. 2020 May 19;16(5):e1008612. doi: 10.1371/journal.pgen.1008612

Table 1. Simulation results: Comparison of mean (std) true and estimated (^) model parameters and derived quantities.

Results for each line, for specified heritability h² and fraction π₁ of causal SNPs, are from 10 independent instantiations with random selection of the n_causal causal SNPs that are assigned a β-value from the standard normal distribution. Defining Y_g = Gβ, where G is the genotype matrix, the total phenotype vector is constructed as Y = Y_g+ε, where the residual random vector ε for each instantiation is drawn from a normal distribution such that var(Y) = var(Y_g)/h² for predefined h². For each of the instantiations, i, this implicitly defines the true value $σ_{β i}^{2}$ , and $σ_{β}^{2}$ is their mean. An example QQ plot for each line entry is shown in in S1 Appendix (p. S15).

h²	${\hat{h}}^{2}$		π₁	${\hat{π}}_{1}$		$σ_{β}^{2}$		${\hat{σ}}_{β}^{2}$		${\hat{σ}}_{0}^{2}$		n_causal	${\hat{n}}_{c a u s a l}$
0.1	0.12	(0.01)	1E-5	1.4E-5	(2E-6)	4.3E-3	(7E-4)	3.6E-3	(5E-4)	1.01	(0.002)	110	151	(20)
0.1	0.10	(0.01)	1E-4	1.0E-4	(2E-5)	4.2E-4	(2E-5)	4.1E-4	(5E-5)	1.01	(0.003)	1101	1130	(206)
0.1	0.09	(0.01)	1E-3	0.9E-3	(1E-4)	4.2E-5	(5E-7)	4.1E-5	(4E-6)	1.02	(0.003)	11015	10340	(1484)
0.1	0.09	(0.01)	1E-2	0.8E-2	(2E-3)	4.2E-6	(4E-8)	5.6E-6	(2E-6)	1.02	(0.002)	110158	83411	(25448)
0.4	0.52	(0.05)	1E-5	2.3E-5	(2E-6)	1.7E-2	(3E-3)	9.1E-3	(1E-3)	1.02	(0.002)	110	259	(20)
0.4	0.45	(0.02)	1E-4	1.2E-4	(8E-6)	1.7E-3	(7E-5)	1.5E-3	(9E-5)	1.04	(0.002)	1101	1310	(92)
0.4	0.39	(0.01)	1E-3	1.0E-3	(5E-5)	1.7E-4	(2E-6)	1.6E-4	(8E-6)	1.05	(0.003)	11015	10607	(578)
0.4	0.37	(0.01)	1E-2	0.9E-2	(1E-3)	1.7E-5	(2E-7)	1.7E-5	(2E-6)	1.06	(0.003)	110158	95135	(10851)
0.7	0.91	(0.09)	1E-5	2.9E-5	(2E-6)	3.0E-2	(5E-3)	1.3E-2	(2E-3)	1.02	(0.003)	110	324	(24)
0.7	0.82	(0.02)	1E-4	1.4E-4	(7E-6)	2.9E-3	(1E-4)	2.4E-3	(1E-4)	1.05	(0.002)	1101	1493	(79)
0.7	0.70	(0.01)	1E-3	1.0E-3	(4E-5)	2.9E-4	(4E-6)	2.8E-4	(1E-5)	1.08	(0.003)	11015	10866	(406)
0.7	0.66	(0.01)	1E-2	0.9E-2	(7E-4)	2.9E-5	(3E-7)	2.9E-5	(2E-6)	1.09	(0.003)	110158	95067	(8191)