RR-BLUP

Subsequently, we give details on our implementation of Ridge Regression Best Linear Unbiased Predictor (RR-BLUP), which is a classical genomic selection approach. References for a more detailed theoretical background can be found at the end of this page, which were also used for writing this text.

RR-BLUP is based on a linear mixed model, for which phenotype values \(\mathbf{y}\) can be calculated as

\[\mathbf{y} = \mathbf{\beta} 1 + \mathbf{Xu} + \mathbf{\epsilon}\]

with the overall mean \(\mathbf{\beta}\), the genotype matrix \(\mathbf{X}\) with corresponding marker effects \(\mathbf{u}\) and the residuals vector \(\mathbf{\epsilon}\). When fitting the model to the training data, \(\mathbf{\beta} and \)mathbf{u}` are determined.

In easyPheno, RR-BLUP is implemented as a child class of ParamFreeBaseModel and is named Blup. As you can see there, the fit() method contains the fitting of the model to match the training data. In its current implementation, RR-BLUP can only be used for continuous traits.

References

1. Meuwissen, T. H., Hayes, B. J., & Goddard, M. E. (2001). Prediction of total genetic value using genome-wide dense marker maps. Genetics, 157(4), 1819–1829.