Bayesian inference for categorical traits with an application to variance component estimation

We implemented statistical models of Bayesian inference that included direc t and maternal genetic effects for genetic parameter estimation of categori cal traits by Gibbs sampling. The estimation errors and variances of estima tes of animal versus sire and maternal grandsire models, of linear versus t hreshold models, of single-trait versus multiple-trait models, and of treat ing herd-year-season as fixed versus random effects in the model were compa red. The results indicated that linear models yielded biased estimates of g enetic parameters for categorical traits. The animal model was improper for analysis of categorical traits using a threshold model and the Gibbs sampl er. Moreover, linear versus threshold models and animal versus sire-materna l 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-corr elations, and the variances of estimates. Efficiency of the single-trait th reshold sire model, as measured by the variance of the estimates, was lower than for a multiple-trait model that included a correlated continuous trai t, 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 affe cted by direct and maternal genetic factors.