A Bayesian Student Model without Hidden Nodes and its Comparison with Item Response Theory
Bibliographic record
Abstract
The Bayesian framework offers a number of techniques for inferring an individual's knowledge state from evidence of mastery of concepts or skills. A typical application where such a technique can be useful is Computer Adaptive Testing (CAT). A Bayesian modeling scheme, POKS, is proposed and compared to the traditional Item Response Theory (IRT), which has been the prevalent CAT approach for the last three decades. POKS is based on the theory of knowledge spaces and constructs item-to-item graph structures without hidden nodes. It aims to offer an effective knowledge assessment method with an efficient algorithm for learning the graph structure from data. We review the different Bayesian approaches to modeling student ability assessment and discuss how POKS relates to them. The performance of POKS is compared to the IRT two parameter logistic model. Experimental results over a 34 item Unix test and a 160 item French language test show that both approaches can classify examinees as master or non-master effectively and efficiently, with relatively comparable performance. However, more significant differences are found in favor of POKS for a second task that consists in predicting individual question item outcome. Implications of these results for adaptive testing and student modeling are discussed, as well as the limitations and advantages of POKS, namely the issue of integrating concepts into its structure.
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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 | 0.022 | 0.077 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".