A comparative study of the impacts of unbalanced sample sizes on the four synthesized methods of meta-analytic structural equation modeling

Alamolhoda, Marzieh; Ayatollahi, Seyyed Mohammad Taghi; Bagheri, Zahra

doi:10.1186/s13104-017-2768-5

Table 2 Relative percentage bias of correlation coefficients in the pooled correlation matrix at stage 1

From: A comparative study of the impacts of unbalanced sample sizes on the four synthesized methods of meta-analytic structural equation modeling

Types	Average	UNIr						UNIz
Types	Average	ρ ₂₁	ρ ₃₁	ρ ₄₁	ρ ₃₂	ρ ₄₂	ρ ₄₃	ρ ₂₁	ρ ₃₁	ρ ₄₁	ρ ₃₂	ρ ₄₂	ρ ₄₃
k = 5
50	E	−0.26	−0.37	−0.81	−0.99	−0.71	−0.46	0.68	0.84	0.31	0.13	0.73	1.10
	M	−0.40	−1.08	−0.41	−1.06	−0.76	−0.78	0.57	0.14	0.70	0.08	0.66	0.78
	H	−0.54	−0.85	−0.52	−1.04	−0.23	0.27	0.43	0.35	0.59	0.16	1.18	1.83
100	E	−0.43	−0.55	−0.39	−0.41	−0.34	−0.92	0.04	0.08	0.18	0.17	0.40	−0.15
	M	−0.19	−0.64	−0.17	−0.54	0.12	−0.02	0.27	−0.01	0.39	0.02	0.86	0.77
	H	−0.30	−0.39	−0.42	−0.57	−0.54	−0.18	0.17	0.21	0.14	−0.01	0.16	0.60
200	E	−0.12	0.15	−0.07	0.15	−0.05	0.70	0.10	0.45	0.18	0.44	0.29	1.08
	M	−0.14	−0.05	−0.23	−0.05	−0.28	−0.65	0.10	0.25	0.04	0.24	0.07	−0.26
	H	−0.03	0.00	−0.11	−0.07	−0.02	0.36	0.20	0.30	0.15	0.21	0.32	0.74
500	E	−0.09	0.02	−0.04	−0.07	−0.17	0.32	0.00	0.13	0.07	0.04	0.04	−0.03
	M	−0.05	−0.05	−0.16	−0.02	−0.02	0.08	0.04	0.07	−0.04	0.09	0.13	0.24
	H	−0.11	−0.08	−0.11	−0.11	−0.06	−0.01	−0.02	0.02	0.00	0.00	0.08	0.14
1000	E	−0.08	−0.13	0.01	−0.12	0.09	0.07	−0.04	−0.07	0.06	−0.07	0.16	0.15
	M	0.00	−0.10	−0.07	0.10	0.02	−0.11	0.04	−0.04	−0.02	0.15	0.09	−0.03
	H	−0.07	−0.03	−0.05	−0.04	−0.11	0.10	−0.02	0.03	0.01	0.01	−0.04	0.18
k = 10
50	E	−0.57	−0.81	−0.34	−0.56	0.05	0.32	0.52	0.59	0.90	0.73	1.73	1.48
	M	−0.71	−0.56	−0.85	−0.77	−1.38	−0.60	0.39	0.86	0.37	0.54	0.25	1.22
	H	−0.51	−0.57	−0.64	−0.59	−0.79	−0.24	0.54	0.80	0.59	0.73	0.82	1.49
