On the reliability of point estimation of model parameters: Taking cognitive diagnostic models as an example

doi:10.3724/SP.J.1041.2023.01712

Abstract

Key words: model parameter estimation, point estimation, convergence criterion, cognitive diagnostic model

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LIU Yanlou, CHEN Qishan, WANG Yiming, JIANG Xiaotong. (2023). On the reliability of point estimation of model parameters: Taking cognitive diagnostic models as an example. Acta Psychologica Sinica, 55(10), 1712-1728.

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URL: https://journal.psych.ac.cn/acps/EN/10.3724/SP.J.1041.2023.01712

https://journal.psych.ac.cn/acps/EN/Y2023/V55/I10/1712

Figures/Tables 3

Table 1 Simulation results for J = 16 when item response data were generated using the saturated CDM

N	Convergence criterion	$LL_{Best}$	$LL_{Bean}$	$LL_{max}$	$LL_{min}$	$LL_{sd}$	$t_{mean}$	$Itr_{mean}$	$Itr_{max}$	$\lambda_{\mathrm{out}}$
500	Gdp4	0	?4948.024	?4847.235	?5054.561	34.436	0.540	180	848	62
	Gdp6	240	?4948.011	?4847.226	?5054.557	34.437	1.181	474	5752	61
	Gdp8	280	?4948.011	?4847.226	?5054.557	34.437	2.068	901	32057	61
	Gip4	0	?4948.027	?4847.234	?5054.561	34.438	0.507	164	730	59
	Gip6	232	?4948.011	?4847.226	?5054.557	34.437	1.131	452	5680	61
	Gip8	279	?4948.011	?4847.226	?5054.557	34.437	1.847	863	28030	61
	Gll4	0	?4948.024	?4847.229	?5054.558	34.438	0.520	169	844	60
	Gll6	48	?4948.017	?4847.226	?5054.557	34.431	0.858	329	1819	61
	Gll8	273	?4948.011	?4847.226	?5054.557	34.437	1.217	531	6760	61
	Gcomp4	0	?4948.022	?4847.229	?5054.558	34.436	0.566	190	848	62
	Gcomp6	240	?4948.011	?4847.226	?5054.557	34.437	1.189	478	5752	61
	Gcomp8	281	?4948.011	?4847.226	?5054.557	34.437	2.062	905	32057	61
	mdp4	0	?4948.021	?4847.234	?5054.560	34.436	0.254	179	877	59
	mdp6	360	?4948.008	?4847.226	?5054.556	34.437	0.461	479	5803	59
	mdp8	498	?4948.008	?4847.226	?5054.556	34.437	0.735	953	32053	59
	mip4	0	?4948.022	?4847.234	?5054.560	34.436	0.241	165	774	58
	mip6	346	?4948.012	?4847.226	?5054.556	34.441	0.432	453	5730	59
