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knowledge_assessment:q-matrix [2012/07/05 13:02] jpetrovic |
knowledge_assessment:q-matrix [2012/07/05 13:34] jpetrovic |
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Factor analysis: | 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. | ||
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+ | 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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