Conditions for effectively deriving a Q-Matrix from data with Non-negative Matrix Factorization
Bibliographic record
Abstract
The process of deciding which skills are involved in a given task is tedious and challenging. Means to automate it are highly desirable, even if only partial automation that provides supportive tools can be achieved. A recent technique based on Non-negative Matrix Factorization (NMF) was shown to offer valuable results, especially due to the fact that the resulting factorization allows a straightforward interpretation in terms of a Q-matrix. We investigate the factors and assumptions under which NMF can effectively derive the underlying high level skills behind assessment results. We demonstrate the use of different techniques to analyse and interpret the output of NMF. We propose a simple model to generate simulated data and to provide lower and upper bounds for quantifying skill effect. Using the simulated data, we show that, under the assumption of independent skills, the NMF technique is highly effective in deriving the Q-matrix. However, the NMF performance degrades under different ratios of variance between subject performance, item difficulty, and skill mastery. The results corroborates conclusions from previous work in that high level skills, corresponding to general topics like World History and Biology, seem to have no substantial effect on test performance, whereas other topics like Mathematics and French do. The analysis and visualization techniques of the NMF output, along with the simulation approach presented in this paper, should be useful for future investigations using NMF for Q-matrix induction from data. 1.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.036 | 0.277 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.006 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".