Recognizing Uncertainty in the Q-Matrix via a Bayesian Extension of the DINA Model
Recognizing Uncertainty in the Q-Matrix via a Bayesian Extension of the DINA Model
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DOI：
10.1177/0146621612449069
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发表时间：
2012-09-01
影响因子：
1.2
通讯作者：
DeCarlo, Lawrence T.
中科院分区：
文献类型：
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作者：
DeCarlo, Lawrence T.
在认知诊断模型的典型应用中，Q 矩阵被假设为已知，该矩阵反映了与项目所指示的技能相关的理论。然而，Q 矩阵通常由专家判断确定，因此其某些元素可能存在不确定性。这里表明，这种不确定性可以通过 DINA（确定性输入噪声）模型的贝叶斯扩展来识别和探索。使用的方法是将 Q 矩阵的某些元素指定为随机的而不是固定的；然后可以使用后验分布来获取有关 Q 矩阵中是否包含有问题的元素的信息。仿真表明，当某些元素存在不确定性时，这种方法有助于恢复真实的 Q 矩阵。 K. K. Tatsuoka 对分数减法数据的应用提出了一种改进的 Q 矩阵，可以提供改进的相对拟合。
In the typical application of a cognitive diagnosis model, the Q-matrix, which reflects the theory with respect to the skills indicated by the items, is assumed to be known. However, the Q-matrix is usually determined by expert judgment, and so there can be uncertainty about some of its elements. Here it is shown that this uncertainty can be recognized and explored via a Bayesian extension of the DINA (deterministic input noisy and) model. The approach used is to specify some elements of the Q-matrix as being random rather than as fixed; posterior distributions can then be used to obtain information about elements whose inclusion in the Q-matrix is questionable. Simulations show that this approach helps to recover the true Q-matrix when there is uncertainty about some elements. An application to the fraction-subtraction data of K. K. Tatsuoka suggests a modified Q-matrix that gives improved relative fit.