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

这是一项关于教育评估统计建模与分析的综合性研究方案。这项研究解决了在教育大数据分析中出现的基本统计问题。研究的重点是对具有复杂相关性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。这些数据源于引入了新的测试学生知识的方法，这些方法依赖于呈现给学生的情景和基于模拟的环境，在模拟环境中测试学生对模拟环境的反应。该研究由哥伦比亚大学与美国教育考试服务中心合作，研究内容包括高维试题反应数据的潜在图形化建模、基于词典模型的过程数据建模与分割、试题-属性关系的估计、降维、理论分析和模型计算方法等。该分析结合了数学和概率中的技术和概念，并将其应用于非线性统计模型和数据分析。对于高维数据，该模型结合了潜在变量和图形方法；对于过程数据的建模，将研究自然语言处理的建模和分割技术的最新进展。在理论发展中，将研究几个代数概念，以描述高维离散空间上的模型可辨识性和执行组合分析。此外，还将利用数值方法的最新进展来开发优化算法。

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.