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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