- Volume 44 Issue 2
Genetic variance and covariance components of the linear traits and the ordered categorical traits, that are usually observed as dichotomous or polychotomous outcomes, were simultaneously estimated in a multivariate threshold animal model with concepts of arbitrary underlying liability scales with Bayesian inference via Gibbs sampling algorithms. A multivariate threshold animal model in this study can be allowed in any combination of missing traits with assuming correlation among the traits considered. Gibbs sampling algorithms as a hierarchical Bayesian inference were used to get reliable point estimates to which marginal posterior means of parameters were assumed. Main point of this study is that the underlying values for the observations on the categorical traits sampled at previous round of iteration and the observations on the continuous traits can be considered to sample the underlying values for categorical data and continuous data with missing at current cycle (see appendix). This study also showed that the underlying variables for missing categorical data should be generated with taking into account for the correlated traits to satisfy the fully conditional posterior distributions of parameters although some of papers (Wang et al., 1997; VanTassell et al., 1998) presented that only the residual effects of missing traits were generated in same situation. In present study, Gibbs samplers for making the fully Bayesian inferences for unknown parameters of interests are played rolls with methodologies to enable the any combinations of the linear and categorical traits with missing observations. Moreover, two kinds of constraints to guarantee identifiability for the arbitrary underlying variables are shown with keeping the fully conditional posterior distributions of those parameters. Numerical example for a threshold animal model included the maternal and permanent environmental effects on a multiple ordered categorical trait as calving ease, a binary trait as non-return rate, and the other normally distributed trait, birth weight, is provided with simulation study.
Threshold animal model;Missing trait;Bayesian nference;Liability;Identifiability
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