On the Sequential Hierarchical Cognitive Diagnostic Model

Abstract

Model data fit plays an important role in any statistical analysis, and the primary goal is to detect the preferred model based on certain criteria. Under the cognitive diagnostic assessment (CDA) framework, a family of sequential cognitive diagnostic models (CDMs) is introduced to handle polytomously scored data, which are attained by answering constructed-response items sequentially. The presence of attribute hierarchies, which can provide useful information about the nature of attributes, will help understand the relation between attributes and response categories. This article introduces the sequential hierarchical CDM (SH-CDM), which adapts the sequential CDM to deal with attribute hierarchy. Furthermore, model fit analysis for SH-CDMs is assessed using eight model fit indices (i.e., three absolute fit indices and five relative fit indices). Two misfit sources were focused; that is, misspecifying attribute structures and misfitting processing functions. The performances of those indices were evaluated via Monte Carlo simulation studies and a real data illustration.