Modelling Heterogeneous Dispersion in Marginal Models for Longitudinal Proportional Data
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Bibliographic record
Abstract
Abstract Continuous proportional data is common in biomedical research, e.g., the pre‐post therapy percent change in certain physiological and molecular variables such as glomerular filtration rate, certain gene expression level, or telomere length. As shown in (Song and Tan, 2000) such data requires methods beyond the common generalised linear models. However, the original marginal simplex model of (Song and Tan, 2000) for such longitudinal continuous proportional data assumes a constant dispersion parameter. This assumption of dispersion homogeneity is imposed mainly for mathematical convenience and may be violated in some situations. For example, the dispersion may vary in terms of drug treatment cohorts or follow‐up times. This paper extends their original model so that the heterogeneity of the dispersion parameter can be assessed and accounted for in order to conduct a proper statistical inference for the model parameters. A simulation study is given to demonstrate that statistical inference can be seriously affected by mistakenly assuming a varying dispersion parameter to be constant in the application of the available GEEs method. In addition, residual analysis is developed for checking various assumptions made in the modelling process, e.g., assumptions on error distribution. The methods are illustrated with the same eye surgery data in (Song and Tan, 2000) for ease of comparison. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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