Efficiency of Generalized Estimating Equations for Binary Responses
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Bibliographic record
Abstract
Summary Using standard correlation bounds, we show that in generalized estimation equations (GEEs) the so-called ‘working correlation matrix’R(α) for analysing binary data cannot in general be the true correlation matrix of the data. Methods for estimating the correlation param-eter in current GEE software for binary responses disregard these bounds. To show that the GEE applied on binary data has high efficiency, we use a multivariate binary model so that the covariance matrix from estimating equation theory can be compared with the inverse Fisher information matrix. But R(α) should be viewed as the weight matrix, and it should not be confused with the correlation matrix of the binary responses. We also do a comparison with more general weighted estimating equations by using a matrix Cauchy–Schwarz inequality. Our analysis leads to simple rules for the choice of α in an exchangeable or autoregressive AR(1) weight matrix R(α), based on the strength of dependence between the binary variables. An example is given to illustrate the assessment of dependence and choice of α.
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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 | 0.005 | 0.105 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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