Bayesian approach for analysis of multidimensional binary and continuous data
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Several discrete responses such as heath status, reproduction performance and meat quality are being routinely collected for several livestock species. However, their use to date in the genetic evaluation for animal selection has been limited mainly due to the lack of practical solution for the implementation of threshold models in the presence of several binary responses. The complexity of such implementation is primarily due to the non-complete randomness of the residual (co)variance matrix. In the current study a multiple binary trait simulation was carried out in order to implement and validate a new procedure for dealing with the consequences of the restrictions imposed to the residual variance using threshold models. Using three and eight binary responses, the proposed method was able to estimate all unknown parameters without any noticeable bias. In fact, for simulated residual correlation ranging from -0.8 to 0.8, the resulting HPD 95% intervals included the true values in all cases. The proposed procedure involved limited added computational cost and it was straightforward to implement independently of the number of binary responses involved in the analysis. The monitoring of the convergence of the procedure has to be conducted at the identifiable scale and special care has to be placed on the selection of the prior of the non- identifiable model. The later could have serious consequences on the final results due to potential truncation of the parameter space.