	mip8	496	?4948.008	?4847.226	?5054.556	34.437	0.690	912	28026	59
	mll4	0	?4948.021	?4847.228	?5054.557	34.437	0.240	168	923	57
	mll6	69	?4948.018	?4847.226	?5054.556	34.435	0.349	335	1978	59
	mll8	485	?4948.008	?4847.226	?5054.556	34.437	0.495	585	6756	59
	mcomp4	0	?4948.019	?4847.228	?5054.557	34.435	0.258	189	923	59
	mcomp6	363	?4948.008	?4847.226	?5054.556	34.437	0.462	485	5803	59
	mcomp8	500	?4948.008	?4847.226	?5054.556	34.437	0.734	958	32053	59
1000	Gdp6	457	?9929.201	?9801.836	?10105.797	49.742	1.057	291	1924	6
	Gdp8	487	?9929.201	?9801.836	?10105.797	49.742	1.660	508	6609	6
	Gll6	117	?9929.201	?9801.836	?10105.797	49.742	0.831	217	713	6
	Gll8	481	?9929.201	?9801.836	?10105.797	49.742	1.107	324	2512	6
	Gcomp6	457	?9929.201	?9801.836	?10105.797	49.742	1.066	295	1924	6
	Gcomp8	487	?9929.201	?9801.836	?10105.797	49.742	1.666	511	6609	6
	mdp6	460	?9929.201	?9801.836	?10105.797	49.742	0.468	288	1950	6
	mdp8	499	?9929.201	?9801.836	?10105.797	49.742	0.726	503	6628	6
	mll6	104	?9929.201	?9801.836	?10105.797	49.742	0.362	213	795	6
	mll8	494	?9929.201	?9801.836	?10105.797	49.742	0.489	323	2509	6
	mcomp6	461	?9929.201	?9801.836	?10105.797	49.742	0.471	291	1950	6
	mcomp8	500	?9929.201	?9801.836	?10105.797	49.742	0.728	507	6628	6
4000	Gdp6	469	?39831.617	?39539.020	?40187.183	102.360	2.588	223	321	0
	Gdp8	500	?39831.617	?39539.020	?40187.183	102.360	3.840	354	506	0
	Gll6	200	?39831.617	?39539.020	?40187.183	102.360	2.334	195	282	0
	Gll8	499	?39831.617	?39539.020	?40187.183	102.360	2.947	261	376	0
	Gcomp6	475	?39831.617	?39539.020	?40187.183	102.360	2.596	224	322	0
	Gcomp8	500	?39831.617	?39539.020	?40187.183	102.360	3.825	356	511	0
	mdp6	463	?39831.617	?39539.020	?40187.183	102.360	1.612	209	312	0
	mdp8	500	?39831.617	?39539.020	?40187.183	102.360	2.376	341	490	0
	mll6	177	?39831.617	?39539.020	?40187.183	102.360	1.443	182	257	0
	mll8	499	?39831.617	?39539.020	?40187.183	102.360	1.774	247	352	0
	mcomp6	471	?39831.617	?39539.020	?40187.183	102.360	1.619	211	312	0
	mcomp8	500	?39831.617	?39539.020	?40187.183	102.360	2.372	342	490	0

