A Sequential General Nonparametric Classification Method for Polytomous Responses

Diagnostic classification models (DCMs) constitute a family of discrete latent variable models designed to classify examinees based on their mastery or non-mastery of fine-grained skills or attributes. The response data from educational assessments often include graded responses, in which the response categories are obtained sequentially and explicitly associated with specific attributes. However, the existing parametric DCMs for graded responses require large sample sizes to estimate item parameters and the attribute mastery patterns of the examinees reliably, thereby hindering their practical application in educational contexts such as classroom settings. This article proposes a sequential general nonparametric classification method for graded responses that demonstrates promising classification accuracy even with a small sample size. The proposed method accommodates polytomous responses, including graded responses, and different condensation rules. Simulation studies showed that the proposed method outperforms the existing parametric polytomous DCMs and nonparametric binary DCMs, specifically when the sample size is small. Additionally, an actual high school test dataset was analyzed to illustrate the utility of the proposed method in educational practice. To promote practical application of the proposed method, a companion R function has been made freely available on the open science framework.