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.
This research addresses issues concerning fundamental statistical inference for the diagnostic classification models. In particular, the research focuses on the statistical inference of the item-attribute relationship, which in the current context is formulated as the so-called Q-matrix. We developed theories of the identifiability of the Q-matrices, constructed consistent estimators of the Q-matrices, and developed asymptotic theory for the computerized adaptive testing for cognitive diagnosis. This study has applications in educational assessments and psychiatric evaluations. In educational applications, the theories developed for the Q-matrices help teachers to obtain a data-driven estimate of the skill requirements for each exam problems and also to validate their subjective belief of such skill requirements based on the data. In psychiatric assessment, the theories improve diagnosis accuracy by learning the symptom-disorder relationship objectively via the data. Computerized adaptive testing (CAT) is a sequential experiment design scheme that tailors the selection of items (such as exam questions) to each subject. Such a design measures subjects attributes more accurately than the traditional prefixed design. The theory developed for CAT provides guidelines of the sequential selection of item (exam problems) based on subjects’ (students) responses to previous items. A direct impact is that teachers can shorten the exam durations while maintaining the quality in measuring students’ mastery of skills.
