Genome-wide Association Study has presented a promising way to understand the association between human genomes and complex traits. Many simple polymorphic loci have been shown to explain a significant fraction of phenotypic variability. However, challenges remain in the non-triviality of explaining complex traits associated with multifactorial genetic loci, especially considering the confounding factors caused by population structure, family structure, and cryptic relatedness. In this paper, we propose a Squared-LMM (LMM2) model, aiming to jointly correct population and genetic confounding factors. We offer two strategies of utilizing LMM2 for association mapping: 1) It serves as an extension of univariate LMM, which could effectively correct population structure, but consider each SNP in isolation. 2) It is integrated with the multivariate regression model to discover association relationship between complex traits and multifactorial genetic loci. We refer to this second model as sparse Squared-LMM (sLMM2). Further, we extend LMM2/sLMM2 by raising the power of our squared model to the LMMn/sLMMn model. We demonstrate the practical use of our model with synthetic phenotypic variants generated from genetic loci of Arabidopsis Thaliana. The experiment shows that our method achieves a more accurate and significant prediction on the association relationship between traits and loci. We also evaluate our models on collected phenotypes and genotypes with the number of candidate genes that the models could discover. The results suggest the potential and promising usage of our method in genome-wide association studies.

中文翻译：

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使用平方稀疏线性混合模型对基因组关联作图进行多重混杂因子校正

全基因组关联研究提出了一种有前途的方法来理解人类基因组和复杂性状之间的关联。许多简单的多态性基因座已被证明可以解释很大一部分表型变异。然而，解释与多因素遗传位点相关的复杂性状的重要性仍然存在，特别是考虑到人口结构、家庭结构和神秘相关性引起的混杂因素。在本文中，我们提出了 Squared-LMM (LMM2) 模型，旨在联合纠正群体和遗传混杂因素。我们提供了两种利用 LMM2 进行关联映射的策略：1）它作为单变量 LMM 的扩展，可以有效地纠正群体结构，但单独考虑每个 SNP。2）与多元回归模型相结合，发现复杂性状与多因素遗传位点之间的关联关系。我们将第二个模型称为稀疏 Squared-LMM (sLMM2)。此外，我们通过将平方模型的幂提高到 LMMn/sLMMn 模型来扩展 LMM2/sLMM2。我们展示了我们的模型与从拟南芥遗传位点生成的合成表型变体的实际用途。实验表明，我们的方法对性状与位点之间的关联关系实现了更准确、更显着的预测。我们还根据收集的表型和基因型以及模型可以发现的候选基因的数量来评估我们的模型。结果表明我们的方法在全基因组关联研究中具有潜在和有前途的用途。