Department of Statistics, University of Illinois at Urbana-Champaign, 725 South Wright Street, Champaign, IL, 61820, USA.
Psychometrika. 2019 Jun;84(2):333-357. doi: 10.1007/s11336-018-9643-8. Epub 2018 Nov 19.
Cognitive diagnosis models (CDMs) are an important psychometric framework for classifying students in terms of attribute and/or skill mastery. The [Formula: see text] matrix, which specifies the required attributes for each item, is central to implementing CDMs. The general unavailability of [Formula: see text] for most content areas and datasets poses a barrier to widespread applications of CDMs, and recent research accordingly developed fully exploratory methods to estimate Q. However, current methods do not always offer clear interpretations of the uncovered skills and existing exploratory methods do not use expert knowledge to estimate Q. We consider Bayesian estimation of [Formula: see text] using a prior based upon expert knowledge using a fully Bayesian formulation for a general diagnostic model. The developed method can be used to validate which of the underlying attributes are predicted by experts and to identify residual attributes that remain unexplained by expert knowledge. We report Monte Carlo evidence about the accuracy of selecting active expert-predictors and present an application using Tatsuoka's fraction-subtraction dataset.
认知诊断模型（CDMs）是一种重要的心理计量学框架，可用于根据属性和/或技能掌握情况对学生进行分类。[公式：见文本]矩阵指定了每个项目所需的属性，是实施 CDMs 的核心。对于大多数内容领域和数据集，[公式：见文本]通常不可用，这对 CDMs 的广泛应用构成了障碍，因此最近的研究开发了完全探索性的方法来估计 Q。然而，当前的方法并不总是提供对发现的技能的清晰解释，并且现有的探索性方法没有利用专家知识来估计 Q。我们考虑使用基于专家知识的先验进行[公式：见文本]的贝叶斯估计，使用一般诊断模型的完全贝叶斯公式。所开发的方法可用于验证专家预测的基础属性，以及识别仍无法用专家知识解释的剩余属性。我们报告了关于选择活动专家预测因子的准确性的蒙特卡罗证据，并展示了使用 Tatsuoka 的分数减法数据集的应用。