Table 1 Simulation results for J = 16 when item response data were generated using the saturated CDM

N	Convergence criterion	$LL_{Best}$	$LL_{Bean}$	$LL_{max}$	$LL_{min}$	$LL_{sd}$	$t_{mean}$	$Itr_{mean}$	$Itr_{max}$	$\lambda_{\mathrm{out}}$
500	Gdp4	0	?4948.024	?4847.235	?5054.561	34.436	0.540	180	848	62
	Gdp6	240	?4948.011	?4847.226	?5054.557	34.437	1.181	474	5752	61
	Gdp8	280	?4948.011	?4847.226	?5054.557	34.437	2.068	901	32057	61
	Gip4	0	?4948.027	?4847.234	?5054.561	34.438	0.507	164	730	59
	Gip6	232	?4948.011	?4847.226	?5054.557	34.437	1.131	452	5680	61
	Gip8	279	?4948.011	?4847.226	?5054.557	34.437	1.847	863	28030	61
	Gll4	0	?4948.024	?4847.229	?5054.558	34.438	0.520	169	844	60
	Gll6	48	?4948.017	?4847.226	?5054.557	34.431	0.858	329	1819	61
	Gll8	273	?4948.011	?4847.226	?5054.557	34.437	1.217	531	6760	61
	Gcomp4	0	?4948.022	?4847.229	?5054.558	34.436	0.566	190	848	62
	Gcomp6	240	?4948.011	?4847.226	?5054.557	34.437	1.189	478	5752	61
	Gcomp8	281	?4948.011	?4847.226	?5054.557	34.437	2.062	905	32057	61
	mdp4	0	?4948.021	?4847.234	?5054.560	34.436	0.254	179	877	59
	mdp6	360	?4948.008	?4847.226	?5054.556	34.437	0.461	479	5803	59
	mdp8	498	?4948.008	?4847.226	?5054.556	34.437	0.735	953	32053	59
	mip4	0	?4948.022	?4847.234	?5054.560	34.436	0.241	165	774	58
	mip6	346	?4948.012	?4847.226	?5054.556	34.441	0.432	453	5730	59
	mip8	496	?4948.008	?4847.226	?5054.556	34.437	0.690	912	28026	59
	mll4	0	?4948.021	?4847.228	?5054.557	34.437	0.240	168	923	57
	mll6	69	?4948.018	?4847.226	?5054.556	34.435	0.349	335	1978	59
	mll8	485	?4948.008	?4847.226	?5054.556	34.437	0.495	585	6756	59
	mcomp4	0	?4948.019	?4847.228	?5054.557	34.435	0.258	189	923	59
	mcomp6	363	?4948.008	?4847.226	?5054.556	34.437	0.462	485	5803	59
	mcomp8	500	?4948.008	?4847.226	?5054.556	34.437	0.734	958	32053	59
1000	Gdp6	457	?9929.201	?9801.836	?10105.797	49.742	1.057	291	1924	6
	Gdp8	487	?9929.201	?9801.836	?10105.797	49.742	1.660	508	6609	6
	Gll6	117	?9929.201	?9801.836	?10105.797	49.742	0.831	217	713	6
	Gll8	481	?9929.201	?9801.836	?10105.797	49.742	1.107	324	2512	6
	Gcomp6	457	?9929.201	?9801.836	?10105.797	49.742	1.066	295	1924	6
	Gcomp8	487	?9929.201	?9801.836	?10105.797	49.742	1.666	511	6609	6
	mdp6	460	?9929.201	?9801.836	?10105.797	49.742	0.468	288	1950	6
	mdp8	499	?9929.201	?9801.836	?10105.797	49.742	0.726	503	6628	6
	mll6	104	?9929.201	?9801.836	?10105.797	49.742	0.362	213	795	6
	mll8	494	?9929.201	?9801.836	?10105.797	49.742	0.489	323	2509	6
	mcomp6	461	?9929.201	?9801.836	?10105.797	49.742	0.471	291	1950	6
	mcomp8	500	?9929.201	?9801.836	?10105.797	49.742	0.728	507	6628	6
4000	Gdp6	469	?39831.617	?39539.020	?40187.183	102.360	2.588	223	321	0
	Gdp8	500	?39831.617	?39539.020	?40187.183	102.360	3.840	354	506	0
	Gll6	200	?39831.617	?39539.020	?40187.183	102.360	2.334	195	282	0
	Gll8	499	?39831.617	?39539.020	?40187.183	102.360	2.947	261	376	0
	Gcomp6	475	?39831.617	?39539.020	?40187.183	102.360	2.596	224	322	0
	Gcomp8	500	?39831.617	?39539.020	?40187.183	102.360	3.825	356	511	0
	mdp6	463	?39831.617	?39539.020	?40187.183	102.360	1.612	209	312	0
	mdp8	500	?39831.617	?39539.020	?40187.183	102.360	2.376	341	490	0
	mll6	177	?39831.617	?39539.020	?40187.183	102.360	1.443	182	257	0
	mll8	499	?39831.617	?39539.020	?40187.183	102.360	1.774	247	352	0
	mcomp6	471	?39831.617	?39539.020	?40187.183	102.360	1.619	211	312	0
	mcomp8	500	?39831.617	?39539.020	?40187.183	102.360	2.372	342	490	0

Table 2 Simulation results for J = 16 when item response data were generated using the hierarchical CDM

