Testing Inference from Logistic Regression Models in Data with Unobserved Heterogeneity at Cluster Levels

Figures & data

Table 1 Estimation of β using the logistic model, β and σ using the logistic-normal for two specifications of cluster due to unobserved heterogeneity as levels 1 and 2, (p ₀, p ₁) = (0.27, 0.73), (n = 364 individual, K = 2 (level 1) and J = 12 (level 2)

		Logistic normal level 2 as level of correlation		Logistic normal level 1 as level of correlation
	Logistic					True	Variance
Estimate	1.67	1.67	0.38	2.01	1.00	1.0	0.0
se	0.16	0.16	0.18	0.24	0.23
Reject %	53	53	61	5	1
Ratio	1.13	1.13	1.50	1.04	1.00
Estimate	1.66	1.71	0.36	2.00	1.00	0.8	0.2
se	0.16	0.16	0.13	0.24	0.23
Reject %	56	46	98	6	1
Ratio	1.00	1.06	0.85	0.96	1.00
Estimate	1.68	1.78	0.54	2.0	0.96	0.6	0.4
se	0.16	0.17	0.16	0.24	0.24
Reject %	50	29	128	5	1
Ratio	1.00	1.00	1.13	1.00	1.04
Estimate	1.68	1.81	0.60	1.99	0.94	0.5	0.5
se	0.16	0.17	0.16	0.24	0.24
Reject %	52	21	67	7	2
Ratio	1.13	1.12	1.19	1.08	1.17
Estimate	1.70	1.86	0.65	1.99	0.90	0.4	0.6
se	0.16	0.17	0.16	0.23	0.25
Reject %	45	15	57	4	1
Ratio	1.13	1.18	1.25	1.00	1.00
Estimate	1.71	1.93	0.77	2.02	0.92	0.2	0.8
se	0.16	0.18	0.17	0.24	0.24
Reject %	46	10	45	2	2
Ratio	1.13	1.06	1.18	0.92	1.08
Estimate	1.74	2.02	0.88	2.02	0.88	0.0	1.0
se	0.16	0.18	0.18	0.23	0.26
Reject %	38	3	26	2	4
Ratio	1.13	1.00	1.22	0.91	1.27

Table 2 Estimation of β using the logistic model, β and σ using the logistic-normal and two specifications of cluster due to unobserved heterogeneity as levels 1 and 2, (p ₀, p ₁) = (0.27, 0.73), (n = 364 individual, K = 12 (level 1) and J = 16 (level 2)

		Logistic normal level 2 as level of correlation		Logistic normal level 1 as level of correlation
		Logistic				True	Variance
Estimate	1.69	1.75	0.39	2.01	0.97	1.0	0.0
se	0.16	0.16	0.14	0.31	0.15
Reject %	53	84	96	7	4
Ratio	1.63	1.75	0.93	1.00	1.13
Estimate	1.69	1.80	0.53	2.03	0.98	0.8	0.2
se	0.16	0.17	0.14	0.31	0.15
Reject %	49	30	85	6	8
Ratio	1.56	1.53	1.21	1.00	1.13
Estimate	1.69	1.84	0.65	2.00	0.97	0.6	0.4
se	0.16	0.17	0.15	0.31	0.15
Reject %	50	29	65	2	6
Ratio	1.56	1.47	1.20	0.87	1.07
Estimate	1.69	1.87	0.70	2.00	0.96	0.5	0.5
se	0.16	0.17	0.16	0.30	0.15
Reject %	48	23	52	2	14
Ratio	1.38	1.41	1.25	0.87	1.27
Estimate	1.68	1.88	0.76	1.98	0.94	0.4	0.6
se	0.16	0.17	0.16	0.30	0.15
Reject %	50	24	45	2	10
Ratio	1.44	1.53	1.25	0.90	1.13
Estimate	1.71	1.95	0.83	2.00	0.90	0.2	0.8
se	0.16	0.18	0.15	0.29	0.15
Reject %	48	9	29	1	23
Ratio	1.06	1.11	1.47	0.72	1.40
Estimate	1.71	2.01	0.92	2.01	0.92	0.0	1.0
se	0.16	0.18	0.15	0.30	0.15
Reject %	44	3	17	0	20
Ratio	1.06	1.00	1.40	0.63	1.40

Table 3 Estimation of β using the logistic model, β and σ using the logistic-normal with correct and incorrect specification for unobserved heterogeneity at levels 1 and 2, (p ₀, p ₁) = (0.12, 0.27), (n = 364 individual, K = 2 (level 1) and J = 12 (level 2)

		Logistic normal level 2 as level of correlation		Logistic normal level 1 as level of correlation
	Logistic					True	Variance
Estimate	0.86	0.87	0.36	1.00	0.99	1.0	0.0
se	0.18	0.18	0.21	0.23	0.27
Reject %	15	14	74	6	6
Ratio	1.17	1.17	1.19	1.09	1.00
Estimate	0.88	0.90	0.40	1.02	0.96	0.8	0.2
se	0.18	0.18	0.16	0.23	0.26
Reject %	10	10	87	4	2
Ratio	1.06	1.06	1.00	1.00	0.96
Estimate	0.87	0.91	0.52	1.00	0.94	0.6	0.4
se	0.18	0.19	0.16	0.23	0.28
Reject %	9	6	67	3	2
Ratio	1.00	1.00	1.19	0.91	1.07
Estimate	0.87	0.93	0.62	1.02	0.94	0.5	0.5
se	0.18	0.19	0.16	0.23	00.291
Reject %	12	7	67	3	0.97
Ratio	1.00	1.00	1.31	0.96
Estimate	0.87	0.94	0.68	1.00	0.95	0.4	0.6
se	0.18	0.19	0.16	0.23	0.28
Reject %	10	4	54	2	2
Ratio	0.94	0.95	1.25	0.91	1.07
Estimate	0.90	0.99	0.75	1.02	0.85	0.2	0.8
se	0.18	0.19	0.16	0.22	0.31
Reject %	7	5	43	3	2
Ratio	1.00	1.00	1.31	0.91	1.03
Estimate	0.88	1.00	0.89	1.00	0.92	0.0	1.0
se	0.18	0.20	0.19	0.22	0.32
Reject %	10	2	3	3	4
Ratio	0.94	0.95	1.21	0.86	0.97