Two-stage polytomous attribute estimation for cognitive diagnostic models: overcoming computational challenges in large-scale assessments with many polytomous attributes

Cognitive diagnosis models (CDMs) have been advocated as a useful tool in calibrating large-scale assessments, yet the computational challenges are inevitably amplified when the modeling complexity (e.g., the number and the levels of attributes) increases. This study presents a critical scenario, a large-scale national medical certification exam, where CDM with many polytomous attributes (mpCDM) is of great utility, but poses great computational challenges to many popular open-source CDM software packages. We developed a novel two-stage estimation method and assessed its performance through a Monte Carlo simulation study under various conditions of attribute number, item number, item quality, and sample size. Results indicate that the proposed method maintains high accuracy in handling large-scale data while effectively overcoming computational capacity limitations, especially in scenarios with many polytomous attributes, large numbers of items, and substantial sample sizes. Furthermore, we applied the proposed method to a large-scale health examination dataset, demonstrating its effectiveness in practice. This study contributes to the field of psychometrics by offering a simple yet effective solution to the computational challenges inherent in implementing mpCDMs for large-scale assessments, providing a practical tool for diagnostic analyses in educational and professional certification contexts.