Variance structure¶
The default variance structure for a random effect is a Kronicker product of an indetety matrix
and a co-variance matrix.
A numper of predefined diferent variance structures can be used in DMU.
PED¶
A pedigree file can be used to define an additive genetic relationship. For the random factor(s) having
this variance structure a $VAR_STR key-word line with the type PED must be specified. On the key-word line
specification of the pedigree file and the type of pedigree information must also be specified.
The r_factor on the $VAR_STR line corresponds to the random factor numbering on the RANDOM line in the $MODEL.
The method used for setting up the relationship matrix is specified on the $VAR_STR keyword line (method),
and can be one of the following:
Method Type of pedigree
______ __________________________________________________
1 Sires and dams, inbred population
2 Sires and dams, noninbred population
3 Sires and maternal grandsires, inbred population
4 Sires and maternal grandsires, non-inbred population
6 Same as 2 but with grouping by phantom parents
The pedigree file can be in ASCII or in binary format. The file must contain the following four variables:
1: ID = ID for the individual included in the random factor (genetic effect) in the model
2: Sire ID = ID for the sire
3: Dam/MGS ID = ID for the dam/maternal grandsire
4: Sort var. = Birth date or equivalent
All variables must be integers, and if binary format is used they must be of type INTEGER*4.
The ID in the pedigree file must correspond to the identifier used for the random factor in the model
directive lines. If the model includes random factors that are formed by merging random effects in the
RANDOM line $MODEL section, such as models with maternal and direct genetic effects, the pedigree file
must contain pedigree information for both random effects.
The sort variable can be any variable that can be used to sort animals in birth date order. Birth dates are
only necessary if inbreeding is taken into account in the model, otherwise it can be left as missing (0).
Great care is necessary when preparing pedigree information.
Genetic groups can be specified in several ways. If the model contains a fixed genetic group effect for each
record an extra variable with group codes must be included in the integer input.
If grouping by phantom parents is desired, this means that the unknown parents must be grouped. Therefore,
the zero's that previously indicated an unknown parent must be replaced by a group code. These group codes
MUST BE NEGATIVE in order to distinguish them from normal animal numbers.
GREL¶
This is for a GBLUP model using a genomic relationship matrix. The user supplied file with the inverse
genomic relationship should contain all non-zero elements (half stored) and have one element per line and
with two integers and one real. The two integers are the ID’s corresponding to row and column in the
inverse genomic matrix and the real is the element. The ID’s must correspond to the ID’s used in the data
file and must contains at least a diagonal element for all individuals in the data file.
DOM¶
Dominance relationship can be included in the model via a user supplied inverse dominance relationship
matrix. In addition to the dominance effect, the model must also include an additive effect (a random
effect with a pedigree structure), and the inverse dominance relationship matrix must be setup for the
same individuals as included in the pedigree structure. The user supplied file with the inverse dominance
relationship should contain all non-zero elements (half stored) and have one element per line and with two
integers and one real. The two integers are the ID’s corresponding to row and column in the inverse
dominance matrix and the real is the element. The ID’s must correspond to the ID’s used in the pedigree
file for the random effect with the same structure as the dominance effect.
The first line in the file can contain the log(determinant) of the dominance relationship matrix. The format
is “0 0 value”, where value is the log(determinant). If the log(determinant) is not specified, inference
between nested models can not be made based on the criterion in the output. In this case, a warning is
written in the output.
COR¶
A general co-variance structure for a random factor can be included via a user supplied inverse co-variance
matrix. The file with the inverse co-variance matrix must contain all non-zero elements (half stored).
Each line must have two integers and one real. The two integers’ identifies row and column using the same
ID’s as in the data file for the random effect(s) in question. The real contains the element in the inverse
co-variance matrix.
The first line in the file can contain the log(determinant) of the co-variance matrix. The format is:
0 0 value
where value is the log(determinant). If the log(determinant) is not specified, inference between nested
models cannot be made based on the criterion in the output. In this case, a warning is written in the output.
GROUP¶
DMU using ITASK 1 or 2 can estimate stratified heterogeneous residual variance i.e a residual co-variance
matrix is estimated for each stratum specified in the data. Stratified heterogeneous residual variance can
be used in prediction (BLUP) models ITASK 11 or 12.
ABS_QTL¶
Marker assisted BLUP can be performed by specifying a variance structure of type “ABS_QTL”.
The implementation is based on ideas of Henderson (1984) and Jafarikia et al. (2006). The method assumes
that the design matrix for the QTL effect has the same structure as another random effect in the model,
which typically will be an effect with a pedigree structure. The method is iteratively and do not need the
inverse IBD matrix and is based on the following procedure.
1. BLUE’s and BLUP’s are computed in a model without the QTL effect
2. QTL solutions are computed based on BLUP’s , variance components and the product of the IBD matrix
and the inverse relationship matrix
3. Adjust data for the current estimates of the QTL effects
4. Repeat step 3 -4 until the solutions to the QTL effects have converged.
The method requires a file with the elements of the IBD matrix. One element per line and with two integers
and one real. The two integers are the ID’s corresponding to row and column in the IBD matrix and the real
is the element. The ID’s must correspond to the ID’s used in the pedigree file for the random effect with
the same structure as the actual QTL effect.
The implementation can handle several QTL’s . At present it is only implemented in dmu4 (the in core solver).