The results of the simulations are displayed in Table 1. EIGENSTRAT is effective in correcting for population stratification at both normally and unusually differentiated markers (Simulation 1), but does not control for family structure (Simulation 2). EMMAX corrects for both stratification and population structure except for a modest residual inflation at unusually differentiated markers, which is completely removed by EMMAX with PC covariates; if the number of unusually differentiated markers is small, modest inflation at such markers may not be a major concern. ROADTRIPS corrects for family structure but not for population stratification at unusually differentiated markers, though incorporation of PC covariates could potentially address this. We note that for each method, dividing association statistics by residual λGC is guaranteed to produce statistics with λGC=1, but this approach may be inadequate for spurious associations at unusually differentiated markers, and/or may not maximize power if family structure (or cryptic relatedness) is not fully modeled.
