4.13 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.