Table 8.

Estimates recovered fitting full model to simulated trait values and derived variables under Model 4 (Duplicate gene epistasis, no G × E)

	Simulated parameters		Estimated parameter values																	σ	r2
			Genetic main effects (G)								Environmental effects (E) and G × E
			Homozygous		Heterogygous		Epistatic				E	Homozygous		Heterozyous		Epistatic
			dA	dB	hA	hB	iAB	jAB	jBA	lAB	βm	βdA	βdB	βhA	βhB	βiAB	βjAB	βjBA	βlAB
			1	1	1	1	−1	−1	−1	−1	0.5	0	0	0	0	0	0	0	0
Data	Method
True latent trait	Normal errors	θ	0.989	0.959	1.023	1.028	−0.983	−0.976	−0.981	−0.991	0.501	0.002	0.008	−0.004	−0.006	−0.004	−0.003	−0.003	−0.002	1.006	0.541
		t	30.39	29.47	22.39	22.34	−30.19	−21.20	−21.47	−15.32	78.63	0.36	1.22	−0.43	−0.67	−0.55	−0.28	−0.30	−0.18	–	–
	Normal errors	θ	0.467	–	0.492	–	–	–	–	–	0.490	0.010	–	0.004	–	–	–	–	–	1.328	0.199
		t	5.39	–	11.53	–	–	–	–	–	82.22	1.63	–	0.47	–	–	–	–	–
	Normal errors	θ	.001	0.998	1.004	0.998	−1.001	−0.988	−0.994	−1.002	0.496	–	–	–	–	–	–	–	–	1.006	0.541
		t	156.7	156.3	111.7	110.6	−156.7	−109.5	−110.6	−78.84	156.3	–	–	–	–	–	–	–	–	–	–
	Logistic regression	θ	2.912	2.988	3.106	3.149	−2.775	−2.787	−3.016	−3.260	0.674	0.218	0.210	0.183	0.176	−0.246	−0.236	−0.203	−0.156	–	–
		t	0.05	0.05	0.05	0.05	−0.04	−0.04	−0.05	−0.05	0.05	0.02	0.02	0.02	0.01	−0.02	−0.02	−0.02	−0.01	–	–
Equal item parameters	Sum score	θ	−0.876	−0.985	−0.621	−0.765	0.082	1.021	0.920	0.880	1.331	0.425	0.450	0.379	0.402	−0.416	−0.415	−0.431	−0.433	3.918	0.218
		t	−6.91	−7.77	−3.49	−4.27	6.47	5.69	5.17	3.49	53.56	17.10	18.13	10.87	11.45	−16.76	−12.66	−12.36	−8.75	–	–
	Square root transformation	θ	−0.025	−0.086	0.029	−0.015	0.014	0.156	0.076	0.040	0.344	0.101	0.113	0.092	0.099	−0.099	−0.105	−0.110	−0.106	0.986	0.292
		t	−0.79	−2.71	0.65	−0.33	0.42	1.23	1.69	0.63	54.98	16.21	18.09	10.45	11.21	−15.77	−11.89	−12.52	−8.49	–	–
Variable item parameters	Sum score	θ	1.268	1.242	1.523	1.532	−1.220	−1.222	−1.355	−1.524	1.271	0.218	0.224	0.173	0.164	−0.230	−0.221	−0.203	−0.172	3.277	0.404
		t	11.95	11.71	10.22	10.21	−11.50	−8.15	−9.10	−7.23	61.17	10.49	10.79	5.93	5.58	−11.05	−7.50	−6.95	−4.16	–	–
	Square root transformation	θ	0.595	0.586	0.623	0.623	−0.584	−0.588	−0.606	−0.621	0.240	−0.006	−0.005	−0.011	−0.013	0.004	0.006	0.008	0.011	0.555	0.534
		t	33.12	32.66	24.71	24.69	−32.53	−23.16	−24.05	−17.40	68.17	−1.83	−1.34	−2.23	−2.62	1.18	1.21	1.68	1.56	–	–

Estimates from fitting logistic regression to dichotomized sum scores are uninformative and not presented for this model