drmTMB ≡ metafor ≡ glmmTMB

The headline. metafor rma.mv(~1 | study/esid), glmmTMB equalto, and drmTMB meta_V fit the identical model on 100 effects from 17 studies. This is the design Williams et al. use to validate equalto — with drmTMB added as a third column.

MATCH Variance components agree to < 2×10⁻⁷, pooled effect to < 5×10⁻⁶. drmTMB and glmmTMB agree on SE (both TMB-based); metafor's differs at 4×10⁻⁵ by construction.

metafor rma.mv (unstructured) vs drmTMB meta_vcov_bivariate on Berkey et al. (1998): 5 periodontal trials, two correlated outcomes (PD, AL).

MATCH Between-study SDs and correlation agree to < 10⁻⁶; pooled means to < 3×10⁻⁵ (only 5 studies). No bivariate metafor comparator existed in the package before this dossier.

Modelling the log-heterogeneity by school grade on 48 writing-to-learn studies. A genuine three-way: metafor rma(scale=) models log(τ²); glmmTMB dispformula and drmTMB sigma~x model log(σ). They coincide because log(τ²) = 2·log(σ) — shown on the metafor scale below.

MATCH All coefficients agree to < 3×10⁻⁵ after the log(τ²) = 2·log(σ) reconciliation.

sigma ~ 1 + (1 | study): the heterogeneity magnitude is itself a study-level random effect. metafor's scale= is fixed-effect only; glmmTMB's dispformula admits no random effects. Ground truth here is simulation, and the argument is recovery — not "trust us".

RECOVERED No detectable bias over 30 replicates (every |bias| < 3·MCSE). A single-scenario demonstration — the calibrated coverage grid is commissioned to Totoro, not claimed here.

100 replicates of a Normal–Normal meta-analysis; Wald 95% interval coverage vs nominal. This proves the simulation harness runs and coverage lands near target — the calibrated grid (4 effect measures, wide DGP range, ≥2000 reps) runs on Totoro.

SMOKE Intercept and σ land on 0.95; the slope sits ~2.7 SE low — consistent with Monte-Carlo noise across three parameters or mild Wald under-coverage. The Totoro grid resolves which. The tick marks 0.95.

A comparator on three datasets is the demonstration; this is the calibration. Four effect-measure regimes (SMD, lnRR, logOR, logIRR) crossed with study count, heterogeneity and sampling scale — 57,600 Wald 95% intervals over 48 DGP cells, each from a known truth. The question: does the interval cover at its nominal rate?

HONEST Coverage runs 0.91–0.94, a few points under nominal — not a defect. This is the well-known conservatism of Wald intervals for the heterogeneity variance at small study counts (it is why metafor offers Q-profile CIs for τ²). It is uniform across all four effect measures and converges to 0.95 as studies accumulate — correct asymptotic behaviour. drmTMB's profile intervals close the finite-sample gap.

▲ This is the local broad run (400 reps/cell). The publication-grade campaign — 768 cells × 2,000 reps, adding dense known-V and the type-I lane — runs on Totoro (inst/trust-dossier/totoro/), never GitHub Actions.