A Modularized Higher-Order Diagnostic Classification Model for Clustered Attribute Hierarchies

Recognizing that complex networks of skills typically exhibit hierarchical and modular organization, this article presents a Modularized Higher-Order Diagnostic Classification Model (MHO-DCM) designed to capture hierarchical relationships among attributes organized into clustered subdomains. Central to the proposed method is a representation of attribute hierarchies in which attributes are grouped into cognitively coherent subgraphs nested within a single higher-order ability continuum. We adopt a nominal response model framework in item response theory and leverage standard maximum likelihood estimation (MLE). In parallel, we demonstrate that sequential higher-order latent structural models can likewise be implemented in a modularized fashion within an MLE framework. The performance of the proposed models is examined through simulation studies assessing parameter recovery, classification accuracy, and null rejection rates of goodness-of-fit measures. An empirical demonstration showcases how the framework can be applied in practice, highlighting its advantages in flexibility, interpretability, and the richer diagnostic insights it affords.