Testing Simultaneous Marginal Homogeneity for Clustered Matched-Pair Multinomial Data
Bibliographic record
Abstract
For matched-pair data with a polychotomous outcome, the Stuart-Maxwell test (1955) and the Bhapkar test(1966) are commonly used to test marginal homogeneity. When the outcome is ordinal, the test proposed by Agresti (1983) can be used to test the marginal homogeneity against stochastic order. In practice, we often face the need to consider multiple categorical outcomes simultaneously to insure Type I error protection. In this paper, we propose three statistics to test simultaneous marginal homogeneity for multiple multinomial outcomes in two dependent samples. Furthermore, when the outcome is ordinal, we also propose a transformed version of the three statistics for testing simultaneous marginal homogeneity against stochastic order in two dependent samples. We then prove their asymptotic properties. Finally, Monte Carlo simulations are conducted to evaluate their performance in small samples with respect to empirical size and power.
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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 | 0.047 | 0.211 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".