A Partition Tree Approach to Combine Techniques to Refine Item to Skills Q-Matrices

The problem of mapping items to skills is gaining interest with the emergence of recent techniques that can use data for both defining this mapping, and for refining mappings given by experts. We investigate the problem of refining mapping from an expert by combining the output of different techniques. The combination is based on a partition tree that combines the suggested refinements of three known techniques from the literature. Each technique is given as input a Q-matrix, that maps items to skills, and student test outcome data, and outputs a modified Q-matrix that constitutes suggested improvements. We test the accuracy of the partition tree combination techniques over both synthetic and real data. The results over synthetic data show a high improvement over the best single technique with a 86% error reduction on average for four different Q-matrices. For real data, the error reduction is 55%. In addition to the substantial error reduction, the partition tree refinements provide a much more stable performance than any single technique. These results suggest that the partition tree is a valuable refinement combination approach that can effectively take advantage of the complementarity of the Q-matrix refinement techniques. It brings the goal of using a data driven approach to refine the item to skill mapping closer to real applications, although challenges remain and are discussed.