A simulation study of sample size for multilevel logistic regression models

Table 1 The effect of number of groups, group size, and ICC on the relative bias ( $\frac{\hat{θ} - θ}{θ} \times 100$ ) of estimates.

Number of groups	Group size	ICC	% converged	γ ₀₀	γ ₀₁	γ ₁₀	γ ₁₁	σ ₀	σ ₁
30	5	0.04	56	8.77	11.12	15.85	13.26	174.04	55.49
		0.17	68	4.75	11.56	10.70	14.93	24.25	54.55
		0.38	76	3.94	12.22	5.91	14.89	15.82	54.02
	30	0.04	94	0.07	1.09	-1.93	3.57	-7.07	-6.81
		0.17	100	-0.08	3.70	-1.60	3.44	-5.89	-7.02
		0.38	100	-0.18	5.74	-1.72	5.31	-3.55	-6.92
	50	0.04	99	-0.39	0.69	-0.18	5.32	-8.47	-7.71
		0.17	100	-0.43	2.65	-1.70	5.74	-6.25	-7.16
		0.38	100	-0.39	4.62	-2.85	4.49	-5.05	-7.30
50	5	0.04	71	3.82	9.32	4.93	5.88	110.80	35.84
		0.17	86	1.44	8.40	2.34	4.73	11.95	25.55
		0.38	90	1.00	5.96	3.50	6.68	6.80	28.11
	30	0.04	99	0.09	0.21	2.01	2.72	-5.16	-2.60
		0.17	100	-0.32	0.28	2.06	3.69	-2.90	-2.55
		0.38	100	-0.37	-0.56	1.89	3.46	-3.24	-2.81
	50	0.04	100	-0.23	0.08	1.25	2.31	-6.18	-3.54
		0.17	100	-0.33	0.51	1.39	2.56	-3.76	-3.59
		0.38	100	-0.53	0.83	1.29	1.73	-3.19	-3.23
100	5	0.04	87	1.64	0.14	2.42	1.55	47.87	7.64
		0.17	98	0.47	-0.50	1.11	0.89	1.84	3.46
		0.38	98	0.95	0.25	2.25	0.41	2.23	8.82
	30	0.04	100	-0.02	-0.12	0.31	0.41	-5.13	-1.25
		0.17	100	-0.11	0.36	-0.06	0.96	-2.14	-1.17
		0.38	100	-0.21	1.04	-0.96	1.07	-2.06	-1.30
	50	0.04	100	0.03	0.35	-0.09	0.48	-3.28	-2.01
		0.17	100	-0.06	0.71	0.05	0.63	-2.12	-1.34
		0.38	100	-0.14	0.62	0.50	1.18	-1.73	-1.52

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