N	Convergence criterion	$LL_{Best}$	$LL_{Bean}$	$LL_{max}$	$LL_{min}$	$LL_{sd}$	$t_{mean}$	$Itr_{mean}$	$Itr_{max}$	$\lambda_{\mathrm{out}}$
500	Gdp4	1	?4775.050	?4640.212	?4885.902	39.080	0.560	184	870	585
	Gdp6	22	?4775.034	?4640.210	?4885.901	39.076	1.276	500	5131	589
	Gdp8	27	?4775.033	?4640.210	?4885.901	39.075	2.175	937	23818	591
	Gip4	1	?4775.051	?4640.212	?4885.904	39.081	0.543	176	795	585
	Gip6	21	?4775.034	?4640.210	?4885.901	39.075	1.231	485	5141	589
	Gip8	27	?4775.033	?4640.210	?4885.901	39.075	2.110	922	23818	591
	Gll4	0	?4775.048	?4640.214	?4885.902	39.080	0.516	161	714	584
	Gll6	12	?4775.036	?4640.210	?4885.901	39.074	0.833	308	1461	588
	Gll8	25	?4775.033	?4640.210	?4885.901	39.075	1.284	535	6486	589
	Gcomp4	1	?4775.048	?4640.212	?4885.902	39.080	0.574	189	870	588
	Gcomp6	22	?4775.034	?4640.210	?4885.901	39.076	1.279	501	5141	589
	Gcomp8	27	?4775.033	?4640.210	?4885.901	39.075	2.179	939	23818	591
	mdp4	4	?4774.975	?4639.179	?4885.899	39.103	0.221	185	739	486
	mdp6	350	?4774.968	?4639.178	?4885.898	39.100	0.403	475	4339	484
	mdp8	469	?4774.964	?4639.178	?4885.898	39.101	0.686	931	14029	483
	mip4	4	?4774.975	?4639.179	?4885.901	39.103	0.214	179	735	490
	mip6	343	?4774.968	?4639.178	?4885.898	39.100	0.387	464	4303	484
	mip8	469	?4774.964	?4639.178	?4885.898	39.101	0.647	916	14029	483
	mll4	0	?4774.980	?4639.184	?4885.898	39.102	0.201	161	910	473
	mll6	72	?4774.969	?4639.178	?4885.898	39.100	0.292	312	1471	482
	mll8	458	?4774.965	?4639.178	?4885.898	39.101	0.431	558	5066	486
	mcomp4	4	?4774.974	?4639.179	?4885.898	39.103	0.223	191	910	481
	mcomp6	351	?4774.968	?4639.178	?4885.898	39.100	0.404	479	4339	484
	mcomp8	473	?4774.964	?4639.178	?4885.898	39.101	0.684	936	14029	483
1000	Gdp6	9	?9577.383	?9408.520	?9787.279	56.515	1.547	450	5095	491
	Gdp8	12	?9577.379	?9408.520	?9787.279	56.515	2.667	843	17947	494
	Gll6	3	?9577.389	?9408.520	?9787.279	56.510	1.054	285	1685	491
	Gll8	11	?9577.385	?9408.520	?9787.279	56.509	1.558	476	5786	495
	Gcomp6	9	?9577.383	?9408.520	?9787.279	56.515	1.546	451	5095	491
	Gcomp8	12	?9577.379	?9408.520	?9787.279	56.515	2.672	844	17947	494
	mdp6	366	?9577.314	?9408.518	?9787.279	56.508	0.635	467	5512	416
	mdp8	484	?9577.313	?9408.518	?9787.279	56.508	1.171	969	18411	411
	mll6	78	?9577.319	?9408.518	?9787.279	56.503	0.410	285	1686	409
	mll8	470	?9577.319	?9408.518	?9787.279	56.503	0.647	510	5843	415
	mcomp6	370	?9577.314	?9408.518	?9787.279	56.508	0.636	469	5512	416
	mcomp8	488	?9577.313	?9408.518	?9787.279	56.508	1.173	972	18411	411
4000	Gdp6	14	?38423.227	?38076.036	?38778.783	117.696	6.011	604	3920	424
	Gdp8	23	?38423.225	?38076.036	?38778.783	117.696	10.439	1132	12509	427
	Gll6	5	?38423.228	?38076.036	?38778.783	117.696	3.937	375	2066	425
	Gll8	22	?38423.226	?38076.036	?38778.783	117.697	6.492	698	4557	425
	Gcomp6	14	?38423.227	?38076.036	?38778.783	117.696	6.082	612	3920	425
	Gcomp8	23	?38423.225	?38076.036	?38778.783	117.696	10.473	1141	12509	427
	mdp6	276	?38423.146	?38076.034	?38778.782	117.698	3.437	595	3957	356
	mdp8	473	?38423.145	?38076.034	?38778.782	117.698	6.393	1233	12714	355
	mll6	28	?38423.146	?38076.034	?38778.782	117.697	2.253	374	2076	357
	mll8	460	?38423.145	?38076.034	?38778.782	117.698	3.831	733	4569	355
	mcomp6	276	?38423.146	?38076.034	?38778.782	117.698	3.472	602	3957	356
	mcomp8	478	?38423.145	?38076.034	?38778.782	117.698	6.424	1241	12714	355

Table 2 Simulation results for J = 16 when item response data were generated using the hierarchical CDM

