# 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.