  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 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 in order 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.
