# Variance Structure Qualifiers

## Fixing/Bounding Variance parameters

!=`s`

is used to
constrain
parameters within variance structures.
!F`r`
supplies an argument for the
OWN variance model.
!G`s`

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 !G`XXXX` 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.
!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.
!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.
!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

1 1 0 # data sorted bids within auctions
0 0 AR1 0.5 !SUBSECTION auction

and for explicit times

1 1 0 # data sorted date within plot
0 date EXP 0.2 !SUBSECTION plot }

!USE '`label`'
indicates that this variance structure is the same
as the structure previously used and named `label`.
More.
!T`r`
sets the type of the variance paremeters for the
OWN variance model.
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