In studies where stratification is not a very serious concern, an appealing and simple approach is to use mixed models without including PC covariates. This may include (i) studies in populations of homogeneous ancestry, (ii) studies in structured populations where structure is due to very recent genetic drift, and (iii) studies in any population in which PCA or related methods, applied either to the entire sample or to a subset of unrelated samples, indicate that there is no substantial stratification, i.e. phenotypes are not highly correlated with any of the top PCs.
