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Mutual Information Item Selection Method in Cognitive Diagnostic Computerized Adaptive Testing With Short Test Length

机译：测试长度短的认知诊断计算机自适应测试中的互信息项选择方法

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摘要

Cognitive diagnostic computerized adaptive testing (CD-CAT) purports to combine the strengths of both CAT and cognitive diagnosis. Cognitive diagnosis models aim at classifying examinees into the correct mastery profile group so as to pinpoint the strengths and weakness of each examinee whereas CAT algorithms choose items to determine those strengths and weakness as efficiently as possible. Most of the existing CD-CAT item selection algorithms are evaluated when test length is relatively long whereas several applications of CD-CAT, such as in interim assessment, require an item selection algorithm that is able to accurately recover examinees' mastery profile with short test length. In this article, we introduce the mutual information item selection method in the context of CD-CAT and then provide a computationally easier formula to make the method more amenable in real time. Mutual information is then evaluated against common item selection methods, such as Kullback-Leibler information, posterior weighted Kullback-Leibler information, and Shannon entropy. Based on our simulations, mutual information consistently results in nearly the highest attribute and pattern recovery rate in more than half of the conditions. We conclude by discussing how the number of attributes, Q-matrix structure, correlations among the attributes, and item quality affect estimation accuracy.
机译：认知诊断计算机自适应测试（CD-CAT）旨在结合CAT和认知诊断的优势。认知诊断模型旨在将考生分类到正确的掌握档案组中，以查明每个考生的长处和短处，而CAT算法选择项目以尽可能有效地确定这些长处和短处。大多数现有的CD-CAT项目选择算法都是在测试长度相对较长时进行评估的，而CD-CAT的多种应用（例如在中期评估中）则需要一种能够在短时间测试中准确恢复被测者的掌握状况的项目选择算法。长度。在本文中，我们在CD-CAT的背景下介绍了互信息项选择方法，然后提供了一个计算上更容易的公式，以使该方法更易于实时使用。然后，根据常见的项目选择方法（如Kullback-Leibler信息，后加权Kullback-Leibler信息和Shannon熵）评估互信息。根据我们的模拟，在一半以上的条件下，相互信息始终会导致几乎最高的属性和模式恢复率。我们通过讨论属性的数量，Q矩阵结构，属性之间的相关性以及项目质量如何影响估计准确性来得出结论。

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