Identifiability of Hidden Markov Models for Learning Trajectories in Cognitive Diagnosis
Identifiability of Hidden Markov Models for Learning Trajectories in Cognitive Diagnosis
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DOI：
10.1007/s11336-023-09904-x
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发表时间：
2023-02-16
期刊：
影响因子：
3
通讯作者：
Chen, Yuguo
中科院分区：
文献类型：
--
作者：
Liu, Ying;Culpepper, Steven Andrew;Chen, Yuguo
隐马尔可夫模型（Hidden Markov Model，HMM）已应用于各个领域，这使得隐马尔可夫模型的可识别性问题受到研究人员的普遍关注。经典的可识别性条件在以往的研究中显示，太强的实际分析。本文提出了有限状态空间离散时间系统的一般可辨识性条件。此外，最近关于认知诊断模型（CDM）的研究应用一阶障碍来跟踪与学习相关的属性的变化。然而，CDM的应用需要一个已知的Q矩阵来推断潜在属性和项目之间的潜在结构，模型参数的可识别性约束也应该被指定。我们提出了通用的可识别性约束我们的限制HMM，然后估计模型参数，包括Q矩阵，通过贝叶斯框架。我们提出的Monte Carlo模拟结果来支持我们的结论，并将开发的模型应用到一个真实的数据集。
Hidden Markov models (HMMs) have been applied in various domains, which makes the identifiability issue of HMMs popular among researchers. Classical identifiability conditions shown in previous studies are too strong for practical analysis. In this paper, we propose generic identifiability conditions for discrete time HMMs with finite state space. Also, recent studies about cognitive diagnosis models (CDMs) applied first-order HMMs to track changes in attributes related to learning. However, the application of CDMs requires a known Q matrix to infer the underlying structure between latent attributes and items, and the identifiability constraints of the model parameters should also be specified. We propose generic identifiability constraints for our restricted HMM and then estimate the model parameters, including the Q matrix, through a Bayesian framework. We present Monte Carlo simulation results to support our conclusion and apply the developed model to a real dataset.