Table 1.
Mean WAIC values and 95% credible intervals for every model
| Areas | Levels | WAIC Mean (95% CI) | ||||
|---|---|---|---|---|---|---|
| Independent | BYM | Leroux | Localised G = 2 | Localised G = 3 | ||
| 2 × 2 | LA LC | 8.7 (4.8, 11.8) | 11.3 (6.7, 16.2) | 11.4 (6.6, 16.3) | 11.4 (6.6, 16.4) | 11.1 (6.5, 16.1) |
| HA LC | 49.6 (5.0, 206.3) | 12.1 (7.2, 18.0) | 12.1 (7.2, 17.9) | 12.1 (7.1, 17.6) | 34.9 (7.1, 180.2) | |
| LA HC | 153.1 (53.7, 358.4) | 79.7 (38.4, 124.3) | 80.0 (37.7, 122.9) | 83.5 (36.6, 144.4) | 163.7 (49.2, 506.6) | |
| HA HC | 524.8 (64.7, 1915.3) | 91.6 (41.4, 151.6) | 91.4 (41.3, 149.3) | 95.2 (41.0, 163.1) | 360.2 (54.6, 2170.8) | |
| 3 × 3 | LA LC | 18.6 (13.4, 23.5) | 19.6 (14.7, 26.7) | 19.7 (14.4, 26.8) | 19.6 (14.5, 26.9) | 19.6 (14.4, 26.6) |
| HA LC | 530.4 (30.6, 446.7) | 19.7 (15.2, 24.9) | 19.5 (15.1, 24.8) | 19.5 (14.9, 25.0) | 35.1 (17.4, 81.9) | |
| LA HC | 253.5 (143.9, 420.3) | 112.3 (65.9, 185.6) | 112.2 (62.0, 187.8) | 112.5 (62.4, 188.9) | 160.0 (78.1, 364.4) | |
| HA HC | 5397.6 (302.7, 5134.2) | 111.1 (73.7, 166.6) | 108.0 (68.9, 163.2) | 108.7 (67.3, 163.3) | 281.0 (98.2, 687.9) | |
| 4 x 4 | LA LC | 33.5 (24.1, 40.9) | 32.6 (24.1, 40.9) | 32.6 (23.9, 40.7) | 32.6 (24.0, 40.9) | 32.6 (23.9, 40.9) |
| HA LC | 177.3 (73.8, 563.5) | 33.6 (25.5, 43.6) | 33.3 (25.2, 43.2) | 36.1 (25.4, 83.3) | 44.5 (28.0, 76.0) | |
| LA HC | 400.2 (244.4, 632.0) | 158.8 (95.5, 240.0) | 156.4 (93.9, 235.1) | 158.0 (95.1, 237.1) | 193.5 (103.9, 310.0) | |
| HA HC | 1820.7 (645.1, 6367.0) | 168.5 (105.1, 272.7) | 162.9 (101.2, 263.1) | 195.3 (101.6, 748.3) | 280.1 (125.0, 568.1) | |
| 5 x 5 | LA LC | 50.7 (39.4, 60.6) | 46.4 (36.8, 60.4) | 46.4 (37.0, 60.6) | 46.4 (37.0, 60.6) | 46.4 (36.9, 60.5) |
| HA LC | 270.7 (111.8, 443.2) | 48.6 (35.7, 62.9) | 48.2 (35.5, 62.6) | 48.9 (35.4, 68.4) | 219.9 (39.8, 115.9) | |
| LA HC | 530.1 (377.7, 717.7) | 205.5 (149.1, 308.3) | 202.9 (150.0, 300.7) | 203.4 (149.6, 298.9) | 225.8 (158.3, 329.2) | |
| HA HC | 2795.1 (1116.3, 4045.0) | 226.6 (135.9, 351.9) | 217.6 (132.6, 333.1) | 227.0 (130.5, 393.5) | 2169.8 (156.8, 1011.9) | |
| 10 x 10 | LA LC | 194.4 (175.2, 214.8) | 166.4 (150.2, 178.9) | 166.1 (150.3, 178.4) | 166.3 (150.3, 178.4) | 166.2 (150.2, 182.4) |
| HA LC | 479.2 (408.2, 563.8) | 186.6 (157.5, 216.7) | 185 (155.5, 215.6) | 190.3 (158.7, 269) | 449.5 (158.7, 222.2) | |
