The Hierarchy Consistency Index: Evaluating Person Fit for Cognitive Diagnostic Assessment
Bibliographic record
Abstract
In this article, we introduce a person‐fit statistic called the hierarchy consistency index (HCI) to help detect misfitting item response vectors for tests developed and analyzed based on a cognitive model. The HCI ranges from −1.0 to 1.0, with values close to −1.0 indicating that students respond unexpectedly or differently from the responses expected under a given cognitive model. A simulation study was conducted to evaluate the power of the HCI in detecting different types of misfitting item response vectors. Simulation results revealed that the detection rate of the HCI was a function of type of misfit, item discriminating power, and test length. The best detection rates were achieved when the HCI was applied to tests that consisted of a large number of highly discriminating items. In addition, whether a misfitting item response vector can be correctly identified depends, to a large degree, on the number of misfits of the item response vector relative to the cognitive model. When misfitting response behavior only affects a small number of item responses, the resulting item response vector will not be substantially different from the expectations under the cognitive model and consequently may not be statistically identified as misfitting. As an item response vector deviates further from the model expectations, misfits are more easily identified and consequently higher detection rates of the HCI are expected.
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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 | 0.040 | 0.184 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.011 | 0.006 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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".