Identification and Estimation of Dynamic Restricted Latent Class Models for Cognitive Diagnosis

这个研究项目将推进动态的，认知诊断评估跟踪学生的技能获取作为学生技能掌握的静态分类的替代方法。现有的形成性评估框架需要广泛的先验知识和理论，关于学生技能掌握的性质和技能的过程中加入，以确定认知表现。该项目将为研究人员提供新的工具，从动态的，纵向的数据推断学习过程中的学生表现，并提供一个框架，评估实质性的理论，学生如何学习。教育科学的一个核心问题是制定和评估干预措施。该项目将为研究人员开发准确的方法，以获得对学习干预有效性的精细理解。新方法将利用学生对纵向评估的反应，为教育工作者和政策制定者提供有关学生掌握教育内容的状况和时间的见解。这些方法还将揭示教育干预的有效性，其目标是建立制定个性化学习干预的策略，以加速学生的学习。为了实现这些目标，该项目将推进统计学和心理测量学的基础理论。除了拓宽方法论之外，该项目还将加强教育评估基础设施。将进行的研究将为实时形成性评估的开发和管理奠定坚实的基础，这些评估适应学生的需求，并为教育工作者提供及时的信息，以告知教学决策。研究生将参与发现过程，理论发展将纳入研究生课程。该研究项目将考虑社会、行为和健康科学核心的统计问题，并将突出心理测量学、潜在类别建模、纵向数据分析和贝叶斯统计学等领域之间的相互作用。该项目将涉及复杂的统计建模，并将解决与计算复杂性有关的问题。动态限制潜在类模型（D-RLCMs）的新方法和算法将被开发。新的贝叶斯方法将用于部署D-RLCM，以随着时间的推移对学生的掌握程度进行分类。纵向技能分类将为教育工作者和利益相关者提供学生表现和学习的细粒度轨迹。该项目将部署一个隐马尔可夫模型（HMM）框架，该框架能够提供有关学生过渡到具有更高内容掌握能力的状态的概率的精确信息。该项目将通过建立新的可识别性理论来准确推断学生的纵向技能概况和学习轨迹，从而推进障碍的数学理论。将制定方法，以提供一个强大的评估的背景因素在学习环境中的作用，如学生或学校的特点和教学技术。该奖项反映了NSF的法定使命，并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，被认为值得支持。

This research project will advance dynamic, cognitive diagnostic assessments for tracking student skill acquisition as an alternative approach to the static classification of student skill mastery. Existing formative assessment frameworks require extensive prior content knowledge and theory concerning the nature of student skill mastery and the process by which skills are joined to determine cognitive performance. This project will provide researchers with new tools for inferring the learning process from dynamic, longitudinal data on student performance and offer a framework for evaluating substantive theory for how students learn. A central concern in the educational sciences is formulating and evaluating interventions. The project will develop accurate methods for researchers to gain a fine-grained understanding as to the effectiveness of learning interventions. The new methods will leverage student responses to longitudinal assessments to offer educators and policymakers with insights regarding the status and timing of student mastery of educational content. The methods also will shed light on the effectiveness of educational interventions with the goal of establishing strategies for formulating personalized learning interventions to accelerate student learning. To achieve these aims, the project will advance fundamental theory in statistics and psychometrics. In addition to broadening methodological theory, the project will strengthen the educational assessment infrastructure. The research to be conducted will create a robust foundation for the development and administration of real-time formative assessments that adapt to the needs of students and provide educators with timely information to inform instructional decisions. Graduate students will be involved in the discovery process, and theoretical developments will be incorporated into the graduate curriculum. Publicly available software will be created to provide researchers and decision makers with cutting-edge tools.This research project will consider statistical problems at the heart of the social, behavioral, and health sciences, and will highlight the interplay among the fields of psychometrics, latent class modeling, longitudinal data analysis, and Bayesian statistics. The project will involve complex statistical modeling and will addresses issues related to computational complexity. New methods and algorithms for dynamic restricted latent class models (D-RLCMs) will be developed. Novel Bayesian methods will be used to deploy D-RLCMs to classify student mastery over time. The longitudinal skill classifications will provide educators and stakeholders with a fine-grained trajectory of student performance and learning. The project will deploy a hidden Markov model (HMM) framework that enables precise information regarding the probability students transition into states with greater content mastery. The mathematical theory of HMMs will be advanced in the project by establishing new identifiability theory to accurately infer student longitudinal skill profiles and learning trajectories. Methods will be developed to provide a powerful evaluation of the role of contextual factors in learning environments, such as student or school characteristics and pedagogical techniques. The methods to be developed will harvest the wealth of longitudinal student response data to provide decision makers and educators with actionable evidence to improve student learning outcomes.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.