# GIV - General Inverse Variance structure

## Function

For the more general situation where the pedigree based inverse
relationship matrix is not the appropriate/required matrix, the user can
provide a particular general inverse variance (
GIV
) matrix explicitly
in a
.giv
file.
The user can prepare a
.giv
file containing this matrix and use it in the analysis.
Alternatively, the user can prepare the relationship matrix in a
.grm
file and \ASReml will invert it to form the GIV matrix.
The syntax for specifying a G matrix file (say
` name`.grm
) or
the G inverse file (say
`name`.giv
)
is

` name`.grm [ !SKIP ` n ` ]
or

` name`.giv [ !SKIP ` n` ]
the named file must have a
.giv
or
.grm
extension,
the G (inverse) files must be specified on the line(s)
immediately prior to the data file line after any pedigree file,
up to 98 G (inverse) matrices may be
defined,
the file must be free format with three
numbers per line, namely

`row column value`

defining the lower triangle row-wise of the matrix,
the file must be sorted
` column`
within
`row,`

1 1 1
2 2 1
3 3 1
4 4 1
5 5 1.0666667
6 5 -0.2666667
6 6 1.0666667
7 7 1.0666667
8 7 -0.2666667
8 8 1.0666667
9 9 1.0666667
10 9 -0.2666667
10 10 1.0666667
11 11 1.0666667
12 11 -0.2666667
12 12 1.0666667

every diagonal element must be represented; missing off-diagonal elements are assumed to be zero cells,
the file is used by associating it with a factor in the model. The number and order of the rows must agree with the
size and order of the associated factor,
the
!SKIP ` n`
qualifier tells ASReml to skip ` n` header lines in the file.
The
.giv
file presented in the code box gives the following G
inverse matrix
The
.giv
file can be associated with a factor in two ways:
the
first is to declare a G structure for the model term and to refer to
the
.giv
file with the corresponding identifier
GIV1, GIV2, GIV3 ...
for example,

animal 1
animal 0 GIV1 0.12

for a one-dimensional structure put the scale parameter (
0.12
in this case) after the
GIVg
identifier,

site.variety 2
site 0 CORUH 0.5
8*1.5
variety 0 GIV1

for a two-dimensional structure.
the second is for one-dimensional structures; in this case the
.giv
structure can be directly associated with the term using the
giv(`factor,i`)
model function which associates the
`i` th
.giv
file with factor `factor`, for example,
giv(animal,1) 0.12
is equivalent to the first of the preceding examples.
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