Special information

4.8 Special information

Finally, the parameter file can select some special features.

4.8.1 Dependencies among fixed effects

WOMBAT requires a coefficient matrix in the mixed model equations which is of full rank. Hence, constraints must be placed on the fixed effects part of the model if more than one fixed effect is fitted. By default, the first level of each cross-classified fixed effect other than the first is ‘zeroed out’ for each trait to account for dependencies. If there are additional dependencies, these should be identified and specified explicitly prior to each analysis.

WOMBAT performs a simple least-squares analysis on the fixed effects part of the model, attempting to find such additional dependencies. However, this procedure should not be relied upon, in particular for large data sets where numerical errors tend to accumulate sufficiently to obscure identification. Dependencies not properly taken into account can lead to problems during estimation !

Additional effects to be zeroed out are specified in a block entry. The block begins with a line containing the code ZEROUT (can be abbreviated to ZER), and finishes with a line beginning with END. The block then should contain one line for each additional dependency. Each line should contain three entries :

(a) The name of the fixed effect, as specified in the MODEL block.
(b) The ‘original’ code for the level to be zeroed out, as encountered in the data file.
(c) The trait number; this can be omitted for univariate analyses.

4.8.2 Random effects to be treated as fixed

In some instances, it is desirable to treat selected levels of a random, genetic effect as if it were ‘fixed’. A typical example is the analysis of dairy data under a sire model. If the data includes highly selected proven bulls which only have records from their second crop of daughters, we might want to treat these bulls as ‘fixed’ as we would expect estimates of the genetic variance to be biased downwards otherwise. In other cases, our pedigree records may include codes for ‘parents’ which are not animals but represent genetic groups, to be treated as fixed effects.

Treating selected random genetic effects levels as fixed is achieved by replacing the diagonal in the numerator relationship matrix by a value of zero when setting up the inverse of the numerator relationship matrix. If there is any pedigree information for the effect, this is ignored.

N.B.: Treating levels of random effect(s) as fixed may lead to additional dependencies in the fixed effects part of the model, especially for multivariate analyses. Great care must be taken to identify these and specify them explicitly, as outlined above (4.8.1). WOMBAT has no provision to account for this possibility !

Random genetic effects levels to treated as fixed are specified in a block entry. The block begins with a line containing the code PSEUDOFX (can be abbreviated to PSE). This can be followed (space separated) by a REAL number. If given, this value (which should be a small positive number, e.g. $0.0001$ or $0.001$ ) is used instead of the value of $0$ when specifying the contributions to the inverse of the numerator relationship matrix. Effectively, this treats the respective effect level as “just a little bit random”. This option is provided as a mean to counteract additional dependencies in the model (see warning above). It is particularly useful for prediction, and should be used very carefully with estimation runs. As usual, the block finishes with a line beginning with END. The block then should contain one line for each effect. Each line should contain two entries :

(a) The name of the random effect, as specified in the MODEL block.
This should be a genetic effect, distributed proportionally to the numerator relationship matrix among animals.
(b) The ‘original’ code for the level to be treated as ’fixed’, as given in the pedigree file.

N.B.: This option has only undergone fairly rudimentary testing !
It is not available in conjunction with the PX-EM algorithm.
Selecting this option prohibits re-use of inverse NRM matrices set up in any previous runs.

4.8.3 Covariance components to be treated as fixed

WOMBAT provides limited facilities to fix certain covariance components at their input values, while maximising the (log) likelihood with respect to the remaining parameters. Again, this information is given in a block entry. The block begins with a line containing the code FIXVAR (no abbreviation) and, as usual, ends with a line containing the code END. Each line within the block is then expected to have the following entries:

(a) The name of the random effect, as specified in the MODEL block.
(b) The code ALL to signify that all pertaining covariances are fixed.

In the moment, no options to fix individual elements of covariance matrices are recognised.

4.8.4 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) An entry of the form $n(w )$ for each component of the weighted sum, with $n$ the running number of the covariance component and $w$ the weight it is to be multiplied with. If $w$ is unity, it can be omitted, i.e. the entry $n$ is interpreted as $n(1)$ .

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) The running number of the covariance component in the numerator.
(c) 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) The running number of the covariance component in the numerator.
(c) The running number of the first covariance component in the denominator.
(d) The running number of the second covariance component in the denominator.

EXAMPLE: 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 $σ2A$ , $σ2PE$ and $σ2E$ (residual), with running numbers 1, 2 and 3, respectively. WOMBAT automatically calculates the phenotypic variance $σ2P$ = $σ2A+ σ2PE + σ2E$ and gives it running number 4. To calculate the repeatability and approximate its sampling error, we first need to define the sum of $σ2A$ and $σ2PE$ as a new covariance (which receives running number 5), and then define the repeatability as the ratio of this component and $2 σP$ .

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

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.

4.8.5 Miscellaneous

A place to collect miscellaneous options which don’t fit into the categories above is provided through a block entry beginning with a line SPECIAL, and ending with a line END. The following options are recognised:

1. A weighted analysis is specified by a line with space separated entries

(a) The code WEIGHT at the beginning of the line.
(b) The name of the column in the data containing the weight.
(c) Optionally, for standard uni- and multivariate analyses, this can be followed by the code DESIGN.

The default for this option is that each record is multiplied by the weight given prior to the analysis. However, when the qualifier DESIGN is given, entries of “1” in the design matrices are replaced with the weight specified instead (i.e. the observations are not scaled).
2. WOMBAT now checks for covariables which have a value of zero. If you fit a covariable which has such values, it expects you to confirm that this is intentional. This is done through a single line with space separated entries:

(a) The code COVZER at the beginning of the line.
(b) The full name of the covariable as given in the model statement (i.e. including brackets, number of coefficients and, if applicable, type).
(c) A three letter option: FIT to confirm that a value of zero for this covariable is a valid code, or IGN to skip such records (any other option will lead to a programmed error stop).

3. Repeated records for a trait for less than 10% of individuals or a model fitting a single random effect only can be enabled by a single line with the code REPEAT at the beginning of the line.

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