Review of cognitive diagnostic models (CDMs): Recent methodological advancements for addressing practical challenges

Cognitive diagnostic models (CDMs) have become essential tools for providing fine-grained information about individuals' mastery of cognitive skills. While prior reviews have emphasized statistical foundations and deep learning-based developments, this article focuses on recent methodological innovations designed to address persistent challenges in applying CDMs across various contexts. We highlight six areas of advancement: (1) extending models to accommodate polytomous attributes, thereby capturing multiple levels of proficiency; (2) discovering attribute relationships to reveal learning trajectories and support instructional design; (3) accelerating estimation through computational strategies that enable scalability to high-dimensional attributes; (4) improving estimation in small-sample contexts, particularly relevant for classroom applications; (5) refining and estimating Q-matrices through both statistical and machine learning approaches; and (6) evaluating model and item fit. Together, these methodological developments enhance the interpretability, efficiency, and applicability of CDMs, broadening their utility in various types of assessment, larger or smaller scales. The review complements existing surveys by emphasizing innovations that directly address application barriers, and it points to promising future directions including integration with deep learning and large language models.