Sire Evaluation for Multiple Binary Responses When Information is Missing on Some Traits

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Abstract
A procedure of sire evaluation for multiple binary responses when information is missing for some traits is described. The genetic model assumes a conceptual underlying mulivariate normal distribution rendered discrete by abrupt thresholds. Statistical inferences are made from a posterior distribution consisting of several conditionally independent likelihood functions and a multivariate normal prior distribution. Each likelihood function corresponds to a particular class of information available. Point estimators and predictors of fixed and random effects are the values that maximize the posterior distribution conditionally on heritabilities and genetic correlations. The procedure involves nonlinear maximization. An example involving joint selection for calving ease and skeletal development illustrates the principles. Application of the methodology as a potential means of removing bias due to selection for categorical traits is discussed.