Mixed models can model population structure, family structure and cryptic relatedness32. The basic approach is to model phenotypes using a mixture of fixed effects and random effects. Fixed effects include the candidate SNP and optional covariates such as gender or age, while random effects are based on a phenotypic covariance matrix, which is modeled as a sum of heritable and non-heritable random variation (see Box 1 for details). Mixed models have historically been a theoretically appealing but computationally intensive approach; however, very recent computational advances have now made it possible to apply them to GWAS33–34 (EMMAX and TASSEL; see Web Resources). Methods that explicitly model population structure, family structure and cryptic relatedness are expected to perform better in the presence of these complexities than methods that do not, and this has now been confirmed33–34. For example, in an analysis of seven Wellcome Trust Case Control Consortium phenotypes, the application of mixed models consistently yielded values of λGC that were less than 1.01, in contrast to other approaches33.
