How many animals do you have?
Either you did not send all 150 or you told ASREML incorrectly. Actually you
only have 106 unique tags with 125 observations. Thus, the most of your other
singularities are coming because most animals only have one record (except the
COR's that have 2 excluding COR1).
For a single trait fixed effects model of the mean, breed and age you should
get 2 singularities due to the dependencies i.e. X is not full rank. In a
more complex model with interactions you will get more because of two
completely missing cells. One should also be careful because you only have 5
observations for breed 2.
For a bivariate analysis, you should get 4 singularities. If you leave the
number of animals at 150 then ASREML reports 48. Where did the extra 44 come
Try 150 minus 106 or the animals that don't have any observations in the data.
With essentially one observation per animal you will need to provide an A
matrix or equivalent.
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