Hierarchical diagnostic classification models: a family of models for estimating and testing attribute hierarchies.

Although latent attributes that follow a hierarchical structure are anticipated in many areas of educational and psychological assessment, current psychometric models are limited in their capacity to objectively evaluate the presence of such attribute hierarchies. This paper introduces the Hierarchical Diagnostic Classification Model (HDCM), which adapts the Log-linear Cognitive Diagnosis Model to cases where attribute hierarchies are present. The utility of the HDCM is demonstrated through simulation and by an empirical example. Simulation study results show the HDCM is efficiently estimated and can accurately test for the presence of an attribute hierarchy statistically, a feature not possible when using more commonly used DCMs. Empirically, the HDCM is used to test for the presence of a suspected attribute hierarchy in a test of English grammar, confirming the data is more adequately represented by hierarchical attribute structure when compared to a crossed, or nonhierarchical structure.