Cognitive diagnostic assessment (CDA) is used to measure the specific knowledge structures and the processing skills that examinees possess. One of the components of CDA is the Q-matrix, a J x K matrix indicating whether an item j requires skill k for correct execution. Although the Q-matrix is usually considered known, emerging evidence indicate otherwise. As such, the purpose of this thesis was to investigate a potential exploratory technique that could be used to supplement theory in finding the Q-matrix of a cognitive diagnostic test in data that satisfy the DINA (Deterministic Input Noisy "And") model. The proposed method is based on principal components analysis. The components model is a reparameterization of the DINA model relating examinee responses to cognitive diagnostic tasks. Understanding the relationship between the components and DINA skills can provide information for Q-matrix development. This relationship was investigated by answering four questions, the first two being analytical and the other two being empirical: 1) When does a skill (dimension) in the Q-matrix correspond to a component in the components analysis? 2) When does a skill (dimension) in the Q-matrix fail to correspond to a component in the components analysis? 3) When does the proposed methodology (components analysis) yield a plausible and useful solution for Q-matrix development? And 4) When does the methodology result in a Q-matrix that improves parameter estimation and examinee classification accuracy? The results indicated that components analysis which is akin to item analysis on a block of items can indeed augment theory in developing Q-matrices especially for items that are designed to be diagnostic and that measure a narrow content domain. Some limitations are discussed and potential areas for further work highlighted.
University of Minnesota Ph.D. dissertation. February 2012. Major: Educational Psychology. Advisors: Mark L. Davison and Ernest C. Davenport, Jr., 1 computer file (PDF); vii, 137 pages, appendices A-D.
Close, Catherine Nyambura.
An exploratory technique for finding the Q-matrix for the DINA model in cognitive diagnostic assessment: combining theory with data..
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