| LA HC | 1460.1 (1349.4, 1557.7) | 612.9 (502.5, 723.9) | 592.9 (489.7, 713.5) | 602.5 (486.8, 741.3) | 610.6 (493.2, 724.1) | |
| HA HC | 4326.9 (3530.2, 5334.6) | 817.9 (537.3, 1210.9) | 771.3 (516.3, 1133.3) | 832.8 (520.5, 1753.0) | 3548.4 (562.6, 1204.5) | |
| 15 x 15 | LA LC | 426.0 (398.2, 448.8) | 367.4 (346.3, 392.2) | 366.7 (345.7, 391.4) | 367.2 (346.0, 392.6) | 367.0 (345.6, 391.6) |
| HA LC | 817.0 (727.8, 905.9) | 404.9 (354.7, 449.2) | 402.2 (351.9, 445.7) | 410.2 (354.3, 446.2) | 411.9 (359.8, 482.4) | |
| LA HC | 2783.0 (2668.2, 2923.1) | 1259.3 (1098.0, 1469.6) | 1210.6 (1066.7, 1411.1) | 1230.4 (1059.5, 1465.1) | 1233.5 (1078.1, 1460.4) | |
| HA HC | 6770.8 (5681.6, 7975.3) | 1621.2 (1133.3, 2217.3) | 1529.4 (1071.5, 2059.6) | 1629.4 (1099.6, 2133.9) | 1637.1 (1145.9, 2353.9) | |
| 20 x 20 | LA LC | 737.6 (704.9, 771.7) | 642.1 (611.7, 671.2) | 640.9 (610.8, 670.0) | 641.7 (610.9, 670.0) | 641.5 (610.6, 670.1) |
| HA LC | 1227.4 (1139.6, 1304.1) | 697.8 (626.7, 778.1) | 694.2 (625.1, 774.8) | 713.6 (625.1, 850.5) | 707.9 (627.1, 787.4) | |
| LA HC | 4374.6 (4240.8, 4543.4) | 2106.5 (1836.8, 2351.5) | 2029.9 (1784.1, 2246.3) | 2062.7 (1786.8, 2359.2) | 2063.2 (1802.1, 2325.0) | |
| HA HC | 9425.4 (8401.6, 10431.7) | 2613.9 (2020.9, 3419.3) | 2483.1 (1972.5, 3207.7) | 2713 (1954.2, 4157.8) | 2632.9 (1992.7, 3451.8) | |
| 50 x 50 | LA LC | 4222.5 (4153.0, 4305.9) | 3880.0 (3757.4, 3981.6) | 3875.3 (3753.6, 3979.0) | 3877.5 (3757.8, 3979.3) | 3876.8 (3752.9, 3977.8) |
| HA LC | 5315.6 (5107.9, 5514.9) | 4064.8 (3901.2, 4234.0) | 4054.3 (3886.6, 4217.4) | 4060.1 (3890.3, 4217.1) | 4076.6 (3896.9, 4360.9) | |
| LA HC | 18863.8 (18370.4, 19290.3) | 11508.6 (10749.7, 12251.0) | 11224.8 (10577.2, 11922.3) | 11415.1 (10696.4, 12376.5) | 11314.8 (10541.2, 12212.4) | |
| HA HC | 30471.4 (27777.6, 32943.7) | 13151.4 (11601.2, 14633.0) | 12731.1 (11244.9, 13969.9) | 12918 (11312.7, 14738.7) | 12977.2 (11292.3, 15994.3) | |
WAIC Watanabe-Akaike Information Criterion, LA LC low autocorrelation and low counts, LA HC low autocorrelation and high counts, HA LC high autocorrelation and low counts, HA HC high autocorrelation and high counts
Underline represents the lowest mean WAIC out of the 5 models
Italics per row indicates that models perform similarly