Fig. 1

Comparison of rejection rates for the proposed fixed effects permutation inference, two different permutation schemes (Simulation 2). Results shown for the null β1 = 0 (a) and alternative (b) for a 5% nominal level based on simulation using a GRM from 300 unrelated individuals and 5000 realizations and 500 permutations each realizations; left column shows results for the free permutation scheme, right for the exchangeability-block constrained method. Monte Carlo confidence interval is (4.40, 5.60%). For non-iterative and fully converged, both permutation schemes could control the error rate at the nominal level, however free permutation is slightly more powerful than the constrained permutation