#### Abstract

Henderson (1977, 1984) described a method for prediction of breeding values for traits not in the model for records. This method may be practical for animal or sire models for the case when no measurements can be obtained on any animals for some traits to be evaluated. The least squares equations are augmented with A^{-1}⊗G_{N}^{-1} rather than with A^{-1}⊗G_{0}^{-1} where A is the numerator relationship and G_{0}and G_{N} are the genetic covariance matrices for measured and for all traits. This method can be used for each unmeasured trait or simultaneously for measured and all unmeasured traits. An option in the MTDFRUN module of the Multiple Trait Derivative Free REML (MTDFREML) program of Boldman et al. (1993) is to obtain solutions for breeding values and their prediction error variances. However, the preparation program (MTDFPREP) must be tricked to set-up equation numbers for breeding values of the unmeasured traits. Adding dummy records for the unmeasured traits but with missing records for the measured traits for dummy animals to the data file of animals with measured traits but with missing unmeasurable traits will result in the needed equations. At least two dummy records are needed to avoid a divide by zero error in calculating the sample standard deviation. The dummy records need to be associated with a level of at least one fixed factor. The dummy animals also must be added to the pedigree file with unknown sires and dams before running the program to obtain the inverse of the numerator relationship matrix (MTDFNRM). In the program to obtain solutions to the multiple trait mixed model equations (MTDFRUN), the full genetic (co)vaiiance matrix, G_{N}, for both measured and unmeasured traits is needed. The residual (co)variance matrix must have zero covariances between pairs of measured and unmeasured traits but the variance of the unmeasured trait must not be zero. This procedure provides direct solutions for breeding values of unmeasured traits based on mixed model predictions of breeding values of the measured traits and also allows calculation of standard errors of prediction for the solutions directly from elements of the inverse of the ugmented coefficient matrix. For example, this procedure can be used to predict breeding values of bulls (which have tenderness measurements) for the correlated trait of tenderness as a steer or heifer which cannot be measured on the bull.

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PREDICTION OF BREEDING VALUES FOR UNMEASURED TRAITS FROM MEASURED TRAITS

Henderson (1977, 1984) described a method for prediction of breeding values for traits not in the model for records. This method may be practical for animal or sire models for the case when no measurements can be obtained on any animals for some traits to be evaluated. The least squares equations are augmented with A^{-1}⊗G_{N}^{-1} rather than with A^{-1}⊗G_{0}^{-1} where A is the numerator relationship and G_{0}and G_{N} are the genetic covariance matrices for measured and for all traits. This method can be used for each unmeasured trait or simultaneously for measured and all unmeasured traits. An option in the MTDFRUN module of the Multiple Trait Derivative Free REML (MTDFREML) program of Boldman et al. (1993) is to obtain solutions for breeding values and their prediction error variances. However, the preparation program (MTDFPREP) must be tricked to set-up equation numbers for breeding values of the unmeasured traits. Adding dummy records for the unmeasured traits but with missing records for the measured traits for dummy animals to the data file of animals with measured traits but with missing unmeasurable traits will result in the needed equations. At least two dummy records are needed to avoid a divide by zero error in calculating the sample standard deviation. The dummy records need to be associated with a level of at least one fixed factor. The dummy animals also must be added to the pedigree file with unknown sires and dams before running the program to obtain the inverse of the numerator relationship matrix (MTDFNRM). In the program to obtain solutions to the multiple trait mixed model equations (MTDFRUN), the full genetic (co)vaiiance matrix, G_{N}, for both measured and unmeasured traits is needed. The residual (co)variance matrix must have zero covariances between pairs of measured and unmeasured traits but the variance of the unmeasured trait must not be zero. This procedure provides direct solutions for breeding values of unmeasured traits based on mixed model predictions of breeding values of the measured traits and also allows calculation of standard errors of prediction for the solutions directly from elements of the inverse of the ugmented coefficient matrix. For example, this procedure can be used to predict breeding values of bulls (which have tenderness measurements) for the correlated trait of tenderness as a steer or heifer which cannot be measured on the bull.