Bayesian Inference for Attribute Hierarchy in Cognitive Diagnosis Models

本研究项目将在认知诊断模型(CDM)的框架内提出属性层次估计和推理的统计方法。CDMS已广泛应用于教育评价、精神病学诊断等社会科学领域。与诊断评估相结合，这种类型的模型使用受试者对专门设计的诊断项目的观察反应来确定潜在属性模式的细粒度分类。属性层次，或属性之间的关系，在设计有效的诊断评估中起着重要作用。然而，缺乏有效的统计工具来从观测数据中估计属性层次。该项目将开发一系列用于估计属性层次的贝叶斯方法。该项目将为新开发的将人工智能与心理测量学相结合的跨学科领域做出贡献。新方法将对教育和心理学以及其他社会科学学科的应用研究有用。研究人员将把新方法应用于教育数据集。研究生将参与这项研究的进行，并将开发公开可用的软件。这一研究项目将为静态和动态清洁发展机制模型开发属性层次的贝叶斯推理，并促进CDMS与属性层次的结合使用，以促进学习。该项目将解决以下方面的主要研究问题：1)静态和动态CDM的贝叶斯框架的形成；2)从这两个设置中的观测数据直接学习属性层次的方法的发展。对于静态CDM，将使用一系列新的贝叶斯估计方法来直接估计属性层次，并显式地强制属性模式的允许性。随机过程和不可约转移将被创建以确保所提出算法的收敛。该项目还将考虑随机搜索变量选择方法来估计CDM满足合取假设时的属性层次。静态疾病预防控制模型的新方法将扩展到在动态疾病预防控制措施框架下对实践中的学习过程进行建模和推理。一组模拟研究将用于评估新方法，这些方法将应用于两个空间旋转学习数据集。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This research project will advance statistical methods for estimation and inference on attribute hierarchy within the framework of cognitive diagnosis models (CDM). CDMs have been widely applied to the field of educational assessment, psychiatric diagnosis, and other social sciences. In conjunction with diagnostic assessments, this type of model uses subjects' observed responses to specifically designed diagnostic items to determine the fine-grained classification of the underlying latent attribute patterns. Attribute hierarchy, or the relationship among attributes, plays an important role in designing an effective diagnostic assessment. However, there is a lack of efficient statistical tools for estimating attribute hierarchy from observed data. This project will develop a series of Bayesian approaches for estimating attribute hierarchy. The project will contribute to the newly developed interdisciplinary field that integrates artificial intelligence with psychometrics. The new methods will be useful for applied research in education and psychology, as well as other social science disciplines. The investigators will apply the new methods to educational data sets. Graduate students will participate in the conduct of this research, and publicly available software will be developed. This research project will develop Bayesian inference on attribute hierarchy for both static and dynamic CDM models and promote the use of CDMs in conjunction with attribute hierarchy to facilitate learning. The project will address major research questions on 1) the formulation of Bayesian framework for static and dynamic CDMs and 2) the development of methods to directly learn attribute hierarchy from the observed data in these two setups. For static CDMs, a series of new Bayesian estimation methods will be employed to directly estimate the attribute hierarchy and explicitly enforce the permissibility of attribute patterns. Stochastic processes and irreducible transitions will be created to ensure the convergence of the proposed algorithms. The project also will consider stochastic search variable selection methods to estimate the attribute hierarchy when the CDM satisfies conjunctive assumptions. The new methods for static CDMs will be extended to model and draw inferences on the process of learning in practice with the framework of dynamic CDMs. A set of simulation studies will be used to evaluate the new methods, and the methods will be applied to two spatial rotation learning datasets.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.