4.14 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 (4.13). 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.