Bayesian Inference for Attribute Hierarchy in Cognitive Diagnosis Models

该研究项目将在认知诊断模型（CDM）框架内推进属性层次估计和推理的统计方法。CDMs已被广泛应用于教育评估、精神病诊断和其他社会科学领域。结合诊断评估，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，目前还缺乏有效的统计工具，估计属性层次结构从观察到的数据。本计画将发展一系列的贝氏方法来估计属性层级。该项目将有助于新开发的跨学科领域，将人工智能与心理测量学相结合。这些新方法将有助于教育学、心理学以及其他社会科学学科的应用研究。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。本研究计划将为静态和动态CDM模型开发属性层次的贝叶斯推理，并促进CDM与属性层次的结合使用，以促进学习。该项目将解决以下主要研究问题：1）静态和动态CDM的贝叶斯框架的制定; 2）开发从这两种设置中的观测数据直接学习属性层次结构的方法。对于静态CDM，一系列新的贝叶斯估计方法将被用来直接估计属性层次结构，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，以确保所提出的算法的收敛性。当CDM满足合取假设时，本计画亦将考虑随机搜寻变数选择方法来估计属性层级。 静态CDMs的新方法将扩展到动态CDMs的框架下，对实践中的学习过程进行建模和推理。 一组模拟研究将被用来评估新的方法，该方法将被应用到两个空间旋转学习datasets.This奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.