Table 1 Deviance Information Criterion and Related Performance Measures for Models of Various Complexities

Table 1
Deviance Information Criterion and Related Performance Measures for Models of Various Complexities

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Model no. Model components (equations 2 and 3) D D(θ) PD DIC DIC/n R2DIC (Freq) R2DIC (Rate) 1/ψ R2ψ (Rate)
1 Alpha(i,t) [Saturated Model] 2026 61 1965 3991 1.99 0.91 0.77    
2 Alpha0 [Constant Frequency Model] 23416 23414 1 23417 11.66 0 -----    
3 Offset+ Alpha0 [Constant Rate Model] 10706 10701 5 10710 5.33 0.59 0    
4 Offset+Alpha0+Beta.Fix 6716 6713 2 6718 3.35 0.78 0.46    
5 Offset+Alpha0+Beta.Fix+Time.Fix 6686 6676 10 6695 3.33 0.78 0.46    
6 Offset+Alpha(j)+Beta.Fix 5126 5090 36 5161 2.57 0.85 0.64    
7 Offset+Alpha(j,t) 5316 5113 202 5518 2.75 0.84 0.6    
8 Offset+Alpha(j,t)+Beta.Fix 4816 4608 208 5024 2.5 0.86 0.65    
9 Offset+Alpha(j,t)+Beta.Fix+Time.Fix 4816 4623 193 5009 2.49 0.86 0.66    
10 Alpha0+e.N 2116 350 1765 3881 1.93 0.91 0.78    
11 Offset+Alpha0+e.Gam 2086 582 1504 3590 1.79 0.93 0.82 0.263 0
12 Offset+Alpha0+e.N 2146 611 1534 3680 1.83 0.92 0.81    
13 Offset+Alpha0+Space.CAR.N1 2846 2473 373 3218 1.6 0.94 0.86    
14 Offset+Alpha(j)+e.N 2156 988 1168 3324 1.66 0.94 0.85    
15 Offset+Alpha(j)+e.Gam 2136 978 1158 3294 1.64 0.94 0.85 0.103 0.61
16 Offset+Alpha(j)+Space.CAR.N1 2846 2483 362 3208 1.6 0.94 0.86    
17 Offset+Alpha(j)+Beta.Fix+e.N 2186 1085 1101 3287 1.64 0.94 0.85    
18 Offset+Alpha(j)+Beta.Fix+e.Gam 2156 1046 1110 3266 1.63 0.94 0.86 0.089 0.66
19 Offset+Alpha(j)+Beta.Fix+Time.AR1+e.N 2176 1080 1096 3272 1.63 0.94 0.85    
20 Offset+Alpha(j)+Beta.Fix+Space.CAR.N1+e.N 2066 1376 689 2755 1.37 0.97 0.91    
21 Offset+Alpha(j)+Beta.Fix+Space.CAR.L1+e.N 2066 1375 691 2757 1.37 0.97 0.91    
22 Offset+Alpha(j)+Beta.Fix+Space.CAR.N1+Time.AR1+e.N 2066 1380 686 2751 1.37 0.97 0.91    
23 Offset+Alpha(j)+Beta.Fix+Space.CAR.N1+Time.Fix+e.N 2056 1377 679 2735 1.36 0.97 0.92    
24 Offset+Alpha(j)+Beta.Fix+Space.CAR.N1+Time.Fix+e.Gam 2026 1342 684 2709 1.35 0.97 0.92 0.022 0.92
25 Offset+Alpha(j)+Beta.N+Space.CAR.N1+Time.Fix+e.Gam 2036 1327 709 2744 1.37 0.97 0.92 0.02 0.92
26 Offset+Alpha(j)+Beta.Fix+Space.CAR.N2+Time.Fix+e.N 2046 1360 686 2731 1.36 0.97 0.92    
27 Offset+Alpha(j)+Beta.Fix+Space.CAR.N2+Time.Fix+e.Gam 2016 1329 687 2703 1.35 0.97 0.92 0.021 0.92
28 Offset+Alpha(j)+Beta.N+Space.CAR.N2+Time.Fix+e.Gam 2026 1318 708 2733 1.36 0.97 0.92 0.02 0.92
29 Offset+Alpha(j)+Beta.Fix+Space.CAR.L1+Time.Fix+e.N 2056 1375 681 2736 1.36 0.97 0.92    
30 Offset+Alpha(j)+Beta.Fix+Space.CAR.L1+Time.Fix+e.Gam 2026 1339 687 2712 1.35 0.97 0.92 0.022 0.92
31 Offset+Alpha(j)+Beta.N+Space.CAR.L1+Time.Fix+e.Gam 2036 1330 706 2742 1.37 0.97 0.92 0.02 0.92
32 Offset+Alpha(j)+Beta.Fix+Space.CAR.L2+Time.Fix+e.N 1966 1181 785 2751 1.37 0.97 0.91    
33 Offset+Alpha(j)+Beta.Fix+Space.CAR.L2+Time.Fix+e.Gam 2016 1327 689 2704 1.35 0.97 0.92    
34 Offset+Alpha(j)+Beta.N+Space.CAR.L2+Time.Fix+e.Gam 2026 1317 709 2735 1.36 0.97 0.92 0.02 0.92
35 Offset+Alpha(j,t)+e.N 2166 917 1249 3415 1.7 0.93 0.84    
36 Offset+Alpha(j,t)+e.Gam 2126 886 1240 3365 1.68 0.94 0.84 0.108 0.59
37 Offset+Alpha(j,t)+Beta.Fix+e.N 2156 965 1191 3347 1.67 0.94 0.85    
38 Offset+Alpha(j,t)+Beta.Fix+e.Gam 2136 962 1174 3310 1.65 0.94 0.85 0.089 0.66
39 Offset+Alpha(j,t)+Beta.Fix+Space.CAR.N1+e.N 1956 1103 853 2808 1.4 0.96 0.91    
40 Offset+Alpha(j,t)+Beta.Fix+Space.CAR.N1+e.Gam 1936 1091 845 2781 1.38 0.96 0.91 0.027 0.9
41 Offset+Alpha(j,t)+Beta.Fix+Space.CAR.N2+e.N 1946 1086 860 2806 1.4 0.96 0.91    
42 Offset+Alpha(j,t)+Beta.Fix+Space.CAR.N2+e.Gam 1926 1072 854 2780 1.38 0.96 0.91 0.027 0.9

Notes: i = county, j = district, and t = time period; n = sample size = 2,008; and the saturated part of the deviance statistics = 2log[f(y)] = -8,894.