### 4.11 Additional functions of covariance components

In addition, users can define other functions of covariance components which should be calculated and for which sampling errors should be approximated. This is done in a block entry, beginning with a line containing the code SE+USR (can be abbreviated to SE+), and ending with a line beginning with END. The block should then contain one line for each function to be calculated. The content of the line depends on the type of function. Three types are recognised.

1.
Linear combinations (weighted sums) of the covariance components in the model of analysis. For these, space separated entries o should be
(a)
The code SUM at the beginning of the line.
(b)
A name to identify the sum to be calculated.
(c)
An entry of the form for each component of the weighted sum, with the running number of the covariance component and the weight it is to be multiplied with. If is unity, it can be omitted, i.e. the entry is interpreted as .
2.
Ratios of two covariance components. For these, the line should have three entries
(a)
The code VRA at the beginning of the line.
(b)
A name for the variance ratio to be calculated.
(c)
The running number of the covariance component in the numerator.
(d)
The running number of the covariance component in the denominator.
3.
Correlations, i.e. the ratio of a covariance component and the square root of the product of two other covariances. Line entries for these are
(a)
The code COR at the beginning of the line.
(b)
A name to identify the correlation to be calculated.
(c)
The running number of the covariance component in the numerator.
(d)
The running number of the first covariance component in the denominator.
(e)
The running number of the second covariance component in the denominator.

EXAMPLE:

SE+USR
SUM  siga+pe  1  2
VRA  repeat   5  4
END

Consider a univariate analysis with repeated records per individual. Fitting additive genetic and permanent environmental effects of the animal, variance components in the model are , and (residual), with running numbers 1, 2 and 3, respectively. WOMBAT automatically calculates the phenotypic variance = and gives it running number 4. To calculate the repeatability and approximate its sampling error, we first need to define the sum of and as a new covariance (which receives running number 5), and then define the repeatability as the ratio of this component and .

HINT: Run WOMBAT with the --setup option to begin with. Inspect the file ListOfCovs generated in this step – this gives a list of running numbers for individual covariance components.