Bayesian Versus Maximum Quasi-Likelihood Methods for Sire Evaluation with Categorical Data

Binary variables arising from an underlying normal distribution with a fixed threshold were simulated in a two-stage selection scheme with a sire model. The model had herd-year-seasons and groups as fixed effects and sires as random variables; a heritability of .25 was used in the simulation. The "best" 20% of the sires were allowed to have additional progeny in the second stage. The criteria used to select these sires were breeding values predicte~ with a Bayesian procedure or with a maximum quasi-likelihood approach. Heritability was estimated from the data used to compute the sire evaluations. The two methods were compared in terms of empirical sampling bias, variance, and mean squared error of estimates of fixed effects and of heritability. The ability of selection based on the two methods to elicit genetic change was studied in terms of realized response to sire selection. Under the conditions examined, the maximum quasi-likelihood procedure had a larger mean squared error of estimates of heritability and of differences between genetic groups. Heritability estimates were biased upwardly by both methods. Differences between true n~nsmitting abilities of bulls selected by each of the methods were negligible. It appears that sire evaluations for categorical data obtained with the Bayesian