100	E	−0.39	−0.50	−0.33	−0.57	−0.94	−0.74	0.15	0.17	0.27	0.07	−0.14	0.11
	M	−0.52	−0.51	−0.43	−0.38	−0.81	−0.24	0.01	0.18	0.18	0.26	−0.02	0.62
	H	−0.23	−0.35	−0.21	−0.41	−0.36	−0.86	0.30	0.34	0.41	0.23	0.43	0.03
200	E	−0.16	−0.14	−0.16	−0.17	−0.05	0.20	0.10	0.20	0.14	0.15	0.35	0.64
	M	−0.13	−0.49	−0.18	−0.29	−0.32	−0.85	0.13	−0.15	0.11	0.03	0.08	−0.41
	H	−0.15	−0.39	−0.28	−0.22	−0.40	−0.48	0.11	−0.05	0.01	0.09	−0.01	−0.06
500	E	−0.06	−0.01	−0.06	−0.02	−0.16	−0.12	0.04	0.13	0.06	0.11	0.00	0.05
	M	−0.02	−0.08	−0.09	−0.18	−0.01	−0.26	0.09	0.06	0.03	−0.05	0.15	−0.09
	H	−0.09	−0.15	−0.08	−0.15	−0.14	−0.38	0.02	−0.01	0.04	−0.03	0.02	−0.21
1000	E	−0.02	−0.03	0.02	−0.02	0.09	0.31	0.03	0.04	0.08	0.04	0.17	0.40
	M	0.02	0.05	−0.03	0.03	0.06	0.11	0.08	0.12	0.03	0.09	0.14	0.19
	H	−0.03	−0.02	−0.06	−0.07	−0.05	−0.28	0.02	0.05	0.00	−0.01	0.03	−0.19
k = 15
50	E	−0.61	−0.69	−0.57	−0.84	−1.04	−1.82	0.51	0.79	0.70	0.49	0.69	0.03
	M	−0.78	−0.84	−0.73	−1.14	−0.90	−1.45	0.33	0.60	0.57	0.22	0.76	0.37
	H	−0.64	−0.66	−0.70	−0.43	−1.21	−1.03	0.50	0.79	0.57	0.92	0.47	0.79
100	E	−0.17	−0.17	−0.30	−0.15	−0.37	0.20	0.38	0.54	0.32	0.51	0.46	1.12
	M	−0.31	−0.33	−0.26	−0.46	−0.44	−0.33	0.24	0.38	0.36	0.20	0.40	0.59
	H	−0.21	−0.13	−0.37	−0.28	−0.17	0.55	0.34	0.60	0.26	0.37	0.67	1.47
200	E	−0.14	−0.20	−0.21	−0.25	−0.11	−0.35	0.13	0.15	0.10	0.06	0.30	0.10
	M	−0.18	−0.27	−0.16	−0.18	−0.32	−0.51	0.09	0.09	0.15	0.15	0.10	−0.07
	H	−0.09	−0.07	−0.15	−0.17	−0.03	0.31	0.18	0.28	0.16	0.16	0.38	0.76
500	E	−0.11	−0.21	−0.16	0.13	−0.18	−0.39	−0.01	−0.07	−0.04	0.00	−0.02	−0.21
	M	−0.10	−0.20	−0.09	−0.20	0.05	−0.28	0.01	−0.06	0.04	−0.07	0.21	−0.10
	H	−0.06	−0.03	−0.02	−0.10	−0.04	0.04	0.05	0.11	0.10	0.03	0.12	0.21
1000	E	−0.01	−0.05	−0.08	−0.05	−0.11	−0.18	0.05	0.03	−0.02	0.03	−0.03	−0.09
	M	−0.02	−0.04	−0.03	−0.02	−0.09	−0.06	0.04	0.03	0.04	0.05	−0.01	0.03
	H	−0.02	−0.03	−0.02	−0.07	−0.06	−0.10	0.03	0.04	0.05	0.00	0.02	−0.01

