Statistical Analysis for Cognitive Assessment

本计画将探讨诊断分类模式之基本统计推论问题。 它的目的是在理论发展和应用到教育研究，精神病学和其他学科使用分类模型。 该项目将集中在多变量潜变量模型分析中具有挑战性的几个方面。 特别是，研究将集中在项目属性关系的统计推断，在当前的上下文中被制定为所谓的Q-矩阵。 研究主题将包括Q矩阵的点估计、假设检验、降维、模型诊断和Q矩阵分类，包括构建基于数据可估计的适当等价类等任务。拟议研究的动机主要是教育评估和精神评估的应用，并有可能对这两个研究领域产生积极影响。 在教育应用中，这项研究将有助于获得每个考试问题的技能要求的数据驱动的估计，并验证基于数据的这种技能要求的主观信念。 在精神科评估中，本研究将有助于通过数据客观地了解精神障碍与疾病之间的关系，从而提高诊断的准确性。

This project will address issues concerning fundamental statistical inference for diagnostic classification models. It aims at both theoretical development and applications to educational study, psychiatry, and other disciplines using classification models. The project will concentrate on several aspects that are challenging in the analysis of multivariate latent variable models. In particular, the research will focus on the statistical inference of the item-attribute relationship, which in the current context is formulated as the so-called Q-matrix. Topics for research will include point estimation of the Q-matrix, hypothesis testing, dimension reduction, model diagnosis, and classifying Q-matrices, including tasks such as constructing appropriate equivalence classes that are estimable based on the data.The proposed research is motivated mainly by applications in educational assessment and psychiatric evaluations and has the potential to positively impact these two areas of study. In educational applications, this research will help to obtain a data-driven estimate of the skill requirements for each exam problem and also validate the subjective belief of such skill requirements based on the data. In psychiatric assessments, this study will help to improve diagnosis accuracy by learning the symptom-disorder relationship objectively via the data.