Bayesian Estimation of Attribute Hierarchy for Cognitive Diagnosis Models

IF 1.9 3区心理学 Q2 EDUCATION & EDUCATIONAL RESEARCH Journal of Educational and Behavioral Statistics Pub Date : 2023-06-13 DOI:10.3102/10769986231174918

Yinghan Chen, Shiyu Wang

引用次数: 1

Abstract

Attribute hierarchy, the underlying prerequisite relationship among attributes, plays an important role in applying cognitive diagnosis models (CDM) for designing efficient cognitive diagnostic assessments. However, there are limited statistical tools to directly estimate attribute hierarchy from response data. In this study, we proposed a Bayesian formulation for attribute hierarchy within CDM framework and developed an efficient Metropolis within Gibbs algorithm to estimate the underlying hierarchy along with the specified CDM parameters. Our proposed estimation method is flexible and can be adapted to a general class of CDMs. We demonstrated our proposed method via a simulation study, and the results from which show that the proposed method can fully recover or estimate at least a subgraph of the underlying structure across various conditions under a specified CDM model. The real data application indicates the potential of learning attribute structure from data using our algorithm and validating the existing attribute hierarchy specified by content experts.

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认知诊断模型属性层次的贝叶斯估计

属性层次是属性之间潜在的前提关系，在应用认知诊断模型设计高效的认知诊断评估中起着重要作用。然而，从响应数据中直接估计属性层次的统计工具有限。在本研究中，我们提出了CDM框架中属性层次的贝叶斯公式，并开发了一种高效的Metropolis within Gibbs算法来估计底层层次以及指定的CDM参数。我们提出的估计方法是灵活的，可以适用于一般类型的cdm。我们通过模拟研究证明了我们提出的方法，结果表明，在特定的CDM模型下，所提出的方法可以在各种条件下完全恢复或估计至少一个底层结构的子图。实际数据应用表明，使用我们的算法从数据中学习属性结构并验证由内容专家指定的现有属性层次结构的潜力。

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来源期刊

Journal of Educational and Behavioral Statistics Multiple-

CiteScore

4.40

自引率

4.20%

发文量

期刊介绍： Journal of Educational and Behavioral Statistics, sponsored jointly by the American Educational Research Association and the American Statistical Association, publishes articles that are original and provide methods that are useful to those studying problems and issues in educational or behavioral research. Typical papers introduce new methods of analysis. Critical reviews of current practice, tutorial presentations of less well known methods, and novel applications of already-known methods are also of interest. Papers discussing statistical techniques without specific educational or behavioral interest or focusing on substantive results without developing new statistical methods or models or making novel use of existing methods have lower priority. Simulation studies, either to demonstrate properties of an existing method or to compare several existing methods (without providing a new method), also have low priority. The Journal of Educational and Behavioral Statistics provides an outlet for papers that are original and provide methods that are useful to those studying problems and issues in educational or behavioral research. Typical papers introduce new methods of analysis, provide properties of these methods, and an example of use in education or behavioral research. Critical reviews of current practice, tutorial presentations of less well known methods, and novel applications of already-known methods are also sometimes accepted. Papers discussing statistical techniques without specific educational or behavioral interest or focusing on substantive results without developing new statistical methods or models or making novel use of existing methods have lower priority. Simulation studies, either to demonstrate properties of an existing method or to compare several existing methods (without providing a new method), also have low priority.