Analyzying Bivariate Ordinal Polytomous Data: A Marginal Multinomial Logistic Approach
Bibliographic record
Abstract
The multinomial cell counts based likelihood and the generalized estimating equations (GEE) approaches are widely used for analysis of bivariate ordinal categorical responses. In both of these approaches, the joint cell probabilities are usually modeled in terms of a global odds ratio as a measure of association and the marginal probabilities for each of the two ordered response variables. These methods utilize the stochastic ordering of the responses by modelling the cumulative margins with certain suitable link functions so that the link function of a cumulative margin is linear in covariates and an intercept representing the ordinal category. This type of modelling, therefore, requires suitable order restricted inference for the cutpoints (intercepts) separating the ordinal categories. These cutpoints are, however, frequently estimated in traditional ways without challenging their order restrictions. In this paper, we distinguish the ordinal categories in a general way so that the covariate effects are generally different under different ordinal categories. This allows one to model the cumulative margins through certain non-linear regression functions which does not require any introduction of the cutpoints.
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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 | 0.011 | 0.056 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".