Limited- and Full-Information Estimation and Goodness-of-Fit Testing in 2<i><sup>n</sup></i>Contingency Tables
Bibliographic record
Abstract
High-dimensional contingency tables tend to be sparse, and standard goodness-of-fit statistics such as X2 cannot be used without pooling categories. As an improvement on arbitrary pooling, for goodness of fit of large 2n contingency tables, we propose classes of quadratic form statistics based on the residuals of margins or multivariate moments up to order r. These classes of test statistics are asymptotically chi-squared distributed under the null hypothesis. Further, the marginal residuals are useful for diagnosing lack of fit of parametric models. We show that when r is small (r = 2, 3), the proposed statistics have better small-sample properties and are asymptotically more powerful than X2 for some useful multivariate binary models. Related to these test statistics is a class of limited-information estimators based on low-dimensional margins. We show that these estimators have high efficiency for one commonly used latent trait model for binary data.
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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 | 0.057 | 0.318 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".