"TABLE 1 Deviance Information Criterion and Related Performance Measures for Models of Various Complexities
  ",,,,,,,,,,,,,
Model no., Model components (equations 2 and 3),D,D(?),PD,DIC,DIC/n,"R2DIC
(Freq)","R2DIC
(Rate)",1/?,"R2?
 (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.",,,,,,,,,,,,,
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