Heteroscedastic Ridge Regression Approaches for Genome-Wide Prediction With a Focus on Computational Efficiency and Accurate Effect Estimation

Ridge regression with heteroscedastic marker variances provides an alternative to Bayesian genome-wide prediction methods. Our objectives were to suggest new methods to determine marker-specific shrinkage factors for heteroscedastic ridge regression and to investigate their properties with respect to computational efficiency and accuracy of estimated effects. We analyzed published data sets of maize, wheat, and sugar beet as well as simulated data with the new methods. Ridge regression with shrinkage factors that were proportional to single-marker analysis of variance estimates of variance components (i.e., RRWA) was the fastest method. It required computation times of less than 1 sec for medium-sized data sets, which have dimensions that are common in plant breeding. A modification of the expectation-maximization algorithm that yields heteroscedastic marker variances (i.e., RMLV) resulted in the most accurate marker effect estimates. It outperformed the homoscedastic ridge regression approach for best linear unbiased prediction in particular for situations with high marker density and strong linkage disequilibrium along the chromosomes, a situation that occurs often in plant breeding populations. We conclude that the RRWA and RMLV approaches provide alternatives to the commonly used Bayesian methods, in particular for applications in which computational feasibility or accuracy of effect estimates are important, such as detection or functional analysis of genes or planning crosses.