基于DINA模型的Q矩阵修正方法

A New Method of Q-matrix Validation Based on DINA Model

本研究开发了一种基于DINA模型的认知诊断测验Q矩阵修正方法——γ法,为侦查并修正Q矩阵中的错误提供方法学支持,从而为保证Q矩阵的合理性提供基础,并为进一步提高认知诊断的准确率服务。本文采用MonteCarlo模拟及与国外同类研究相比较的方法进行,研究发现:(1)不论在何种作答失误概率(5%,10%,15%)情况下,当s,g临界值为0.2,0.25或0.3时,本研究提出的γ法均能有效地修正错误Q矩阵;同时,当Q矩阵无错误时,γ法对该Q矩阵未做任何修改。表明γ法对Q矩阵是否存在错误具有较强的识别能力及修正能力。(2)与国外同类研究相比,本研究提出的γ法具有较理想的修正率,且与delaTorre(2008)提出δ法的修正效果相当。但相比较而言,γ法较δ法更为简单。(3)γ法不仅能有效地修正错误的Q矩阵,而且还可以进一步提高认知诊断的正确率,尤其是对模式判准率(PMR),诊断正确率的最高增幅高达40%,大大改善了认知诊断的准确率。

Recently more and more attentions were paid on cognitive diagnosis （CD）. The recognition of Q matrix was the basis and proposition of CD, and it was the only information media about cognitive attributes and test items. Only if it was recognized correctly, then the following cognitive analysis might be reliable. This paper developed a new modification method of Q matrix （called γmethod） based on DINA model. The method could detect and modify the mistakes on Q matrix that could make the Q matrix rationally and promote the correct match ratio of CD. Monte Carlo simulation method was use here, and some comparisons with western similar studies were done. Findings showed： （1） Under any response slip probability （5%, 10%, 15%） context, when the critical value of parameters s and g was set to be 0.2, 0.25 or 0.3, γmethod could modify the mistakes of Q matrix efficiently. When Q matrix was recognized correctly, no modification will be done by γmethod. These indicated that γmethod could work well on recognition and modification on Q matrix whether it has mistakes or not. （2） Compared to the similar western studies, the correct modification ratio of γmethod was relatively great and similar with the consequences of δmethod suggested by de la Tarre （2008）. But γmethod was simpler than δ method. （3） The γmethod could not only rectify the mistakes of Q matrix efficiently but also promote the correct match ratio of CD. Especially the correct match ratio of PMR increased greater than 40% which was a wonderful work.