Cross-validation of best linear unbiased predictions of breeding values using an efficient leave-one-out strategy

Empirical estimates of the accuracy of estimates of breeding values (EBV) can be obtained by cross-validation. Leave-one-out cross-validation (LOOCV) is an extreme case of k-fold cross-validation. Efficient strategies for LOOCV of predictions of phenotypes have been developed for a simple model with an overall mean and random marker or animal genetic effects. The objective here was to develop and evaluate an efficient LOOCV method for prediction of breeding values and other random effects under a general mixed linear model with multiple random effects. Conventional LOOCV of EBV requires inverting an (n-1)×(n-1) covariance matrix for each of n (= number of observations) data sets. Our efficient LOOCV obtains the required inverses from the inverse of the covariance matrix for all n observations. The efficient method can be applied to complex models with multiple fixed and random effects, but requires fixed effects to be treated as random, with large variances. An alternative is to precorrect observations using estimates of fixed effects obtained from the complete data, but this can lead to biases. The efficient LOOCV method was compared to conventional LOOCV of predictions of breeding values in terms of computational demands and accuracy. For a data set with 3,205 observations and a model with multiple random and fixed effects, the efficient LOOCV method was 962 times faster than the conventional LOOCV with precorrection for fixed effects based on each training data set but resulted in identical EBV. A computationally efficient LOOCV for prediction of breeding values for single- and multiple-trait mixed models with multiple fixed and random effects was successfully developed. The method enables cross-validation of predictions of breeding values and of any linear combination of random and/or fixed effects, along with leave-one-out precorrection of validation phenotypes.