Cognitive Diagnosis Models: Identifiability, Estimation, and Applications

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Cognitive diagnosis models (CDMs) are state-of-the-art psychometric models in education, psychology, and other social sciences. This research project will introduce a comprehensive theoretical and methodological framework that will make construction and analysis of CDM-based assessments more practicable. This development will provide a better understanding of the skills and cognitive processes involved in cognitive assessments. From a societal perspective, the integration of CDMs with cognitive and learning sciences will provide a powerful tool for identifying specific problems and difficulties that students encounter in skill acquisition. This interdisciplinary research project will help design a blueprint for mapping out timely, appropriate, and targeted interventions. The results of this project have the potential to positively impact STEM education and the training of students. Graduate students will be involved in the conduct of the research. Publicly available software also will be developed.This research project addresses fundamental identifiability and estimation issues of CDMs. Specifically, the project will address identifiability issues for general CDMs and provide practical guidelines for designing identifiable and statistical valid diagnosis tests. The project will address the challenging issue of Q-matrix validation and estimation. The research will develop computationally efficient methods to estimate the Q-matrix and detect possible misspecification of the Q-matrix and provide the related theoretical justification. The project also will develop an accessible computer program that can be used in conjunction with the proposed theory and methods. Extensive simulation studies will be performed to validate the performance of the estimation methods, and a variety of real data sets will be analyzed.