Mixed models view phenotypes as modeled using a fixed set of genotypes. However, as an alternative to mixed models, genotypes can be modeled using a fixed set of phenotypes, a theoretically appealing approach that makes fewer assumptions about phenotypic covariance structure37–38. Simulations in the absence of unusually differentiated markers have shown that using the genotypic covariance matrix to account for both population and family structure can effectively control spurious associations under a variety of settings37 (ROADTRIPS; see Web Resources). However, in the case of unusually differentiated markers, normality assumptions (about genotype distributions) underlying the test statistics will be violated, and stratification may lead to confounding unless PC covariates are used. The question of whether to model random effects only or to include PC covariates as fixed effects is analogous to the mixed model framework. When viewing phenotypes as fixed, PC covariates may be particularly essential since modeling only random effects leads to a uniform correction factor in the absence of missing data37.
