LBG - FS2024 – Solution 10

Author

Peter von Rohr

Problem 1: Reliability of Predicted Breeding Values

Use the dataset given below to predict breeding values for the response variable Weight using a BLUP animal model. The model contains Herd as fixed effect and BreastCircumference as regression covariate. Compute reliabilities (\(B\%\)) for all predicted breeding values.

Hints

  • The phenotypic variance \(\sigma_p^2\) can be computed from the variance of the weight values given in the dataset.
  • Heritability (\(h^2\)) is assumed to be 0.25 for the trait Weight.

Data

The dataset is available from

Solution

  • Setup the mixed model equations (MME). Start with design matrix \(X\) for fixed effects
  • Design matrix \(Z\) for random breeding values
  • Inverse numerator relationship matrix
  • Setting up mixed model equations
  • Compute accuracies from inverse of coefficient matrix of MME
  • Convert numbers to \(B%\)