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Abstract:
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A fundamental goal of educational research is identifying students' current stage of skill mastery. As the number of examinees, items, and skills increases, the estimation of even simple cognitive diagnosis models becomes difficult. A faster, simpler approach is to cluster a "capability matrix" representing each student's knowledge for each skill to generate skill set profile clusters of students. We extend this approach with the introduction of an automatic subspace clustering method that identifies skills with obvious student separation and then clusters smaller partitioned subspaces. We demonstrate our method on simulated and real data, comparing the results to the DINA cognitive diagnosis model. In addition, we explore the effect of test design on the methods' performance. We comment on computational advantages of our approach and show that it gives faster, more reasonable results.
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