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

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BTS Home > Publications > Journal of Transportation and Statistics > Volume 6 Number 1 > Paper 3

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)	P_D	DIC	DIC/n	R²*_DIC(Freq)***	R²*_DIC(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.

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