In the context of cognitive diagnosis models (CDMs), a Q-matrix reflects the correspondence between attributes and items. The Q-matrix construction process is typically subjective in nature, which may lead to misspecifications. All this can negatively affect the attribute classification accuracy. In response, several methods of empirical Q-matrix validation have been developed. The general discrimination index (GDI) method has some relevant advantages such as the possibility of being applied to several CDMs. However, the estimation of the GDI relies on the estimation of the latent group sizes and success probabilities, which is made with the original (possibly misspecified) Q-matrix. This can be a problem, especially in those situations in which there is a great uncertainty about the Q-matrix specification. To address this, the present study investigates the iterative application of the GDI method, where only one item is modified at each step of the iterative procedure, and the required cutoff is updated considering the new parameter estimates. A simulation study was conducted to test the performance of the new procedure. Results showed that the performance of the GDI method improved when the application was iterative at the item level and an appropriate cutoff point was used. This was most notable when the original Q-matrix misspecification rate was high, where the proposed procedure performed better 96.5% of the times. The results are illustrated using Tatsuoka’s fraction-subtraction data set.

中文翻译：

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使用迭代和动态过程提高 Q 矩阵验证的稳健性。

在认知诊断模型 (CDM) 的背景下，Q 矩阵反映了属性和项目之间的对应关系。Q 矩阵构建过程本质上通常是主观的，这可能会导致错误指定。所有这些都会对属性分类的准确性产生负面影响。为此，开发了几种经验 Q 矩阵验证方法。一般区分指数（GDI）方法具有一些相关的优点，例如可以应用于多个CDM。然而，GDI 的估计依赖于对潜在组大小和成功概率的估计，这是使用原始（可能是错误指定的）Q 矩阵进行的。这可能是一个问题，特别是在 Q 矩阵规范存在很大不确定性的情况下。为了解决这个问题，本研究研究了 GDI 方法的迭代应用，其中迭代过程的每一步仅修改一项，并考虑新的参数估计来更新所需的截止值。进行了模拟研究来测试新程序的性能。结果表明，当应用程序在项目级别进行迭代并使用适当的截止点时，GDI 方法的性能会得到改善。当原始 Q 矩阵错误指定率较高时，这一点最为显着，而所提出的程序在 96.5% 的情况下表现更好。结果使用 Tatsuoka 的分数减法数据集进行说明。