# Ridge Regression and Other Kernels for Genomic Selection with R Package rrBLUP

## Jeffrey B. Endelman

### 2011

The results demonstrate that the performance of Gaussian model compared to RR depends on both the structure of the population and the phenotype

## Highlights

• The ability to predict complex traits from marker data is becoming increasingly important in plant breeding
• The focus over the last decade has been on genomic selection methods, in which all markers are included in the prediction model
• One of the first methods proposed for genomic selection was ridge regression, which is equivalent to best linear unbiased prediction in the context of mixed models
• At the core of the rrBLUP package is the function mixed.solve, which solves any mixed model of the form where X is a full‐rank design matrix for the fixed effects β, Z is the design matrix for the random effects u, K is a positive semidefinite matrix, and the residuals are normal with constant variance
• Variance components are estimated by either maximum likelihood or restricted maximum likelihood using the spectral decomposition algorithm of Kang et al
• The expected mean for the progeny can be calculated as the mean of the parental genomic‐estimated breeding values, but the marker effects are needed to compute the variance of the population, which is important for genetic gain