Model determination in a case of heterogeneity of variance using sampling techniques

A sampling determination procedure has been described in a case of heterogeneity of variance. The procedure makes use of the predictive distributions of each data given the rest of the data and the structure of che assumed model. The computation of these predictive distributions is carried out using a Gibbs Sampling procedure. The final criterion to compare between models is the Mean Square Error between the expectation of predictive distributions and real data. The procedure has been applied to a data set of weight at 210 days in the Spanish Pirenaica beef cattle breed. Three proposed models have been compared: (a) Single Trait Animal Model; (b) Heterogeneous Variance Animal Model; and (c) Multiple Trait Animal Model. After applying the procedure, the most adjusted model was the Heterogeneous Variance Animal Model. This result is probably due to a compromise between the complexity of the model and the amount of available information. The estimated heritabilities under the preferred model have been 0.489+/-0.076 for males and 0.331+/-0.082 for females.