Restricted maximum likelihood estimation of genetic parameters accounting for genomic relationships has been reported to impose computational burdens which typically are many times higher than those of corresponding analyses considering pedigree based relationships only. This can be attributed to the dense nature of genomic relationship matrices and their inverses. We outline a reparameterisation of the multivariate linear mixed model to principal components and its effects on the sparsity pattern of the pertaining coefficient matrix in the mixed model equations. Using two data sets we demonstrate that this can dramatically reduce the computing time per iterate of the widely used ‘average information’ algorithm for restricted maximum likelihood. This is primarily due to the fact that on the principal component scale, the first derivatives of the coefficient matrix with respect to the parameters modelling genetic covariances between traits are independent of the relationship matrix between individuals, i.e. are not afflicted by a multitude of genomic relationships.

中文翻译：

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使用基因组关系矩阵减少受限最大似然估计的计算需求

据报道，考虑基因组关系的遗传参数的受限最大似然估计会施加计算负担，这通常比仅考虑基于谱系的关系的相应分析高出许多倍。这可以归因于基因组关系矩阵及其逆矩阵的密集性质。我们概述了多元线性混合模型对主成分的重新参数化及其对混合模型方程中相关系数矩阵的稀疏模式的影响。我们使用两个数据集证明，这可以显着减少广泛使用的受限最大似然“平均信息”算法的每次迭代计算时间。这主要是因为在主成分尺度上，