Revisit two default priors: sigma_subject and factor-loading geometry

[ethanbuckley]

Note

Drafted by an LLM-based AI tool (Claude Code/Opus 4.8).

From the critical prior-analysis review (PR #380, notes/202607211500-prior-critical-review.md). Two default priors are in genuine tension with the data; the core effect priors (tau, gamma_cross, alpha, kappa, GP eta) are correctly scaled and should be left as-is.

• sigma_subject — widen from HalfNormal(0.5) to HalfNormal(1.0) for the high-variance Down-syndrome verbal/reading measures in rlm-hg/rlm-jc. The current scale is in genuine prior-data conflict (DS posteriors 1.25–1.39, at/beyond the 99th prior percentile) and mildly biases the reported between-child spread downward.
• mm/rlm-mm loadings — replace HalfNormal(1) on loadings-and-residuals with a communality-scale or (0,1)-bounded loading prior that respects λ²+σ²≈1 (current: ~32% prior mass on loadings >1, Heywood-adjacent), and switch LKJCholeskyCov→LKJCorr (as the longitudinal analogue already does) to drop the phantom factor-SD nuisances that dominate the rlm-mm R̂ failures.

[frankbuckley]

Note

Drafted by a LLM-based AI tool (Claude Code/Opus 4.8).

Two updates to the second checklist item (mm / rlm-mm loadings), from the #412 decision recorded in notes/202607241200-mm001-gate-exception.md.

The rlm-mm-001 half has partly landed. #412 replaced the HalfNormal(1) loading-and-residual pair with a communality-scale parameterisation (the free parameter is the communality c ∈ (0, 1); loading and residual are derived so λ² + σ² ≈ 1), which removed the Heywood ridge and cut divergences 143 → 72. It did not clear the gate: the residual divergences are intrinsic to a near-singular correlation matrix (the wave-3 domains correlate 0.81–0.95 and the first eigenvalue carries ≈ 89.5% of the variance), so the model now ships a recorded, signed-off gate exception waiving the divergences check only, with R-hat, ESS and BFMI still live. Raising target_accept 0.99 → 0.999 cut divergences to ~12 but starved the chains (min ESS 749 → 99, max R-hat 1.006 → 1.045), so 0.99 is the committed operating point.

The mm (RLI) half has not, and the whole family is gate-failing. The communality parameterisation was added to the RLM builder; the RLI mm models still use the old loading/residual form. Stored reporting fits:

Model	divergences	max R-hat	min ESS	Gate
lrp-rli-mm-001	1	1.0195	354	fail
lrp-rli-mm-002	0	1.0478	64	fail
lrp-rli-mm-101	57	1.0213	260	fail

mm-002 is the one worth naming explicitly on this issue: it fails on mixing alone — zero divergences, R-hat 1.048, min ESS 64 — which is exactly the failure mode the LKJCholeskyCov → LKJCorr switch is meant to address (dropping the phantom factor-SD nuisances that never enter the likelihood but do enter the all-free-RV gate). The mm-001 gate-exception note flags that route as separate work and states plainly that a divergence waiver does not transfer to it. Suggest adding it as its own checklist line so it is not read as covered by the rlm-mm rescue:

• mm-002 (and the RLI mm family) mixing — carry the communality parameterisation to the RLI builder and switch LKJCholeskyCov → LKJCorr (L @ Lᵀ, as lcf already does); target R-hat ≤ 1.01 and ESS ≥ 400 on mm-001, mm-002 and mm-101, none of which currently pass.

Note this is separate from the mm-002 beta_code / beta_G prior-scale refit tracked on #382 — that one is about whether the headline slope is under-scaled at N(0, 0.3), this one is about whether the posterior is sampled well enough to report at all. The scale refit should follow the parameterisation fix, not precede it.