Table 5 Percent models converged, percent relative bias, and percent non-coverage (in brackets).
From: A simulation study of sample size for multilevel logistic regression models
| Â | Â | Â | Group Size = 5 | Â | Group Size = 30 | Â | Group Size = 50 | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Model | Number of Groups | % converged | γ 00 | γ 01 | γ 10 | γ 11 | σ 0 | σ 1 | % converged | γ 00 | γ 01 | γ 10 | γ 11 | σ 0 | σ 1 | % converged | γ 00 | γ 01 | γ 10 | γ 11 | σ 0 | σ 1 |
1 | 30 | 80 | -3.9 (25) | 12.3 (22) | -0.6 (23) | 2.2 (22) | 14.2 (29) | 44.9 (25) | 100 | -1.9 (4) | -4.6 (6) | 7.0 (5) | -5.4 (8) | -3.4 (11) | -9.7 (14) | 100 | -2.8 (5) | 2.7 (6) | 5.9 (2) | -9.0 (4) | -7.1 (15) | -9.8 (9) |
2 | Â | 84 | 0.3 (18) | 18.0 (20) | 8.0 (19) | -16.0 (20) | 41.1 (31) | 4.8 (25) | 100 | -1.0 (7) | 1.4 (8) | 9.7 (2) | -21.6 (6) | -1.7 (13) | -5.3 (9) | 100 | -1.8 (5) | 0.9 (4) | 6.0 (3) | -25.0 (7) | -5.6 (11) | -6.4 (11) |
3 | Â | 99 | -2.3 (6) | 0.7 (4) | -12.5 (2) | -11.0 (8) | 5.8 (19) | 0.8 (18) | 100 | -3.9 (6) | 0.4 (5) | 15.5 (1) | -7.7 (3) | -4.5 (17) | -5.9 (9) | 100 | -3.2 (7) | 3.5 (3) | 15.1 (4) | -8.4 (7) | -4.1 (12) | -4.3 (12) |
4 | Â | 41 | 12.9 (60) | 8.3 (62) | 70.9 (60) | -215 (61) | 33.8 (64) | 469 (64) | 76 | -0.2 (31) | -11.2 (30) | 4.0 (26) | -29.0 (27) | 0.3 (30) | 9.7 (24) | 94 | 0.61 (11) | -9.2 (10) | -1.4 (12) | 35.1 (16) | 0.3 (16) | -4.7 (14) |
5 | Â | 53 | 16.5 (50) | 54.1 (49) | -7.6 (50) | -103 (47) | 58.9 (50) | 507 (52) | 93 | -0.9 (12) | 28.3 (8) | 7.1 (7) | 43.0 (13) | 3.2 (13) | 0.2 (12) | 97 | 0.7 (12) | -4.3 (6) | -9.0 (6) | 23.4 (13) | -1.5 (9) | 2.2 (10) |
6 | Â | 93 | 2.1 (9) | -9.6 (11) | 23.9 (8) | 15.3 (11) | -13.3 (27) | 1.9 (20) | 100 | -3.2 (5) | -1.2 (5) | -4.1 (4) | -3.3 (8) | -15.3 (30) | -7.3 (24) | 100 | -3.3 (4) | -4.3 (4) | -5.0 (6) | -14.0 (6) | -15.0 (29) | -3.9 (28) |
7 | Â | 76 | 2.5 (5) | -4.8 (3) | 27.1 (3) | 12.9 (4) | -0.6 (19) | -11.5 (23) | 99 | -4.4 (13) | -10.7 (7) | 0.0 (8) | -3.6 (7) | -18.9 (33) | -26.6 (39) | 97 | -4.6 (18) | -15.0 (7) | -0.7 (7) | -2.7 (10) | -15.5 (28) | -20.3 (35) |
8 | Â | 80 | -1.0 (23) | -4.9 (25) | 17.2 (23) | 18.6 (24) | -1.5 (28) | -2.5 (27) | 100 | 1.2 (7) | -2.4 (11) | -8.2 (11) | 5.9 (12) | -15.1 (25) | -19.3 (26) | 100 | 2.6 (6) | -0.7 (12) | -5.5 (10) | 3.6 (10) | -7.1 (18) | -20.7 (32) |
1 | 50 | 88 | 5.4 (14) | -4.3 (16) | -6.1 (13) | -4.3 (17) | 19.2 (15) | 23.5 (15) | 100 | 3.0 (7) | 4.7 (5) | -0.5 (9) | -4.2 (4) | 2.1 (14) | -1.8 (10) | 100 | 3.4 (9) | 2.0 (8) | -0.3 (5) | -4.18 (7) | -3.9 (11) | -4.1 (6) |
2 | Â | 94 | 10.5 (10) | -0.8 (7) | -2.5 (10) | -5.9 (10) | 22.4 (17) | 15.3 (15) | 100 | 5.0 (7) | 6.5 (7) | -6.4 (8) | -7.8 (6) | -0.4 (8) | -0.2 (10) | 100 | 3.3 (6) | 4.8 (8) | -7.8 (8) | -10.0 (4) | -3.8 (10) | -3.6 (7) |
3 | Â | 99 | 11.9 (4) | 14.7 (4) | -1.7 (8) | 5.6 (5) | 20.1 (10) | 13.8 (14) | 100 | 7.1 (6) | 4.2 (7) | -6.5 (7) | -5.2 (7) | -2.9 (13) | -3.4 (5) | 100 | 6.0 (7) | 3.7 (6) | -8.4 (8) | -3.3 (4) | -2.8 (12) | -2.9 (9) |
