Department of Animal Science, Iowa State University, Ames, IA, USA.
J Anim Breed Genet. 2021 Sep;138(5):519-527. doi: 10.1111/jbg.12545. Epub 2021 Mar 17.
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.
可以通过交叉验证获得对育种值（EBV）估计准确性的经验估计。留一法交叉验证（LOOCV）是 k 折交叉验证的一个极端情况。已经为具有总体均值和随机标记或动物遗传效应的简单模型开发了用于预测表型的 LOOCV 的有效策略。这里的目标是为具有多个随机效应的一般混合线性模型下的育种值和其他随机效应的预测开发和评估有效的 LOOCV 方法。传统的 EBV LOOCV 要求为 n（=观测值的数量）个数据集的每个数据集都要反转 (n-1)×(n-1)协方差矩阵。我们的高效 LOOCV 从所有 n 个观测值的协方差矩阵的逆中获取所需的逆。高效方法可应用于具有多个固定和随机效应的复杂模型，但需要将固定效应视为随机，方差较大。另一种方法是使用从完整数据中获得的固定效应的估计值预先校正观测值，但这可能会导致偏差。高效 LOOCV 方法在计算需求和准确性方面与 EBV 预测的传统 LOOCV 进行了比较。对于具有 3205 个观测值和具有多个随机和固定效应的模型，高效 LOOCV 方法比基于每个训练数据集的固定效应预校正的传统 LOOCV 快 962 倍，但结果相同 EBV。成功开发了具有多个固定和随机效应的单个性状和多性状混合模型的育种值预测的高效 LOOCV。该方法能够对育种值的预测以及随机和/或固定效应的任何线性组合进行交叉验证，同时对验证表型进行留一法预校正。
