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Acta Psychologica Sinica
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A Simple Cognitive Diagnosis Method Based on Q-Matrix Theory
LUO Zhaosheng; LI Yujun; YU Xiaofeng; GAO Chunlei; PENG Yafeng
(School of Psychology, Jiangxi Normal University, Nanchang 330022, China)
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Abstract  

Cognitive diagnosis has recently gained prominence in educational assessment, psychiatric evaluation, and many other fields. Researchers have been trying their best to develop a new Cognitive Diagnosis Model (CDM) or to improve existing ones’ performance for respondent classification. As a new CDM, GDD (Sun, Zhang, Xin, & Bao, 2011) receives more and more attention due to its classification accuracy which is as high as DINA. This article introduces a new approach called Hamming Distance Discrimination (HDD) which is inspired by GDD and based on the Q-matrix theory (Tatsuoka, 1991) modified by Leighton et al. (2004) and Ding et al. (2009, 2010). HDD uses Hamming Distance (HD) to measure the distance between an examinee’s Observed Response Pattern (ORP) and an Expected Response Pattern (ERP). When there are more than one ERPs with the same minimum HD for an examinee’s ORP, two solutions based on HD are proposed: the random method (Method R) and the Bayesian method (Method B). Method R randomly chooses one ERP from those share the same minimum HD whereas in method B, we apply Bayesian Discriminant to distinguish which ERP the examinee belongs to. Monte Carlo simulation was used to compare the accuracy of respondent classification between HDD and GDD. In the Monte Carlo simulation study, the pattern match ratio and average attribute match ratio were used as criteria to evaluate the classification accuracy of GDD and HDD. Five attribute hierarchical structures in attribute hierarchical model (AHM) of Leighton et al. (2004) and Tatsuoka (1995, 2009) with 6 attributes were simulated. Under each type of Q-matrix, we set the slip at four levels (2%, 5%, 10%, 15%) to simulate ORPs of examinees (N=1000). The results of this study demonstrate that HDD is superior, especially under the unstructured hierarchy and independent structure. Moreover, method B presented higher classification accuracy than method R. Further research on HDD’s validity and performance in other situations is warranted.

Keywords GDD      Q-matrix      knowledge states      Hamming Distance     
Corresponding Authors: LI Yujun, E-mail: pheebie2008@163.com    
Issue Date: 25 February 2015
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LUO Zhaosheng
LI Yujun
YU Xiaofeng
GAO Chunlei
PENG Yafeng
Cite this article:   
LUO Zhaosheng,LI Yujun,YU Xiaofeng, et al. A Simple Cognitive Diagnosis Method Based on Q-Matrix Theory[J]. Acta Psychologica Sinica, 10.3724/SP.J.1041.2015.00264
URL:  
http://journal.psych.ac.cn/xlxb/EN/10.3724/SP.J.1041.2015.00264     OR     http://journal.psych.ac.cn/xlxb/EN/Y2015/V47/I2/264
[1] YU Xiaofeng; LUO Zhaosheng; QIN Chunying; GAO Chunlei; LI Yujun. Joint Estimation of Model Parameters and Q-Matrix Based on Response Data[J]. Acta Psychologica Sinica, 2015, 47(2): 273-282.
[2] TU Dong-Bo,CAI Yan,DAI Hai-Qi. A New Method of Q-matrix Validation Based on DINA Model[J]. , 2012, 44(4): 558-568.
[3] TU Dong-Bo;CAI Yan;DAI Hai-Qi;DING Shu-Liang. A New Multiple-Strategies Cognitive Diagnosis Model: the MSCD Method[J]. Acta Psychologica Sinica, 2012, 44(11): 1547-1553.
[4] SUN Jia-Nan,ZHANG Shu-Mei,XIN Tao,BAO Yu. A Cognitive Diagnosis Method Based on Q-Matrix and Generalized Distance[J]. , 2011, 43(09): 1095-1102.
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