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Meta-Regression

Fit a random-effects meta-regression with one moderator. Paule-Mandel τ² + Knapp-Hartung t(k−2) CIs (with max(1, …) floor). R² and Q_E reported. Bubble plot with fitted regression line and CI band.

Studies

Data
Four columns required. Lines starting with # are ignored. One numeric moderator only; use the four-column format shown above.
Display

Bubble plot

τ² via Paule-Mandel bisection; CIs use Knapp-Hartung t(k−2) with q = max(1, RSS/(k−2)) floor (HKSJ). R² measures the proportion of τ² explained by the moderator; Q_E tests residual heterogeneity (df = k−2). Export the R script to replicate with metafor::rma(yi, vi, mods=~x, method="PM", test="adhoc").

Multiple moderators and model comparison

Fit nested maximum-likelihood models with two or three numeric moderators. Enter independent study effects and their sampling variances. For categorical moderators, supply numeric indicator columns. Missing or invalid rows are refused.

Initial rows: metadat::dat.bcg, log risk ratios and sampling variances, with year and absolute latitude.

Checked against metafor rma(method="ML") run to tight convergence (control=list(threshold=1e-12*max(1,var(yi)), stepadj=0.5, maxiter=10000)). With metafor's default settings, results can differ from these in the third decimal place.

Header line yi,vi,name1,name2 (optionally a third moderator). One study per line, comma-separated, numbers only. Press Ctrl+Enter in the box to fit.