Information related to pooling of covariance components using a (penalized)
maximum likelihood approach is specified in a block entry, beginning with a line
containing the code POOL and ending with a line beginning with END. Within the
block, the following directives are recognized:
**
PSEUPED **followed (space separated) by a three letter code specifying the assumed
pedigree structure and values on sizes or numbers of families. The following
pseudo-pedigree codes are available:
**
PHS **denotes a simple balanced paternal half-sib design. Optionally, two
integer numbers giving the numbers of sires and the number of
progeny per sire, respectively, can be given (space separated, on the
same line) after the code. If not given, default values of and
are used.

This option is suitable for a simple animal model only.
WOMBAT will check that a) there is only one random effect fitted,
and b) that this has covariance option NRM. If the MINPAR option
(see below) is used, WOMBAT cannot perform these checks; hence
the DIRADD code together with the name of the random effect, as
described below, need to be given.
**
HFS **implies a balanced hierarchical full-sib design comprised of sires,
dams per sire and progeny per dam. Assumed values for
, and can be given (space-separated) on the same line.
If omitted, default values of , and are used.
This option is suitable for a simple animal model or a model fitting
maternal permanent environmental effects in addition. Again, if the
MINPAR option is used, codes DIRADD and MATPE need to be given in
addition.
**
BON **selects a design comprising 8 individual per family in two generations,
due to Bondari et al. [4]. Optionally, this code can be followed (space
separated) by the number of such families (integer); if not given, a
default value of 2 is used. For this design, expectations of covariances
between relatives due to direct and maternal effects are available.
In order for WOMBAT to ‘know’ which random effect has which
structure, additional information is required. This should comprise
one additional line per random effect fitted, with each line consisting
of a keyword specifying the type of random effect followed (space
separated) by the name of the effect as specified in the model of
analysis. Keywords recognized are DIRADD for direct additive genetic,
MATADD for maternal genetic and MATPE for maternal permanent
environmental effects.

EXAMPLE:

MODEL

RAN animal NRM

...

END MOD

VAR animal 4 NOSTART

VAR residual 4 NOSTART

POOL

PSEUPED USR 5

1.0 0.50 0.50 0.50 0.50

1.0 0.25 0.25 0.25

1.0 0.25 0.25

1.0 0.25

1.0

END

RAN animal NRM

...

END MOD

VAR animal 4 NOSTART

VAR residual 4 NOSTART

POOL

PSEUPED USR 5

1.0 0.50 0.50 0.50 0.50

1.0 0.25 0.25 0.25

1.0 0.25 0.25

1.0 0.25

1.0

END

This shows the coefficients for direct additive genetic effects for a family comprising a sire (individual 1) with four progeny from unrelated dams.

The minimum information to be given in the parameter file must comprise:

- 1.
- The ANALysis statement
- 2.
- A VAR line for each covariance matrix, together with the NOSTART option telling WOMBAT not to expect a matrix of starting values.
- 3.
- The POOL block, including statements showing which random effect represents which type of genetic or non-genetic effect.

Either COVARM or CORREL can be followed (space separated) by the keyword MAKETAR. If this is given, WOMBAT determines the shrinkage target as the phenotypic covariance (or correlation) matrix obtained by summing estimates of covariances for all sources of variation from the preceding, unpenalized analysis. If this is not given, the upper triangle of the target matrix is expected to be read from a file with the standard name PenTargetMatrix; see 6.6.7.1.

The last entry on the line relates to the tuning factor(s) to be used: If a single penalized analysis is to be carried out, the corresponding tuning factor should be given (real value). To specify multiple penalized analyses, specify the number of separate tuning factors multiplied by as an integer value (e.g. -3 means 3 analyses), and list the corresponding tuning factors space separated on the next line.

EXAMPLE:

- 1.
- Shrink all correlation matrices towards the phenotypic correlation matrix using a single tuning factor of , and calculate the shrinkage target from unpenalized results.
- 2.
- Shrink canonical eigenvalues on the logarithm scale towards their mean, using 5 different tuning factors