Bayesian analysis of ordinal categorical data under a mixed inheritance model

The effectiveness of proposed Gibbs sampling (GS) algorithm to detect single loci determining livestock threshold traits under a different hypothetical breeding and statistical modeling scenarios was examined. The following factors were included into the analysis: the presence of fixed effects, knowledge of one threshold, the size of the population (1 212 and 3 070 pedigreed individuals, respectively) and proportions of individuals in three genotypic classes. Five threshold and one linear unitrait animal model were employed to analysis of these datasets. The GS algorithm was applied to estimate fixed effects (optionally), additive polygenic variance, single allele frequencies, genotypic effects and one threshold (optionally). For each case, 2 000 000 rounds of GS were conducted. The first 1 000 000 steps were discarded as a burn-in-period. The results were collected from every 20th iteration. In general, the accuracy of parameter estimates is not satisfactory. However, taking into account the scant amount of information provided by the ordinal categorical data, it seems that such an analysis is a good first approach. Except for one case in which the estimate was very close to the true value, in all the other cases the estimated gene effect was smaller than the true effect. In general, the algorithm proposed does not provide overestimated effects of single locus.