Department of Educational Psychology and Counseling, National Taiwan Normal University, 162, Section 1, Heping E. Road, 10610, Taipei, Taiwan.
Centre for Educational Measurement, University of Oslo, Oslo, Norway.
Psychometrika. 2020 Jun;85(2):322-357. doi: 10.1007/s11336-020-09707-4. Epub 2020 Jul 6.
In diagnostic classification models (DCMs), the Q matrix encodes in which attributes are required for each item. The Q matrix is usually predetermined by the researcher but may in practice be misspecified which yields incorrect statistical inference. Instead of using a predetermined Q matrix, it is possible to estimate it simultaneously with the item and structural parameters of the DCM. Unfortunately, current methods are computationally intensive when there are many attributes and items. In addition, the identification constraints necessary for DCMs are not always enforced in the estimation algorithms which can lead to non-identified models being considered. We address these problems by simultaneously estimating the item, structural and Q matrix parameters of the Deterministic Input Noisy "And" gate model using a constrained Metropolis-Hastings Robbins-Monro algorithm. Simulations show that the new method is computationally efficient and can outperform previously proposed Bayesian Markov chain Monte-Carlo algorithms in terms of Q matrix recovery, and item and structural parameter estimation. We also illustrate our approach using Tatsuoka's fraction-subtraction data and Certificate of Proficiency in English data.
在诊断分类模型 (DCM) 中，Q 矩阵编码了每个项目所需的哪些属性。Q 矩阵通常由研究人员预先确定，但在实际应用中可能会出现指定错误，从而导致不正确的统计推断。与其使用预先确定的 Q 矩阵，不如同时估计 DCM 的项目和结构参数。不幸的是，当属性和项目很多时，当前的方法计算量很大。此外，估计算法中并不总是强制实施 DCM 所需的识别约束，这可能导致考虑未识别的模型。我们通过使用受限的 Metropolis-Hastings Robbins-Monro 算法同时估计确定性输入噪声“与”门模型的项目、结构和 Q 矩阵参数来解决这些问题。模拟结果表明，新方法计算效率高，在 Q 矩阵恢复以及项目和结构参数估计方面，可以优于以前提出的贝叶斯马尔可夫链蒙特卡罗算法。我们还使用 Tatsuoka 的分数减法数据和英语能力证书数据说明了我们的方法。
