Cognitive diagnostic analysis using hierarchically structured skills

This dissertation proposes two modified cognitive diagnostic models (CDMs), the deterministic, inputs, noisy, "and" gate with hierarchy (DINA-H) model and the deterministic, inputs, noisy, "or" gate with hierarchy (DINO-H) model. Both models incorporate the hierarchical structures of the cognitive skills in the model estimation process, and can be used for situations where the attributes are ordered hierarchically. The Trends in International Mathematics and Science Study (TIMSS) 2003 data are analyzed to illustrate the proposed approaches. The simulation study evaluates the effectiveness of the proposed approaches under various conditions (e.g., various numbers of attributes, test lengths, sample sizes, and hierarchical structures). The simulation study attempts to address the model fits, items fit, and accuracy of item parameter recovery when the skills are in a specified hierarchy and varying estimation models are applied. The simulation analysis examines and compares the impacts of the misspecification of a skill hierarchy on various estimation models under their varying assumptions of dependent or independent attributes. The study is unique in incorporating a skill hierarchy with the conventional DINA and DINO models. It also reduces the number of possible latent classes and decreases the sample size requirements. The study suggests that the DINA-H/ DINO-H models, instead of the conventional DINA/ DINO models, should be considered when skills are hierarchically ordered. Its results demonstrate the proposed approaches to analyzing the hierarchically structured CDMs, illustrate the usage in applying cognitive diagnosis models to a large-scale assessment, and provide researchers and test users with practical guidelines.