Chunk-Based Higher-Order Hierarchical Diagnostic Classification Models: A Maximum Likelihood Estimation Approach

This paper presents a class of higher-order diagnostic classification models (HO–DCMs) capable of capturing complex, nonlinear hierarchical relationships among attributes. Building on and extending prior work, we adopt a nominal response model framework in item response theory and leverage standard maximum likelihood estimation (MLE). In parallel, we demonstrate that sequential HO–DCMs can likewise be implemented within an MLE framework. Furthermore, we introduce a novel chunk-based approach for representing attribute hierarchies, wherein attributes are organized into cognitively coherent subgraphs (chunks) nested within a continuous general ability continuum. The performance of the models is validated through simulation studies evaluating parameter recovery, classification accuracy, and null rejection rates of goodness-of-fit measures. An empirical demonstration showcases how the proposed framework can be applied in practice, highlighting its advantages in model flexibility, interpretability, and the additional diagnostic insights it affords.