The recent development of the Bayes factor methodology to test between nested competing models has allowed to evaluate the genetic component of continuous traits through a methodology based on the reparameterization of a variance component model in terms of intra-class correlation. In this study, we present a modification of that procedure to compare between threshold models that only differ in a bounded variable. An extra data-augmentation step is required to sample liability, an underlying continuous variable related with phenotypic records through an adequate number of thresholds. In this context, we describe a procedure to sample from a truncated multivariate normal distribution with non-null covariances between records, taking as starting point the Cholesky factorization and the inclusion of linear restrictions. The method was tested by computer simulations with satisfactory results.