4 | Â | 55 | 11.7 (54) | 17.6 (50) | 52.1 (52) | 129 (53) | 17.9 (54) | 162 (58) | 92 | 0.9 (14) | 21.1 (11) | 7.3 (17) | -36.1 (11) | -5.4 (18) | -6.3 (14) | 100 | 0.9 (4) | 32.0 (7) | -6.3 (8) | -14.6 (7) | -5.3 (9) | -3.5 (9) |
5 | Â | 58 | 5.2 (46) | -30.3 (49) | 49.9 (46) | 4.0 (47) | 25.9 (53) | 224 (52) | 98 | 3.3 (8) | 5.6 (7) | 9.1 (9) | -34.3 (11) | 7.1 (2) | -2.6 (7) | 100 | 2.1 (5) | 10.2 (7) | 5.9 (9) | -48.3 (7) | 4.3 (4) | -6.8 (9) |
6 | Â | 100 | 1.5 (3) | -4.0 (7) | -0.5 (4) | 2.12 (3) | -15.0 (20) | -11.4 (22) | 100 | -4.1 (4) | -0.3 (8) | 3.4 (4) | -4.7 (5) | -12.9 (35) | -16.9 (32) | 100 | -3.0 (6) | -1.1 (10) | 1.1 (5) | -10.7 (6) | -6.2 (28) | -10.4 (30) |
7 | Â | 80 | 2.4 (4) | 8.3 (6) | 27.6 (2) | 8.2 (2) | -3.7 (9) | -6.3 (20) | 98 | -1.4 (7) | -2.6 (9) | 7.0 (6) | -2.4 (8) | -11.0 (22) | -22.5 (38) | 95 | -5.7 (7) | -4.0 (8) | 8.1 (3) | 0.0 (5) | -9.3 (25) | -20.8 (36) |
8 | Â | 98 | -3.1 (4) | 3.2 (4) | -11.1 (4) | 5.4 (8) | -3.5 (11) | -3.5 (19) | 100 | -2.6 (8) | -0.8 (10) | -13.4 (6) | 1.2 (3) | -9.0 (13) | -9.0 (17) | 100 | -3.3 (9) | 0.7 (7) | -10.4 (7) | 0.8 (3) | -10.1 (18) | -5.6 (18) |
1 | 100 | 100 | -0.5 (2) | -8.2 (7) | 5.4 (3) | 2.3 (4) | 0.9 (4) | 2.3 (10) | 100 | -2.4 (6) | 0.8 (7) | 2.6 (4) | -6.9 (4) | -2.6 (10) | -1.7 (4) | 100 | -2.4 (6) | -0.3 (13) | 3.1 (3) | -6.0 (3) | -4.0 (11) | -2.8 (4) |
2 | Â | 100 | -2.5 (6) | -1.8 (2) | 1.4 (5) | -11.0 (5) | 11.8 (6) | 1.9 (9) | 100 | -1.9 (5) | -0.4 (12) | 6.5 (2) | -11.9 (4) | -6.3 (9) | -1.6 (5) | 100 | -2.2 (7) | 0.0 (15) | 3.7 (0) | -8.4 (4) | -4.8 (8) | -3.6 (3) |
3 | Â | 100 | -3.4 (4) | -0.9 (6) | -0.7 (1) | 0.6 (5) | 4.6 (12) | 2.4 (9) | 100 | -5.6 (3) | -0.3 (9) | 6.4 (4) | -5.9 (3) | -3.0 (8) | -2.4 (8) | 100 | -5.1 (7) | -2.1 (10) | 6.5 (2) | -4.7 (5) | -3.7 (7) | -3.7 (6) |
4 | Â | 66 | 3.4 (39) | 22.5 (38) | 32.2 (38) | -8.4 (36) | 1.7 (41) | 137 (38) | 100 | -0.4 (4) | 12.2 (7) | 3.9 (3) | 7.3 (5) | -0.7 (7) | -3.7 (10) | 100 | 0.1 (7) | 17.0 (9) | -7.9 (3) | -29.5 (8) | -1.3 (10) | -1.5 (10) |
5 | Â | 69 | 7.7 (40) | 5.7 (34) | -12.6 (33) | -57.5 (34) | 19.4 (38) | 169 (36) | 99 | 0.8 (7) | -11.5 (6) | -0.5 (8) | -20.1 (11) | 6.2 (2) | 0.4 (5) | 100 | 0.9 (6) | -10.9 (3) | -4.6 (6) | -16.5 (9) | 5.0 (1) | 1.3 (4) |
6 | Â | 100 | -4.0 (4) | 4.1 (4) | 2.7 (2) | 17.2 (7) | -13.8 (16) | -20.9 (22) | 100 | -6.0 (11) | 1.1 (5) | 3.7 (3) | 10.7 (10) | -14.6 (29) | -18.2 (34) | 100 | -5.8 (10) | -3.8 (4) | 1.3 (4) | 10.4 (7) | -9.7 (28) | -10.8 (32) |
7 | Â | 94 | -3.0 (7) | 1.6 (7) | 16.1 (2) | 6.2 (5) | -16.6 (22) | -26.0 (26) | 98 | -2.6 (10) | -1.6 (7) | 12.2 (3) | 0.4 (4) | -13.9 (33) | -22.5 (46) | 94 | -3.2 (11) | -0.6 (8) | 8.8 (5) | -3.2 (7) | -13.6 (35) | -17.8 (37) |
8 | Â | 100 | 0.6 (7) | 9.2 (4) | -10.4 (5) | 6.4 (7) | -2.2 (9) | -10.2 (10) | 100 | 1.9 (8) | 4.0 (3) | 0.3 (6) | -0.3 (4) | -4.5 (16) | -8.1 (17) | 100 | 1.1 (4) | 3.1 (5) | -2.0 (3) | 2.3 (7) | -5.8 (20) | -6.4 (11) |