An approach that can validate both Q-matrices and attribute hierarchies in cognitive diagnosis models: From the empirical application perspective

doi:10.3724/SP.J.1041.2025.1295

Acta Psychologica Sinica ›› 2025, Vol. 57 ›› Issue (7): 1295-1308.doi: 10.3724/SP.J.1041.2025.1295

• Reports of Empirical Studies • Previous Articles

An approach that can validate both Q-matrices and attribute hierarchies in cognitive diagnosis models: From the empirical application perspective

WANG Ling-Ling¹(), SUN Xiao-Jian²

¹School of Educational Science, Shenyang Normal University, Shenyang 110034, China
²College of Teacher Education, Southwest University, Chongqing 400715, China

Published:2025-07-25 Online:2025-04-24
Contact: WANG Ling-Ling, E-mail: wling-007@163.com

WANG Ling-Ling, SUN Xiao-Jian. (2025). An approach that can validate both Q-matrices and attribute hierarchies in cognitive diagnosis models: From the empirical application perspective. Acta Psychologica Sinica, 57(7), 1295-1308.

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URL: https://journal.psych.ac.cn/acps/EN/10.3724/SP.J.1041.2025.1295

https://journal.psych.ac.cn/acps/EN/Y2025/V57/I7/1295

Figures/Tables 3

Table 1 Number of completely correct corrections for both hierarchies in attribute redundancy scenario (run 100 times)

Attribute redundancy			divergent		unstructured
Q-error	test length	g-s	2000	1000	2000	1000
0%	25	0.05-0.25	100	100	100	100
	25	0.05-0.4	100	100	100	100
	40	0.05-0.25	100	100	100	100
	40	0.05-0.4	100	100	100	100
10%	25	0.05-0.25	98	98	100	98
	25	0.05-0.4	96	92	99	86
	40	0.05-0.25	100	100	100	93
	40	0.05-0.4	100	100	100	90
20%	25	0.05-0.25	90	89	90	89
	25	0.05-0.4	82	64	83	49
	40	0.05-0.25	100	95	100	87
	40	0.05-0.4	95	93	90	80
30%	25	0.05-0.25	64	60	63	57
	25	0.05-0.4	60	54	49	46
	40	0.05-0.25	80	75	90	80
	40	0.05-0.4	80	65	58	55

Table 1 Number of completely correct corrections for both hierarchies in attribute redundancy scenario (run 100 times)

Attribute redundancy			divergent		unstructured
Q-error	test length	g-s	2000	1000	2000	1000
0%	25	0.05-0.25	100	100	100	100
	25	0.05-0.4	100	100	100	100
	40	0.05-0.25	100	100	100	100
	40	0.05-0.4	100	100	100	100
10%	25	0.05-0.25	98	98	100	98
	25	0.05-0.4	96	92	99	86
	40	0.05-0.25	100	100	100	93
	40	0.05-0.4	100	100	100	90
20%	25	0.05-0.25	90	89	90	89
	25	0.05-0.4	82	64	83	49
	40	0.05-0.25	100	95	100	87
	40	0.05-0.4	95	93	90	80
30%	25	0.05-0.25	64	60	63	57
	25	0.05-0.4	60	54	49	46
	40	0.05-0.25	80	75	90	80
	40	0.05-0.4	80	65	58	55

Table 2 Correction accuracy of Q matrix in attribute redundancy Scenarios (PCR and AACR)

			PCR of Attribute redundancy				AACR of Attribute redundancy
			divergent		unstructured		divergent		unstructured
Q-error	test length	g-s	2000	1000	2000	1000	2000	1000	2000	1000
10%	25	0.05-0.25	0.929	0.861	0.909	0.854	0.985	0.971	0.982	0.969
	25	0.05-0.4	0.81	0.678	0.826	0.711	0.957	0.929	0.964	0.937
	40	0.05-0.25	0.968	0.909	0.953	0.88	0.993	0.98	0.991	0.976
	40	0.05-0.4	0.876	0.791	0.865	0.783	0.974	0.954	0.973	0.955
20%	25	0.05-0.25	0.867	0.782	0.828	0.755	0.969	0.95	0.958	0.944
	25	0.05-0.4	0.651	0.761	0.704	0.504	0.909	0.944	0.928	0.876
	40	0.05-0.25	0.936	0.868	0.93	0.81	0.986	0.97	0.986	0.958
	40	0.05-0.4	0.814	0.695	0.8	0.703	0.955	0.925	0.958	0.935
30%	25	0.05-0.25	0.681	0.595	0.612	0.534	0.908	0.883	0.883	0.871
	25	0.05-0.4	0.502	0.581	0.449	0.254	0.852	0.88	0.827	0.772
	40	0.05-0.25	0.855	0.719	0.858	0.718	0.96	0.926	0.967	0.926
	40	0.05-0.4	0.616	0.575	0.61	0.478	0.891	0.884	0.887	0.854

Table 2 Correction accuracy of Q matrix in attribute redundancy Scenarios (PCR and AACR)

			PCR of Attribute redundancy				AACR of Attribute redundancy
			divergent		unstructured		divergent		unstructured
Q-error	test length	g-s	2000	1000	2000	1000	2000	1000	2000	1000
10%	25	0.05-0.25	0.929	0.861	0.909	0.854	0.985	0.971	0.982	0.969
	25	0.05-0.4	0.81	0.678	0.826	0.711	0.957	0.929	0.964	0.937
	40	0.05-0.25	0.968	0.909	0.953	0.88	0.993	0.98	0.991	0.976
	40	0.05-0.4	0.876	0.791	0.865	0.783	0.974	0.954	0.973	0.955
20%	25	0.05-0.25	0.867	0.782	0.828	0.755	0.969	0.95	0.958	0.944
	25	0.05-0.4	0.651	0.761	0.704	0.504	0.909	0.944	0.928	0.876
	40	0.05-0.25	0.936	0.868	0.93	0.81	0.986	0.97	0.986	0.958
	40	0.05-0.4	0.814	0.695	0.8	0.703	0.955	0.925	0.958	0.935
30%	25	0.05-0.25	0.681	0.595	0.612	0.534	0.908	0.883	0.883	0.871
	25	0.05-0.4	0.502	0.581	0.449	0.254	0.852	0.88	0.827	0.772
	40	0.05-0.25	0.855	0.719	0.858	0.718	0.96	0.926	0.967	0.926
	40	0.05-0.4	0.616	0.575	0.61	0.478	0.891	0.884	0.887	0.854

Table 3 The fitting index of the model modified by BN to empirical data

Attribute hierarchy	Q matrix	BIC
a→b→c	original	43815.53
a→c, b→c	BN revised	44071.94
a→b→c	BN revised	43724.51

Table 3 The fitting index of the model modified by BN to empirical data

Attribute hierarchy	Q matrix	BIC
a→b→c	original	43815.53
a→c, b→c	BN revised	44071.94
a→b→c	BN revised	43724.51

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