The Sufficient and Necessary Condition for the Identifiability and Estimability of the DINA Model
The Sufficient and Necessary Condition for the Identifiability and Estimability of the DINA Model
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DOI：
10.1007/s11336-018-9619-8
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发表时间：
2019-06-01
期刊：
影响因子：
3
通讯作者：
Xu, Gongjun
中科院分区：
文献类型：
--
作者：
Gu, Yuqi;Xu, Gongjun
认知诊断模型（CDMs）是认知诊断评估中有用的统计工具。然而，与许多其他潜在变量模型一样，cdm经常遭受不可识别性问题的困扰。这项工作为基本DINA模型的可识别性提供了充分和必要的条件，这不仅解决了Xu和Zhang （Psychometrika 81:625-649, 2016）关于可识别性最低要求的开放性问题，而且还为更一般的cdm的研究提供了启发，这些cdm通常将DINA作为一子模型。此外，我们还证明了可辨识条件保证了模型参数估计的一致性。从实际应用的角度来看，可辨识性条件仅依赖于q矩阵结构，且易于验证，这将为设计统计有效和可估计的认知诊断测试提供指导。
Cognitive diagnosis models (CDMs) are useful statistical tools in cognitive diagnosis assessment. However, as many other latent variable models, the CDMs often suffer from the non-identifiability issue. This work gives the sufficient and necessary condition for identifiability of the basic DINA model, which not only addresses the open problem in Xu and Zhang (Psychometrika 81:625-649, 2016) on the minimal requirement for identifiability, but also sheds light on the study of more general CDMs, which often cover DINA as a submodel. Moreover, we show the identifiability condition ensures the consistent estimation of the model parameters. From a practical perspective, the identifiability condition only depends on the Q-matrix structure and is easy to verify, which would provide a guideline for designing statistically valid and estimable cognitive diagnosis tests.