EM update is applied to all of the variance parameters in the particular US model and cannot be applied to only a subset of them.
  • !SUBSECTION f allows for a set of independent autocorrelated series to have a common variance and correlation parameter but to have varying lengths. This extends the R structure definition from being a direct sum of direct products in that to a direct sum of a direct sum with common parameters. So, for generic times 
     residual ar1(units    0.5 !SUBSECTION auction )
    and for explicit times 
    residual  exp(date 0.2 !SUBSECTION plot )
  • !USE 'label' indicates that this variance structure is the same as the structure previously used and named label. More.
  • !Tr sets the type of the variance paremeters for the OWN variance model.
  • !COORD 'coordinates' supplies coordinate points for spatial (kriging) structures that require them. 

    expv(fac(X))
    does not require them because the distinct values in covariate X are used. 

    expv(Trait !COORD 1 3 5 8 12).Subject
    does require them.

    The following qualifiers pertain to the old syntax only

  • !NAME 'label' is used to associate a label f with a variance structure so that the same structure can be used elsewhere in the variance model via the !USE 'label' qualifier. More. It is not required under the wrapper function syntax.
  • !S2=r
    sets the initial value of the error variance within the section to r. The !S2= qualifier may be used in R structure definitions to represent the residual variance associated with the particular section. There is always an error variance parameter associated with a section R structure. In multiple section analyses the !S2= qualifier is used on the first of the c lines for each section to set the initial error variance for that section. If this is not supplied, ASReml calculates an initial value that is half the simple variance of the data in the site. To fix the variance !S2== r is used.
  • !S2==r
    is similar to !S2= except that the variance is fixed at r.
  • !S2==1
    is used in the analysis of multiple section data and in multivariate analyses and when variance parameters are included in the R structure. An example.

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