Enriching Meta-Analytic Models of Summary Data: A Thought Experiment and Case Study
Bibliographic record
Abstract
Meta-analysis typically involves the analysis of summary data (e.g., means, standard deviations, and sample sizes) from a set of studies via a statistical model that is a special case of a hierarchical (or multilevel) model. Unfortunately, the common summary-data approach to meta-analysis used in psychological research is often employed in settings where the complexity of the data warrants alternative approaches. In this article, we propose a thought experiment that can lead meta-analysts to move away from the common summary-data approach to meta-analysis and toward richer and more appropriate summary-data approaches when the complexity of the data warrants it. Specifically, we propose that it can be extremely fruitful for meta-analysts to act as if they possess the individual-level data from the studies and consider what model specifications they might fit even when they possess only summary data. This thought experiment is justified because (a) the analysis of the individual-level data from the studies via a hierarchical model is considered the “gold standard” for meta-analysis and (b) for a wide variety of cases common in meta-analysis, the summary-data and individual-level-data approaches are, by a principle known as statistical sufficiency, equivalent when the underlying models are appropriately specified. We illustrate the value of our thought experiment via a case study that evolves across five parts that cover a wide variety of data settings common in meta-analysis.
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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 | 0.638 | 0.687 |
| Meta-epidemiology (narrow) | 0.004 | 0.003 |
| Meta-epidemiology (broad) | 0.006 | 0.008 |
| Bibliometrics | 0.008 | 0.008 |
| Science and technology studies | 0.007 | 0.028 |
| Scholarly communication | 0.013 | 0.028 |
| Open science | 0.007 | 0.012 |
| Research integrity | 0.015 | 0.013 |
| 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; the direct Gemma label and the distilled Codex classifier agree on what is shown here.
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".