Types	Average	MGLS						TSSEM
Types	Average	ρ ₂₁	ρ ₃₁	ρ ₄₁	ρ ₃₂	ρ ₄₂	ρ ₄₃	ρ ₂₁	ρ ₃₁	ρ ₄₁	ρ ₃₂	ρ ₄₂	ρ ₄₃
k = 5
50	E	−0.26	−0.37	−0.81	−0.99	−0.71	−0.46	0.64	0.75	0.24	0.10	0.63	1.00
	M	−0.40	−1.07	−0.40	−1.05	−0.75	−0.77	0.52	0.04	0.63	0.05	0.56	0.57
	H	−0.54	−0.85	−0.51	−1.04	−0.23	0.28	0.40	0.31	0.53	0.14	1.08	1.69
100	E	−0.43	−0.55	−0.39	−0.41	−0.34	−0.92	0.03	0.03	0.15	0.14	0.36	−0.19
	M	−0.19	−0.64	−0.17	−0.54	0.12	−0.02	0.26	−0.07	0.36	0.00	0.80	0.72
	H	−0.29	−0.39	−0.42	−0.57	−0.54	−0.19	0.16	0.16	0.12	−0.03	0.12	0.53
200	E	−0.12	0.15	−0.08	0.15	−0.05	0.70	0.09	0.43	0.17	0.43	0.26	1.04
	M	−0.14	−0.05	−0.23	−0.05	−0.28	−0.65	0.09	0.24	0.02	0.23	0.04	−0.29
	H	−0.03	0.00	−0.11	−0.07	−0.02	0.36	0.18	0.28	0.14	0.20	0.29	0.70
500	E	−0.09	0.02	−0.04	−0.07	−0.17	0.32	0.00	0.13	0.07	0.04	−0.03	0.47
	M	−0.05	−0.05	−0.16	−0.02	−0.02	0.08	0.04	0.06	−0.05	0.09	0.11	0.23
	H	−0.11	−0.09	−0.11	−0.11	−0.06	−0.01	−0.02	−0.02	−0.01	−0.01	0.07	0.12
1000	E	−0.08	−0.13	0.01	−0.12	0.09	0.07	−0.04	−0.07	0.06	−0.07	0.15	0.14
	M	0.00	−0.10	−0.07	0.10	0.02	−0.11	0.04	−0.04	−0.02	0.15	0.08	−0.04
	H	−0.07	−0.03	−0.05	−0.04	−0.11	0.10	−0.02	0.02	0.00	0.01	−0.05	0.17
k = 10
50	E	−0.57	−0.82	−0.35	−0.56	0.05	0.32	0.49	0.50	0.84	0.71	1.63	1.35
	M	−0.71	−0.55	−0.85	−0.76	−1.38	−0.60	0.34	0.76	0.31	0.51	0.13	1.09
	H	−0.50	−0.56	−0.64	−0.59	−0.78	−0.24	0.50	0.69	0.52	0.68	0.69	1.30
100	E	−0.39	−0.50	−0.33	−0.57	−0.94	−0.74	0.13	0.13	0.23	0.05	−0.21	0.05
	M	−0.52	−0.51	−0.43	−0.38	−0.81	−0.24	−0.01	0.13	0.15	0.24	−0.08	0.57
	H	−0.23	−0.34	−0.20	−0.41	−0.36	−0.86	0.28	0.30	0.38	0.21	0.39	−0.03
200	E	−0.16	−0.14	−0.16	−0.17	−0.05	0.20	0.09	0.18	0.12	0.14	0.31	0.59
	M	−0.13	−0.49	−0.18	−0.29	−0.32	−0.85	0.12	−0.17	0.09	0.02	0.04	−0.47
	H	−0.15	−0.39	−0.28	−0.22	−0.40	−0.48	0.10	−0.07	−0.01	0.09	−0.05	−0.10
500	E	−0.06	−0.01	−0.06	−0.02	−0.16	−0.12	0.04	0.12	0.05	0.11	−0.01	0.04
	M	−0.02	−0.08	−0.09	−0.18	−0.01	−0.26	0.09	0.05	0.02	−0.05	0.14	−0.09
	H	−0.09	−0.15	−0.08	−0.15	−0.14	−0.38	0.01	−0.01	0.04	−0.03	0.01	−0.22
100	E	−0.02	−0.03	0.02	−0.02	0.09	0.31	0.03	0.03	0.08	0.04	0.16	0.39
	M	0.02	0.05	−0.03	0.03	0.06	0.11	0.07	0.12	0.02	0.09	0.13	0.19
	H	−0.03	−0.02	−0.06	−0.07	−0.05	−0.28	0.02	0.05	−0.01	−0.01	0.02	−0.20
k = 15
50	E	−0.61	−0.69	−0.57	−0.84	−1.04	−1.82	0.46	0.68	0.64	0.46	0.54	−0.13
	M	−0.78	−0.84	−0.72	−1.14	−0.90	−1.44	0.29	0.52	0.49	0.19	0.62	0.25
	H	−0.63	−0.65	−0.70	−0.43	−1.21	−1.03	0.46	0.71	0.52	0.91	0.35	0.65
100	E	−0.17	−0.17	−0.30	−0.15	−0.37	0.20	0.35	0.49	0.28	0.49	0.39	1.04
	M	−0.31	−0.33	−0.26	−0.46	−0.44	−0.33	0.22	0.34	0.33	0.19	0.34	0.51
	H	−0.21	−0.13	−0.37	−0.28	−0.17	0.56	0.31	0.53	0.22	0.35	0.59	1.39
200	E	−0.14	−0.20	−0.21	−0.25	−0.11	−0.35	0.11	0.12	0.08	0.05	0.26	0.04
	M	−0.18	−0.27	−0.16	−0.18	−0.32	−0.51	0.08	0.06	0.13	0.14	0.06	−0.11
	H	−0.09	−0.07	−0.15	−0.17	−0.03	0.31	0.17	0.27	0.14	0.15	0.35	0.73
500	E	−0.11	−0.21	−0.16	−0.13	−0.18	−0.39	−0.01	−0.08	−0.04	0.00	−0.04	−0.23
	M	−0.10	−0.20	−0.08	−0.20	0.05	−0.28	0.01	−0.06	0.03	−0.07	0.20	−0.11
	H	−0.06	−0.03	−0.02	−0.10	−0.04	0.04	0.04	0.10	0.10	0.03	0.11	0.20
1000	E	−0.01	−0.05	−0.08	−0.05	−0.11	−0.18	0.04	0.02	−0.02	0.01	−0.03	−0.09
	M	−0.02	−0.04	−0.03	−0.02	−0.09	−0.06	0.04	0.03	0.03	0.05	−0.01	0.02
	H	−0.02	−0.03	−0.02	−0.07	−0.06	−0.10	0.03	0.04	0.04	0.00	0.01	−0.02

All of the notations are described in Table 1

Back to article page

ISSN: 1756-0500

Contact us

Submission enquiries: bmcresearchnotes@biomedcentral.com
General enquiries: ORSupport@springernature.com

BMC Research Notes

Contact us