Learning Attribute Hierarchies From Data: Two Exploratory Approaches

In cognitive diagnostic assessment, multiple fine-grained attributes are measured simultaneously. Attribute hierarchies are considered important structural features of cognitive diagnostic models (CDMs) that provide useful information about the nature of attributes. Templin and Bradshaw first introduced a hierarchical diagnostic classification model (HDCM) that directly takes into account attribute hierarchies, and hence, HDCM is nested within more general CDMs. They also formulated an empirically driven hypothesis test to statistically test one hypothesized link (between two attributes) at a time. However, their likelihood ratio test statistic does not have a known reference distribution, so it is cumbersome to perform hypothesis testing at scale. In this article, we studied two exploratory approaches that could learn the attribute hierarchies directly from data, namely, the latent variable selection (LVS) approach and the regularized latent class modeling (RLCM) approach. An identification constraint was proposed for the LVS approach. Simulation results revealed that both approaches could successfully identify different types of attribute hierarchies, when the underlying CDM is either the deterministic input noisy and gate model or the saturated log-linear CDM. The LVS approach outperformed the RLCM approach, especially when the total number of attributes increases.