A Gibbs Sampler for the Multidimensional Item Response Model

Table 4

Posterior estimates and Gelman-Rubin 𝑅 statistics for 𝛼₁, 𝛼₂, and 𝛽 for the CBASE data, assuming uniform priors (chain length = 10,000, burn-in = 5,000).

𝑗	𝛼1	𝑅	𝛼2	𝑅	𝛽̂	𝑅
1	0.0807	1.0546	0.5486	1.0226	−0.5861	1.0020
2	0.1396	1.0313	0.3630	1.0089	−0.6092	1.0001
3	0.0758	1.0178	0.3234	1.0001	−1.0515	0.9996
4	0.0737	1.0579	0.4157	1.0471	−1.4012	1.0183
5	0.1608	1.0259	0.4287	1.0040	−1.2238	1.0025
6	0.3050	1.0558	0.6824	1.0106	−0.9232	1.0243
7	0.1306	1.0066	0.2844	1.0227	−0.4324	1.0002
8	0.2804	1.0080	0.3106	1.0307	−1.2559	1.0024
9	0.1905	1.0478	0.4238	1.0176	−0.1286	1.0000
10	0.2425	1.0145	0.4838	1.0052	−0.0581	1.0005
11	0.1250	1.0272	0.3620	1.0016	0.4158	1.0028
12	0.0466	1.0076	0.4509	1.0154	−0.8238	1.0046
13	0.1177	1.0351	0.4070	1.0061	−0.2584	1.0019
14	0.0514	1.0115	0.3165	1.0065	−0.0282	0.9998
15	0.1378	1.0354	0.4790	1.0029	−0.8686	1.0005
16	0.1698	1.0299	0.3259	1.0113	−0.0595	1.0017
17	0.1797	1.0300	0.3652	1.0037	−0.2178	1.0004
18	0.2006	1.0100	0.1696	1.0026	−0.2419	1.0001
19	0.3423	1.0486	0.4101	1.0374	0.2914	1.0035
20	0.3028	1.1008	0.8084	1.0204	−1.2920	1.0084
21	0.2741	1.0435	0.4980	1.0020	−0.2798	1.0018
22	0.3171	1.0810	0.3796	1.0272	−0.4662	1.0045
23	0.2517	1.0528	0.5849	1.0080	−0.9708	1.0087
24	0.3044	1.0269	0.3127	1.0388	−0.1639	0.9997
25	0.2126	1.0359	0.2268	1.0244	−0.3475	1.0008
26	0.1996	1.0497	0.4524	1.0142	−0.8906	1.0007
27	0.2709	1.0072	0.1593	1.0205	−0.9018	1.0025
28	0.1758	1.0547	0.4325	1.0450	−0.6202	1.0031
29	0.2979	1.0322	0.2235	1.0454	−0.2678	1.0013
30	0.2800	1.0731	0.4221	1.0215	−0.3751	1.0011
31	0.5042	1.0055	0.2511	1.0202	−0.9097	1.0005
32	0.6259	1.0326	0.3144	1.0243	−0.9608	1.0122
33	0.2224	1.0256	0.1425	1.0027	−0.3856	1.0012
34	0.5000	1.0014	0.0972	1.0461	−0.7270	1.0012
35	0.5429	1.0106	0.2085	1.0693	−0.2614	1.0024
36	0.4537	1.0295	0.1994	1.0359	0.4221	1.0060
37	0.4280	1.0037	0.0814	1.0230	0.3117	1.0018
38	0.4286	0.9996	0.0981	1.0251	−0.4062	0.9997
39	0.3901	1.0492	0.3072	1.0351	−0.6239	1.0044
40	0.6940	1.0144	0.0697	1.0656	−0.3961	0.9997
41	0.3930	1.0049	0.0436	1.0270	−0.3781	1.0006