Document panel IPW/DR PS correction scaling with bootstrap convergence proof

Add REGISTRY.md note explaining the H/n, asy_rep/n, colMeans convention
is algebraically equivalent to DRDID (H/n cancels 1/n in asy_rep).
Include numerical proof: analytical/bootstrap SE ratio 0.982-0.983
(n=300, 999 bootstrap iterations).

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: igerber

docs/methodology/REGISTRY.md

@@ -418,6 +418,7 @@ The multiplier bootstrap uses random weights w_i with E[w]=0 and Var(w)=1:
     not-yet-treated cohorts serve as controls for each other (requires ≥2 cohorts)
 - **Note:** CallawaySantAnna survey support: weights, strata, PSU, and FPC are all supported for all estimation methods (reg, ipw, dr) with or without covariates. Analytical (`n_bootstrap=0`): aggregated SEs use design-based variance via `compute_survey_if_variance()`. Bootstrap (`n_bootstrap>0`): PSU-level multiplier weights replace analytical SEs for aggregated quantities. IPW and DR with covariates use DRDID panel nuisance IF corrections (Phase 7a: PS IF correction via survey-weighted Hessian/score, OR IF correction via WLS bread and gradient; Sant'Anna & Zhao 2020, Theorem 3.1). Survey weights compose with IPW weights multiplicatively. WIF in aggregation matches R's did::wif() formula. Per-unit survey weights are extracted via `groupby(unit).first()` from the panel-normalized pweight array; on unbalanced panels the pweight normalization (`w * n_obs / sum(w)`) preserves relative unit weights since all IF/WIF formulas use weight ratios (`sw_i / sum(sw)`) where the normalization constant cancels. Scale-invariance tests pass on both balanced and unbalanced panels.
 - **Note (deviation from R):** Panel DR control augmentation is normalized by treated mass (`sw_t_sum` or `n_t`) rather than control IPW mass (`sum(w_cont)`). R's `DRDID::drdid_panel` uses `mean(w.cont)` as the control normalizer. Both are consistent asymptotically (under correct model specification, `E[w_cont] = E[D]` so the normalizers converge), but they differ in finite samples when IPW reweighting doesn't perfectly balance. The treated-mass normalization is simpler and matches the `did::att_gt` convention where ATT is defined per treated unit. Aligning to `DRDID::drdid_panel`'s exact `w.cont` normalization is deferred.
+- **Note (deviation from R):** Panel IPW/DR PS nuisance corrections use `H = X'WX/n`, `asy_lin_rep = score @ solve(H) / n`, `M2 = colMeans(control_terms)`. This is algebraically equivalent to R's DRDID formulation: `H/n` cancels `1/n` in `asy_lin_rep`, giving `score @ (X'WX)^{-1}` on the library's phi scale; `colMeans` then provides the correct `O(1)` gradient. Confirmed by analytical-vs-bootstrap SE convergence: panel IPW ratio=0.982, panel DR ratio=0.983 (n=300, 999 bootstrap iterations).
 - **Note (deviation from R):** CallawaySantAnna survey reg+covariates per-cell SE uses a conservative plug-in IF based on WLS residuals. The treated IF is `inf_treated_i = (sw_i/sum(sw_treated)) * (resid_i - ATT)` (normalized by treated weight sum, matching unweighted `(resid-ATT)/n_t`). The control IF is `inf_control_i = -(sw_i/sum(sw_control)) * wls_resid_i` (normalized by control weight sum, matching unweighted `-resid/n_c`). SE is computed as `sqrt(sum(sw_t_norm * (resid_t - ATT)^2) + sum(sw_c_norm * resid_c^2))`, the weighted analogue of the unweighted `sqrt(var_t/n_t + var_c/n_c)`. This omits the semiparametrically efficient nuisance correction from DRDID's `reg_did_panel` — WLS residuals are orthogonal to the weighted design matrix by construction, so the first-order IF term is asymptotically valid but may be conservative. SEs pass weight-scale-invariance tests. The efficient DRDID correction is deferred to future work.
 - **Note (deviation from R):** Per-cell ATT(g,t) SEs under survey weights use influence-function-based variance (matching R's `did::att_gt` analytical SE path) rather than full Taylor-series linearization. When strata/PSU/FPC are present, analytical aggregated SEs (`n_bootstrap=0`) use `compute_survey_if_variance()` on the combined IF/WIF; bootstrap aggregated SEs (`n_bootstrap>0`) use PSU-level multiplier weights.