Using the Attribute Hierarchy Method to Make Diagnostic Inferences about Examinees' Cognitive Skills in Algebra on the SAT.
Bibliographic record
Abstract
The purpose of this study is to apply the attribute hierarchy method (AHM) to a subset of SAT algebra items administered in March 2005 to promote cognitive diagnostic inferences about examinees. The AHM is a psychometric method for classifying examinees’ test item responses into a set of structured attribute patterns associated with different components from a cognitive model of task performance. An attribute is a description of the procedural or declarative knowledge needed to perform a task. These attributes form a hierarchy of cognitive skills that represent a cognitive model of task performance. The study was conducted in two steps. In step 1, a cognitive model was developed by having content specialists, first, review the SAT algebra items, identify their salient attributes, and order the item-based attributes into a hierarchy. Then, the cognitive model was validated by having a sample of students think aloud as they solved each item. In step 2, psychometric analyses were conducted on the SAT algebra cognitive model by evaluating the model-data fit between the expected response patterns generated by the cognitive model and the observed response patterns produced from a random sample of 5000 examinees who wrote the items. Attribute probabilities were also computed for this random sample of examinees so diagnostic inferences about their attribute-level performances could be made. We conclude the study by describing key limitations, highlighting challenges inherent to the development and analysis of cognitive diagnostic assessments, and proposing directions for future research. This article contains embedded media (video and audio files) and may take a few minutes to download. You will need Flash Player 9.0 (available from www.adobe.com) to play the files. An alternate, smaller version of this article, that does not contain media files is available below under the Alternate Version heading.
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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 | 0.021 | 0.101 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.007 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".