The Monotonic Polynomial Graded Response Model: Implementation and a Comparative Study
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We present a monotonic polynomial graded response (GRMP) model that subsumes the unidimensional graded response model for ordered categorical responses and results in flexible category response functions. We suggest improvements in the parameterization of the polynomial underlying similar models, expand upon an underlying response variable derivation of the model, and in lieu of an overall discrimination parameter we propose an index to aid in interpreting the strength of relationship between the latent variable and underlying item responses. In applications, the GRMP is compared to two approaches: (a) a previously developed monotonic polynomial generalized partial credit (GPCMP) model; and (b) logistic and probit variants of the heteroscedastic graded response (HGR) model that we estimate using maximum marginal likelihood with the expectation-maximization algorithm. Results suggest that the GRMP can fit real data better than the GPCMP and the probit variant of the HGR, but is slightly outperformed by the logistic HGR. Two simulation studies compared the ability of the GRMP and logistic HGR to recover category response functions. While the GRMP showed some ability to recover HGR response functions and those based on kernel smoothing, the HGR was more specific in the types of response functions it could recover. In general, the GRMP and HGR make different assumptions regarding the underlying response variables, and can result in different category response function shapes.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.015 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it