We implemented statistical models of Bayesian inference that included direct and maternal genetic effects for genetic parameter estimation of categorical traits by Gibbs sampling. The estimation errors and variances of estimates of animal versus sire and maternal grandsire models, of linear versus threshold models, of single-trait versus multiple-trait models, and of treating herd-year-season as fixed versus random effects in the model were compared. The results indicated that linear models yielded biased estimates of genetic parameters for categorical traits. The animal model was improper for analysis of categorical traits using a threshold model and the Gibbs sampler. Moreover, linear versus threshold models and animal versus sire-maternal grandsire models resulted in larger Monte Carlo errors and increased auto-correlations among posterior samples. Treating herd-year-seasons as random effects in the threshold models decreased the Monte Carlo error, auto-correlations, and the variances of estimates. Efficiency of the single-trait threshold sire model, as measured by the variance of the estimates, was lower than for a multiple-trait model that included a correlated continuous trait, but both estimates were unbiased. Therefore, the threshold single-trait sire and maternal grandsire model is a feasible alternative to the multiple-trait model for analysis of variance components of categorical traits affected by direct and maternal genetic factors.

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