N	Convergence criterion	$LL_{Best}$	$LL_{Bean}$	$LL_{max}$	$LL_{min}$	$LL_{sd}$	$t_{mean}$	$Itr_{mean}$	$Itr_{max}$	$\lambda_{\mathrm{out}}$
500	Gdp4	1	?4775.050	?4640.212	?4885.902	39.080	0.560	184	870	585
	Gdp6	22	?4775.034	?4640.210	?4885.901	39.076	1.276	500	5131	589
	Gdp8	27	?4775.033	?4640.210	?4885.901	39.075	2.175	937	23818	591
	Gip4	1	?4775.051	?4640.212	?4885.904	39.081	0.543	176	795	585
	Gip6	21	?4775.034	?4640.210	?4885.901	39.075	1.231	485	5141	589
	Gip8	27	?4775.033	?4640.210	?4885.901	39.075	2.110	922	23818	591
	Gll4	0	?4775.048	?4640.214	?4885.902	39.080	0.516	161	714	584
	Gll6	12	?4775.036	?4640.210	?4885.901	39.074	0.833	308	1461	588
	Gll8	25	?4775.033	?4640.210	?4885.901	39.075	1.284	535	6486	589
	Gcomp4	1	?4775.048	?4640.212	?4885.902	39.080	0.574	189	870	588
	Gcomp6	22	?4775.034	?4640.210	?4885.901	39.076	1.279	501	5141	589
	Gcomp8	27	?4775.033	?4640.210	?4885.901	39.075	2.179	939	23818	591
	mdp4	4	?4774.975	?4639.179	?4885.899	39.103	0.221	185	739	486
	mdp6	350	?4774.968	?4639.178	?4885.898	39.100	0.403	475	4339	484
	mdp8	469	?4774.964	?4639.178	?4885.898	39.101	0.686	931	14029	483
	mip4	4	?4774.975	?4639.179	?4885.901	39.103	0.214	179	735	490
	mip6	343	?4774.968	?4639.178	?4885.898	39.100	0.387	464	4303	484
	mip8	469	?4774.964	?4639.178	?4885.898	39.101	0.647	916	14029	483
	mll4	0	?4774.980	?4639.184	?4885.898	39.102	0.201	161	910	473
	mll6	72	?4774.969	?4639.178	?4885.898	39.100	0.292	312	1471	482
	mll8	458	?4774.965	?4639.178	?4885.898	39.101	0.431	558	5066	486
	mcomp4	4	?4774.974	?4639.179	?4885.898	39.103	0.223	191	910	481
	mcomp6	351	?4774.968	?4639.178	?4885.898	39.100	0.404	479	4339	484
	mcomp8	473	?4774.964	?4639.178	?4885.898	39.101	0.684	936	14029	483
1000	Gdp6	9	?9577.383	?9408.520	?9787.279	56.515	1.547	450	5095	491
	Gdp8	12	?9577.379	?9408.520	?9787.279	56.515	2.667	843	17947	494
	Gll6	3	?9577.389	?9408.520	?9787.279	56.510	1.054	285	1685	491
	Gll8	11	?9577.385	?9408.520	?9787.279	56.509	1.558	476	5786	495
	Gcomp6	9	?9577.383	?9408.520	?9787.279	56.515	1.546	451	5095	491
	Gcomp8	12	?9577.379	?9408.520	?9787.279	56.515	2.672	844	17947	494
	mdp6	366	?9577.314	?9408.518	?9787.279	56.508	0.635	467	5512	416
	mdp8	484	?9577.313	?9408.518	?9787.279	56.508	1.171	969	18411	411
	mll6	78	?9577.319	?9408.518	?9787.279	56.503	0.410	285	1686	409
	mll8	470	?9577.319	?9408.518	?9787.279	56.503	0.647	510	5843	415
	mcomp6	370	?9577.314	?9408.518	?9787.279	56.508	0.636	469	5512	416
	mcomp8	488	?9577.313	?9408.518	?9787.279	56.508	1.173	972	18411	411
4000	Gdp6	14	?38423.227	?38076.036	?38778.783	117.696	6.011	604	3920	424
	Gdp8	23	?38423.225	?38076.036	?38778.783	117.696	10.439	1132	12509	427
	Gll6	5	?38423.228	?38076.036	?38778.783	117.696	3.937	375	2066	425
	Gll8	22	?38423.226	?38076.036	?38778.783	117.697	6.492	698	4557	425
	Gcomp6	14	?38423.227	?38076.036	?38778.783	117.696	6.082	612	3920	425
	Gcomp8	23	?38423.225	?38076.036	?38778.783	117.696	10.473	1141	12509	427
	mdp6	276	?38423.146	?38076.034	?38778.782	117.698	3.437	595	3957	356
	mdp8	473	?38423.145	?38076.034	?38778.782	117.698	6.393	1233	12714	355
	mll6	28	?38423.146	?38076.034	?38778.782	117.697	2.253	374	2076	357
	mll8	460	?38423.145	?38076.034	?38778.782	117.698	3.831	733	4569	355
	mcomp6	276	?38423.146	?38076.034	?38778.782	117.698	3.472	602	3957	356
	mcomp8	478	?38423.145	?38076.034	?38778.782	117.698	6.424	1241	12714	355

