A Sequential Generalized Nonparametric Classification Method for Small-Scale Cognitive Diagnostic Assessment

Small-scale (e.g., classroom) assessment represents the most common and needed scenario for cognitive diagnostic testing. In such settings, polytomously scored items (e.g., constructed-response tasks) are widely used, as they provide more fine-grained measurement of students' skills and cognitive processes. However, a significant gap remains between the current methods and pressing practical needs. On one hand, parametric cognitive diagnosis models capable of handling polytomous response data require large samples for stable estimation, making them unsuitable for small-scale classroom use. On the other hand, existing nonparametric classification methods, while robust in small samples, are largely confined to dichotomous (0/1) response data. There is a lack of dedicated nonparametric methods for polytomous responses, creating a disconnect between practical testing and diagnostic tools. To address this real-world necessity, this study proposes the seq-GNPED method. It extends the generalized nonparametric classification framework to polytomous data by introducing weighted ideal category response and a collapsed class iterative algorithm. Simulations and empirical applications confirm that seq-GNPED achieves robust and accurate diagnosis under small sample conditions where parametric models falter, effectively leveraging the informational richness of polytomous items. This work bridges a critical gap by providing a practical, nonparametric tool tailored for fine-grained, classroom-ready cognitive diagnosis.