在隐藏的马尔科夫诊断分类模型中的动态Q矩阵和属性轨迹的贝叶斯推理.
1Department of Educational Psychology and Counseling, National Taiwan Normal University, Taipei, Taiwan.
The British journal of mathematical and statistical psychology
|January 21, 2026
概括
本研究介绍了隐藏马尔科夫诊断分类模型的贝叶斯算法,使得随着时间的推移可以跟踪学生的学习. 新方法准确地估计了纵向教育评估的关键参数.
科学领域:
- 教育测量和心理测量学
- 认知科学 认知科学
- 统计建模 统计建模
背景情况:
- 传统的诊断分类模型 (DCM) 提供了对学生知识的洞察力,但往往缺乏纵向跟踪能力.
- 了解认知属性的时间动态对于有效的,适应性的指导和评估至关重要.
- 现有的方法可能无法充分捕捉学生掌握在多次评估场合的不断变化的性质.
研究的目的:
- 为诊断分类模型 (DCM) 引入一个新的贝叶斯马尔科夫链蒙特卡洛 (MCMC) 算法.
- 为了能够共同估计时间变化的参数,包括Q矩阵,潜伏属性,项目参数和过渡矩阵.
- 为纵向诊断分类提供强大的计算工具.
主要方法:
- 开发一个针对时间变化的DCM量身定制的贝叶斯式MCMC算法.
- 在一个新的R包"hmdcm"中实现算法.
- 通过蒙特卡洛模拟验证参数恢复和经验评估轨迹跟踪.
主要成果:
- 蒙特卡洛模拟表明,在拟议的算法下,模型参数的准确恢复.
- 该算法在经验概率概念评估中成功追踪了属性轨迹.
- "hmdcm" R包为实施开发的方法提供了一个功能性工具.
结论:
- 提出的贝叶斯式MCMC算法为纵向诊断分类提供了一个强大的方法.
- 精确的参数估计和属性轨迹追踪支持其在研究和教育实践中的实用性.
- 这种方法提高了对随着时间推移认知属性的演变进行建模和理解的能力.
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