线性混合模型（Linear mixed models，LMM）是全基因组关联研究（genome wide association studies，GWAS）中遗传力估计的常用模型。在标准的遗传力估计方法中，必须指定遗传关系矩阵（GRM）。在GWAS中，GRM通常是从研究人群的基因型估计的相关矩阵，其对应于归一化的欧几里得距离核。在本文中，我们表明，依赖于欧几里德距离内核有助于几个未解决的建模不一致的遗传力估计GWAS。在连锁不平衡（LD）存在的情况下，这些不一致可能导致有偏倚的遗传力估计，这取决于因果变异的分布。我们表明，这些偏见可以解决（至少在建模水平），如果采用基于马氏距离的GRM的LMM分析。此外，我们提出了一个新的定义分区遗传力-遗传力归因于一个子集的基因或单核苷酸多态性（SNP）-使用Mahalanobis GRM，并表明它继承了许多很好的一致性特性，在我们原来的分析。分割遗传力是GWAS分析的一个相对较新的领域，其中与LD相关的不一致问题以前被认为是特别有害的。
英文摘要：
Linear mixed models (LMMs) are widely used for heritability estimation in genome-wide association studies (GWAS). In standard approaches to heritability estimation with LMMs, a genetic relationship matrix (GRM) must be specified. In GWAS, the GRM is frequently a correlation matrix estimated from the study population's genotypes, which corresponds to a normalized Euclidean distance kernel. In this paper, we show that reliance on the Euclidean distance kernel contributes to several unresolved modeling inconsistencies in heritability estimation for GWAS. These inconsistencies can cause biased heritability estimates in the presence of linkage disequilibrium (LD), depending on the distribution of causal variants. We show that these biases can be resolved (at least at the modeling level) if one adopts a Mahalanobis distance-based GRM for LMM analysis. Additionally, we propose a new definition of partitioned heritability -- the heritability attributable to a subset of genes or single nucleotide polymorphisms (SNPs) -- using the Mahalanobis GRM, and show that it inherits many of the nice consistency properties identified in our original analysis. Partitioned heritability is a relatively new area for GWAS analysis, where inconsistency issues related to LD have previously been known to be especially pernicious.