Table 3 Simulation results for J = 32

Data generating model	N	Convergence criterion	$LL_{Best}$	$LL_{Bean}$	$LL_{max}$	$LL_{min}$	$LL_{sd}$	$t_{mean}$	$Itr_{mean}$	$Itr_{max}$
Saturated	500	Gdp8	485	?9334.716	?9163.342	?9521.124	61.640	0.551	77	311
		Gll8	484	?9334.716	?9163.342	?9521.124	61.640	0.452	53	328
		Gcomp8	485	?9334.716	?9163.342	?9521.124	61.640	0.552	77	328
		mdp8	500	?9334.716	?9163.342	?9521.124	61.640	0.235	77	619
		mll8	499	?9334.716	?9163.342	?9521.124	61.640	0.203	54	609
		mcomp6	492	?9334.716	?9163.342	?9521.124	61.640	0.205	52	320
		mcomp8	500	?9334.716	?9163.342	?9521.124	61.640	0.235	77	619
	1000	Gdp8	500	?18731.384	?18516.735	?19016.929	93.430	0.682	65	95
		Gll8	500	?18731.384	?18516.735	?19016.929	93.430	0.574	47	66
		Gcomp8	500	?18731.384	?18516.735	?19016.929	93.430	0.682	65	95
		mdp8	500	?18731.384	?18516.735	?19016.929	93.430	0.315	64	95
		mll8	500	?18731.384	?18516.735	?19016.929	93.430	0.266	46	66
		mcomp6	498	?18731.384	?18516.735	?19016.929	93.430	0.263	44	64
		mcomp8	500	?18731.384	?18516.735	?19016.929	93.430	0.315	64	95
	4000	Gdp8	500	?75137.975	?74638.007	?75645.526	185.720	1.998	60	71
		Gll8	500	?75137.975	?74638.007	?75645.526	185.720	1.811	48	55
		Gcomp8	500	?75137.975	?74638.007	?75645.526	185.720	1.993	60	71
		mdp8	500	?75137.975	?74638.007	?75645.526	185.720	1.463	58	72
		mll8	500	?75137.975	?74638.007	?75645.526	185.720	1.210	46	56
		mcomp6	489	?75137.975	?74638.007	?75645.526	185.720	1.108	39	50
		mcomp8	500	?75137.975	?74638.007	?75645.526	185.720	1.457	58	72
hierarchical	500	Gcomp8	83	?8944.542	?8746.172	?9101.048	63.686	0.823	143	4521
		mdp8	416	?8944.529	?8746.349	?9100.836	63.714	0.309	162	3678
		mll8	417	?8944.529	?8746.349	?9100.836	63.714	0.241	109	1701
		mcomp6	390	?8944.531	?8746.349	?9100.836	63.713	0.240	101	1575
		mcomp8	417	?8944.529	?8746.349	?9100.836	63.714	0.310	163	3678
	1000	Gcomp8	44	?17941.473	?17692.040	?18203.752	96.770	1.375	179	6530
		mdp8	456	?17941.322	?17692.038	?18205.384	96.780	0.607	218	12877
		mll8	452	?17941.322	?17692.038	?18205.384	96.780	0.411	124	1840
		mcomp6	408	?17941.322	?17692.038	?18205.384	96.780	0.420	115	3035
		mcomp8	456	?17941.322	?17692.038	?18205.384	96.780	0.610	219	12877
	4000	Gcomp8	51	?71973.595	?71443.652	?72679.347	198.161	7.854	278	7908

