Statistical Analysis for Cognitive Diagnosis - Theory and Applications

诊断分类模型是认知诊断中一种重要的统计工具，可应用于教育评价和临床心理学等多个学科。本课题研究的重点是认知评估的统计分析。这项研究涉及基本的统计推断和实验设计。它既着眼于理论发展，又着眼于应用。首先，该项目将侧重于项目-属性关系的统计推断，在目前的情况下，这一关系被表述为所谓的Q-矩阵。主题包括Q-矩阵的点估计、假设检验、降维和模型诊断。第二，该项目将重点放在项目的个性化适应性设计上，以便用更少的项目更准确地测量属性分布。特别地，首次提出了一种基于大偏差理论的选题规则效率的衡量标准。此外，为了逼近最优设计，还提出了自适应的项目选择方案。这项研究的动机是使用分类模型在教育评估、精神病学评估和其他学科中的应用。在教育应用中，这项研究将有助于对考试问题的技能要求进行数据驱动的校准，并验证这些技能要求的主观信念，从而更好、更准确地评估学生的知识状况和技能掌握情况。在精神病学评估中，这项研究将有助于通过更准确地识别症状与障碍的关系来改进循证诊断。适应性项目选择有助于缩短考试(在教育测试中)和面谈(在精神病学评估中)的长度，同时保持评估和诊断的准确性。项目成果有可能对这些和其他研究领域产生积极影响。

Diagnostic classification models are an important statistical tool in cognitive diagnosis and can be employed in a number of disciplines, including educational assessment and clinical psychology. This project focuses on the statistical analysis of cognitive assessment. The research addresses issues concerning fundamental statistical inference and experimental design. It aims at both theoretical development and applications. First, the project will focus on the statistical inference of the item-attribute relationship, which in the current context is formulated as the so-called Q-matrix. The topics include point estimation of the Q-matrix, hypothesis testing, dimension reduction, and model diagnosis. Second, the project will focus on the individualized adaptive design of items so as to measure the attribute profiles more accurately with fewer items. In particular, a criterion is first proposed to measure the efficiency of an item-selection rule based on the large deviations theory. In addition, adaptive item selection schemes are proposed to approach the optimal design. This research is motivated by applications in educational assessments, psychiatric evaluations, and other disciplines using classification models. In educational applications, the research will help to obtain a data-driven calibration of the skill requirements for exam problems and also to validate the subjective beliefs of such skill requirements, so that better and more accurate assessments of students' knowledge status and skill mastery are obtained. In psychiatric assessment, this study will help to improve evidence-based diagnosis by more accurately identifying the symptom-disorder relationship. The adaptive item selection helps by shortening the lengths of exams (in educational testing) and interviews (in psychiatric evaluation) while maintaining the assessment and diagnosis accuracy. Project results have the potential to positively impact these and other areas of study.