Motivated by empirical arguments that are well known from the genome-wide association studies (GWAS) literature, we study the statistical properties of linear mixed models (LMMs) applied to GWAS. First, we study the sensitivity of LMMs to the inclusion of a candidate single nucleotide polymorphism (SNP) in the kinship matrix, which is often done in practice to speed up computations. Our results shed light on the size of the error incurred by including a candidate SNP, providing a justification to this technique to trade off velocity against veracity. Second, we investigate how mixed models can correct confounders in GWAS, which is widely accepted as an advantage of LMMs over traditional methods. We consider two sources of confounding factors—population stratification and environmental confounding factors—and study how different methods that are commonly used in practice trade off these two confounding factors differently.
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