A brief note on the random-effects meta-analysis model and its relationship to other models
Bibliographic record
Abstract
Meta-analysis is a statistical method for combining quantitative results across studies. A fundamental decision in undertaking a meta-analysis is choosing an appropriate model for analysis. This is the second of two companion articles which have the joint aim of describing the different meta-analysis models. In the first article, we focused on the common-effect (also known as fixed-effect [singular]) model, and in this article, we focus on the random-effects model. We describe the key assumptions underlying the random-effects model, how it is related to the common-effect and fixed-effects [plural] models, and present some of the arguments for selecting one model over another. We outline some of the methods for fitting a random-effects model. Finally, we present an illustrative example to demonstrate how the results can differ depending on the chosen model and method. Understanding the assumptions of the different meta-analysis models, and the questions they address, is critical for meta-analysis model selection and interpretation.
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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 | 0.076 | 0.134 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.005 | 0.009 |
| Bibliometrics | 0.005 | 0.008 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.007 | 0.011 |
| Open science | 0.007 | 0.005 |
| Research integrity | 0.008 | 0.021 |
| Insufficient payload (model declined to judge) | 0.006 | 0.003 |
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".