Department of Mathematics & Statistics, University of Nevada, Reno, 1664 N. Virginia Street, Reno, NV, 89557 , USA.
Department of Statistics, University of Illinois at Urbana-Champaign, 725 South Wright Street, Champaign, IL, 61820 , USA.
Psychometrika. 2018 Mar;83(1):89-108. doi: 10.1007/s11336-017-9579-4. Epub 2017 Aug 31.
Cognitive diagnosis models are partially ordered latent class models and are used to classify students into skill mastery profiles. The deterministic inputs, noisy "and" gate model (DINA) is a popular psychometric model for cognitive diagnosis. Application of the DINA model requires content expert knowledge of a Q matrix, which maps the attributes or skills needed to master a collection of items. Misspecification of Q has been shown to yield biased diagnostic classifications. We propose a Bayesian framework for estimating the DINA Q matrix. The developed algorithm builds upon prior research (Chen, Liu, Xu, & Ying, in J Am Stat Assoc 110(510):850-866, 2015) and ensures the estimated Q matrix is identified. Monte Carlo evidence is presented to support the accuracy of parameter recovery. The developed methodology is applied to Tatsuoka's fraction-subtraction dataset.
认知诊断模型是部分有序潜在类别模型，用于将学生分类为技能掌握情况。确定性输入、噪声“与”门模型（DINA）是认知诊断的一种流行心理测量模型。DINA 模型的应用需要 Q 矩阵的内容专家知识，该矩阵映射掌握一组项目所需的属性或技能。已经表明，Q 的错误指定会导致有偏差的诊断分类。我们提出了一种用于估计 DINA Q 矩阵的贝叶斯框架。所开发的算法基于先前的研究（Chen、Liu、Xu 和 Ying，在 J Am Stat Assoc 110(510):850-866，2015），并确保估计的 Q 矩阵是可识别的。提出了蒙特卡罗证据来支持参数恢复的准确性。所开发的方法应用于 Tatsuoka 的分数减法数据集。
