Multilevel Meta-Analysis of Multiple Regression Coefficients from Single-Case Experimental Studies.
Bibliographic record
Abstract
The focus of the current study is on handling the dependence among multiple regression coefficients representing the treatment effects when meta-analyzing data from single-case experimental studies. We compare the results when applying three different multilevel meta-analytic models (i.e., a univariate multilevel model avoiding the dependence, a multivariate multilevel model ignoring covariance at higher levels, and a multivariate multilevel model modeling the existing covariance) to deal with the dependent effect sizes. The results indicate better estimates of the overall treatment effects and variance components when a multivariate multilevel model is applied, independent of modeling or ignoring the existing covariance. These findings confirm the robustness of multilevel modeling to misspecifying the existing covariance at the case and study level in terms of estimating the overall treatment effects and variance components. The results also show that the overall treatment effect estimates are unbiased regardless of the underlying model, but the between-case and between-study variance components are biased in certain conditions. In addition, the between-study variance estimates are particularly biased when the number of studies is smaller than 40 (i.e., 10 or 20) and the true value of the between-case variance is relatively large (i.e., 8). The observed bias is larger for the between-case variance estimates compared to the between-study variance estimates when the true between-case variance is relatively small (i.e., 0.5).
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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 | 0.171 | 0.444 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.009 | 0.041 |
| Bibliometrics | 0.015 | 0.014 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.006 | 0.004 |
| Open science | 0.005 | 0.004 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.008 | 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".