BIGDATA: Collaborative Research: IA: F: Latent and Graphical Models for Complex Dependent Data in Education

这是一个关于教育评估统计建模与分析的综合性研究方案。这项研究解决了教育大数据分析中出现的基本统计问题。研究的重点是具有复杂依赖和结构的大规模数据（如高维响应和过程数据）的建模和推理。这些数据产生于引入新的方法来测试学生的知识，依赖于向学生呈现的场景和基于模拟的环境，学生对模拟环境的反应进行测试。本研究是哥伦比亚大学与美国教育考试服务中心合作开展的，主要研究内容包括：高维项目反应数据的隐图建模、基于字典模型的过程数据建模与分割、项目-属性关系估计、降维、模型的理论分析和计算方法。该分析结合了数学和概率的技术和概念，并将其应用于非线性统计模型和数据分析。该模型结合了潜在变量和图形化的方法为高维数据建模过程数据，建模和分割技术的自然语言处理的最新进展将进行调查。在理论发展中，将研究几个代数概念，以制定模型可识别性和高维离散空间进行组合分析。此外，将利用数值方法的最新进展开发优化算法。

This is a comprehensive research proposal on the statistical modeling and analysis for educational assessment. This research addresses issues concerning fundamental statistical problems that arise in the analysis of Big Data in education. The research focus is on modeling and inference for large-scale data with complex dependence and structures (such as high-dimensional response and process data). These data arise from the introduction of new methods of testing student knowledge that rely on scenarios presented to the students and on simulation-based environments where student responses to a simulated environment are tested. This research is collaborative between Columbia University and the Educational Testing Service.The topics studied include latent graphical modeling for high-dimensional item response data, modeling and segmentation of process data via dictionary models, estimation of item-attribute relationship, dimension reduction, theoretical analysis and computational methods for the proposed models. The analysis combines techniques and concepts from mathematics and probability and applies them to nonlinear statistical models and data analysis. The proposed model combines latent variable and graphical approaches for high-dimensional data; for modeling process data, recent advances in modeling and segmenting techniques for natural language processing will be investigated. In the theoretical development, several algebraic concepts to formulate model identifiability and perform combinatorial analysis on high-dimensional discrete spaces will be studied. In addition, optimization algorithms will be developed using recent advances in numerical methods.