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Table 1 Mean WAIC values and 95% credible intervals for every model

From: Evaluating the impact of a small number of areas on spatial estimation

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)
  1. 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
  2. Underline represents the lowest mean WAIC out of the 5 models
  3. Italics per row indicates that models perform similarly