Efficient Computation of Ridge-Regression Best Linear Unbiased Prediction in Genomic Selection in Plant Breeding

Computational efficiency of procedures for genomic selection is an important issue when cross-validation is used for model selection and evaluation. Moreover, limited computational resources may be a bottleneck when processing large datasets. This paper reviews several options for computing ridge-regression best linear unbiased prediction (RR-BLUP) in genomic selection and compares their computational efficiencies when using a mixed model package. Attention is also given to the problem of singular genetic variance-covariance. Annotated code is provided for implementing and evaluating the methods using the MIXED procedure of SAS. It is concluded that a recently proposed method based on a spectral decomposition of the variance-covariance matrix of the data is preferable compared to established methods because of its superior computational efficiency and applicability also for singular genetic variance-covariance.