Table 3 Simulation results for J = 32

Data generating model	N	Convergence criterion	$LL_{Best}$	$LL_{Bean}$	$LL_{max}$	$LL_{min}$	$LL_{sd}$	$t_{mean}$	$Itr_{mean}$	$Itr_{max}$
Saturated	500	Gdp8	485	?9334.716	?9163.342	?9521.124	61.640	0.551	77	311
		Gll8	484	?9334.716	?9163.342	?9521.124	61.640	0.452	53	328
		Gcomp8	485	?9334.716	?9163.342	?9521.124	61.640	0.552	77	328
		mdp8	500	?9334.716	?9163.342	?9521.124	61.640	0.235	77	619
		mll8	499	?9334.716	?9163.342	?9521.124	61.640	0.203	54	609
		mcomp6	492	?9334.716	?9163.342	?9521.124	61.640	0.205	52	320
		mcomp8	500	?9334.716	?9163.342	?9521.124	61.640	0.235	77	619
	1000	Gdp8	500	?18731.384	?18516.735	?19016.929	93.430	0.682	65	95
		Gll8	500	?18731.384	?18516.735	?19016.929	93.430	0.574	47	66
		Gcomp8	500	?18731.384	?18516.735	?19016.929	93.430	0.682	65	95
		mdp8	500	?18731.384	?18516.735	?19016.929	93.430	0.315	64	95
		mll8	500	?18731.384	?18516.735	?19016.929	93.430	0.266	46	66
		mcomp6	498	?18731.384	?18516.735	?19016.929	93.430	0.263	44	64
		mcomp8	500	?18731.384	?18516.735	?19016.929	93.430	0.315	64	95
	4000	Gdp8	500	?75137.975	?74638.007	?75645.526	185.720	1.998	60	71
		Gll8	500	?75137.975	?74638.007	?75645.526	185.720	1.811	48	55
		Gcomp8	500	?75137.975	?74638.007	?75645.526	185.720	1.993	60	71
		mdp8	500	?75137.975	?74638.007	?75645.526	185.720	1.463	58	72
		mll8	500	?75137.975	?74638.007	?75645.526	185.720	1.210	46	56
		mcomp6	489	?75137.975	?74638.007	?75645.526	185.720	1.108	39	50
		mcomp8	500	?75137.975	?74638.007	?75645.526	185.720	1.457	58	72
hierarchical	500	Gcomp8	83	?8944.542	?8746.172	?9101.048	63.686	0.823	143	4521
		mdp8	416	?8944.529	?8746.349	?9100.836	63.714	0.309	162	3678
		mll8	417	?8944.529	?8746.349	?9100.836	63.714	0.241	109	1701
		mcomp6	390	?8944.531	?8746.349	?9100.836	63.713	0.240	101	1575
		mcomp8	417	?8944.529	?8746.349	?9100.836	63.714	0.310	163	3678
	1000	Gcomp8	44	?17941.473	?17692.040	?18203.752	96.770	1.375	179	6530
		mdp8	456	?17941.322	?17692.038	?18205.384	96.780	0.607	218	12877
		mll8	452	?17941.322	?17692.038	?18205.384	96.780	0.411	124	1840
		mcomp6	408	?17941.322	?17692.038	?18205.384	96.780	0.420	115	3035
		mcomp8	456	?17941.322	?17692.038	?18205.384	96.780	0.610	219	12877
	4000	Gcomp8	51	?71973.595	?71443.652	?72679.347	198.161	7.854	278	7908

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[4]	LUO-Huan,DING Shu-Liang,WANG Wen-Yi,YU Xiao-Feng,CAO Hui-Yuan. Attribute Hierarchy Method Based on Graded Response Model with Different Scoring-Weight for Attributes [J]. , 2010, 42(04): 528-538.