Observations on sire evaluation with categorical data using heteroscedastic mixed linear models

The ability of three mixed linear models to rank sires correctly for dichotomous and ordered tetrachotomous traits was studied using simulated half-sib progeny data. The models differed in the assumptions made regarding homogeneity of residual variance. Ranking ability was assessed by estimating the realized response to truncation selection (20% of the candidates selected) upon sire evaluations in populations consisting of 50 such sires. Results suggested that weighting for unequal residual variances, in spite of reducing apparent prediction error variance, impairs the ability of best linear unbiased prediction to identify superior sires. This is consistent with theoretical arguments stemming from threshold models.