Statistical Analysis for Cognitive Assessment

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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.