Collaborative Research: Bayesian Estimation of Restricted Latent Class Models

该研究项目将推进被称为认知诊断模型（CDM）的统计方法。CDM是将认知理论与在线学习技术应用联系起来的统计机器。它们作为一个框架，为在课堂内外取得成功所需的技能和属性提供细粒度的分类。稳健的认知理论对于确保CDM的准确推断至关重要。本项目将开发新的统计方法，用于在CDM的背景下验证认知理论。现代课堂从计算机化的学生评估中产生了大量的纵向信息。该项目的创新将为人类发展提供一个框架，收集现有信息，以跟踪技能发展，并支持教师真实的教学决定。新方法将更广泛地适用于其他学科，如社会科学，神经科学，医学和商业，作为一种方法来获得有关人类判断和决策的认知过程的更详细和细致入微的信息。将公开提供在项目过程中为执行所制定的程序而开发的软件，该项目将通过开发贝叶斯方法来估计一般类别模型的Q矩阵，从而推进统计和心理计量学理论。认知理论将通过指定一个Q矩阵来整合到CDM中，该矩阵将每个任务所需的技能进行分类。认知理论Q矩阵的普遍不可用的大多数内容领域和研究领域构成了广泛应用的CDM的障碍。该项目将为现有的研究提供一些进展。该项目将为最一般的限制潜在类模型开发估计Q的程序。将采用贝叶斯估计方法，明确执行可识别性条件，以确保参数恢复的一致性和准确性。当潜在属性的个数先验未知时，将创建随机过程和不可约转移来估计Q。该项目还将考虑在统计模型中纳入专家知识的方法，以改善Q的估计，并加强对未覆盖属性的解释。从研究这一重要问题中获得的心理测量学见解可以导致认知诊断模型Q矩阵估计的基础统计理论的重大发展，并可能对教育和心理学以外的广泛应用产生影响，例如根据一组底层特征对二进制数据进行聚类的机器学习应用程序。该奖项反映了NSF的法定使命，通过使用基金会的知识价值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 known as cognitive diagnosis models (CDMs). CDMs are the statistical machinery that link cognitive theory with applications in online learning technology. They serve as a framework for providing fine-grained classification of the skills and attributes needed for success in the classroom and beyond. Robust cognitive theory is central to ensure accurate inferences with CDMs. This project will develop new statistical methods for validating cognitive theory in the context of CDMs. The modern classroom generates a wealth of longitudinal information from computerized student assessments. The innovations from this project will provide a framework for human development that harvests the available information to track skill development and to support teachers' instructional decisions in real time. The new methods will be applicable more broadly to other disciplines, such as the social sciences, neuroscience, medicine, and business, as an approach to gain more detailed and nuanced information about cognitive processes underlying human judgment and decision making. Software developed during the course of the project to implement the developed procedures will be made publicly available.The project will advance statistical and psychometric theory by developing Bayesian methods for estimating the Q matrix for a general class of models. Cognitive theory will be incorporated into CDMs by specifying a Q matrix that catalogues the skills required by each task. The general unavailability of cognitive theory Q matrices for most content areas and research domains poses a barrier to widespread application of CDMs. The project will offer several advances to existing research. The project will develop procedures for estimating Q for the most general restricted latent class model. Bayesian estimation methods will be employed that explicitly enforce identifiability conditions to ensure consistency and accuracy of parameter recovery. Stochastic processes and irreducible transitions will be created to estimate Q when the number of latent attributes is unknown a priori. The project also will consider methods that incorporate expert knowledge in the statistical model to improve estimation of Q and to enhance interpretation of uncovered attributes. Psychometric insights gained from working on this important problem can lead to significant developments in the underlying statistical theory for estimation of cognitive diagnosis model Q matrices and could potentially have an impact on the broad spectrum of applications beyond education and psychology, such as machine learning applications that seek to cluster binary data according to a set of underlying features.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.