knowledge_assessment:q-matrix
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knowledge_assessment:q-matrix [2012/07/05 12:53] jpetrovic |
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| * The alternative to this strategy is to design a method to extract a q-matrix, which explains student behavior, and reveals the underlying relationships between questions. Experts can examine the resulting q-matrix 25 to ensure that the extracted relationships seem to be valid, and then use that q-matrix to guide the generation of new problems. | * The alternative to this strategy is to design a method to extract a q-matrix, which explains student behavior, and reveals the underlying relationships between questions. Experts can examine the resulting q-matrix 25 to ensure that the extracted relationships seem to be valid, and then use that q-matrix to guide the generation of new problems. | ||
| + | Factor analysis: | ||
| How to automatically determine concepts? Using covariance matrix. Number of concepts should be smaller than number of questions. Still, this methos has proven to be less fault tollerant. | How to automatically determine concepts? Using covariance matrix. Number of concepts should be smaller than number of questions. Still, this methos has proven to be less fault tollerant. | ||
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| + | ==== Q-matrix method ==== | ||
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| + | The q-matrix method is a simple hill-climbing algorithm that creates a matrix | ||
| + | representing relationships between concepts and questions directly. The algorithm varies | ||
| + | c, the number of concepts, and the values in the q-matrix, minimizing the total error for | ||
| + | all students for a given set of n questions. To avoid of local minima, each hill-climbing | ||
| + | search is seeded with different random Q-matrices and the best of these is kept. | ||
| + | |||
| + | When forming a correlation matrix, we lose individual student data in favor of calculating average relationships between questions. The q-matrix method is optimized to assign each student the most appropriate knowledge state, using all available response data for each student. | ||
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| + | As Sellers found in her research, the results obtained through | ||
| + | q-matrix analysis seem to describe relationships among variables in interpretable ways. | ||
| + | Factor analysis and principal components analysis, on the other hand, do not readily offer | ||
| + | interpretable results. | ||
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| + | Later researchers found that, although the q-matrix model was a good way to compare student data to a concept model, expert-constructed q-matrices did not correspond to student data any better than random q-matrices did. | ||
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| + | the findings in Brewer's previous research, which found that the factor analysis method performed poorly in comparison with the q-matrix | ||
| + | method when fewer observations were available. | ||
knowledge_assessment/q-matrix.txt ยท Last modified: 2023/06/19 18:03 (external edit)
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