Multiple-trait analysis using Bayesian methods in animal breeding: A Gibbs sampling approach

Most animal breeding experiments are based on more than one economically important trait measured in each individual. In the statistical analysis of the resulting data, traits recorded in the same individuals are often considered one at a time. Usually we are interested, however, not only in the mode of inheritance of a particular trait but also in its relationships with other traits. Multivariate analyses are required to make inferences about genetic and phenotypic correlations between traits, but point estimates of such parameters can be poor even when breeding data on hundreds of animals are used. Bayesian methods exclude variance matrices which are not within the parameter space, and make use of all the information on parameters in the likelihood function and prior distribution, rather than just providing point estimates. In this study, a balanced one-way multiple-trait sire model representing half-sib families is investigated using a Gibbs sampling approach with two different prior specifications. Inverse Wishart distributions for the two variance matrices and a uniform distribution for the mean vector are used as priors. The results of Gibbs sampling are compared with estimates of the parameters obtained from the analysis of variance method. It is shown that a Bayesian analysis using a Gibbs sampling algorithm provides an estimate of the complete marginal posterior distribution of each unknown parameter and also gives point estimates which are within the parameter space, in contrast to conventional procedures.