Fix CS reg nuisance IF scaling, add SE scale-invariance test

- Remove spurious /n_c from regression nuisance IF correction in
  _outcome_regression survey covariate branch. asy_lin_rep_reg is already
  per-observation, so dividing by n_c double-scaled.
- Add test_reg_covariates_survey_se_scale_invariance: verifies ATT and SE
  are invariant to weight rescaling for reg+covariates+survey.

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

Author: igerber

diff_diff/staggered.py

@@ -1633,7 +1633,7 @@ def _outcome_regression(
                 # Influence function (survey-weighted)
                 inf_treated = sw_t_norm * (treated_residuals - att)
                 inf_control = (
-                    -sw_c_norm * (control_change - np.dot(X_c, beta)) + inf_control_reg_corr / n_c
+                    -sw_c_norm * (control_change - np.dot(X_c, beta)) + inf_control_reg_corr
                 )
                 inf_func = np.concatenate([inf_treated, inf_control])
 

tests/test_survey_phase4.py

@@ -658,6 +658,41 @@ def test_reg_covariates_survey_works(self, staggered_survey_data, survey_design_
         )
         assert np.isfinite(result.overall_att)
 
+    def test_reg_covariates_survey_se_scale_invariance(self, staggered_survey_data):
+        """SE for reg + covariates + survey must be invariant to weight rescaling."""
+        data = staggered_survey_data.copy()
+        data["x1"] = np.random.default_rng(42).normal(0, 1, len(data))
+        data["weight2"] = data["weight"] * 4.3
+        sd1 = SurveyDesign(weights="weight")
+        sd2 = SurveyDesign(weights="weight2")
+        est = CallawaySantAnna(estimation_method="reg")
+        r1 = est.fit(
+            data,
+            "outcome",
+            "unit",
+            "period",
+            "first_treat",
+            covariates=["x1"],
+            aggregate="simple",
+            survey_design=sd1,
+        )
+        r2 = est.fit(
+            data,
+            "outcome",
+            "unit",
+            "period",
+            "first_treat",
+            covariates=["x1"],
+            aggregate="simple",
+            survey_design=sd2,
+        )
+        assert np.isclose(
+            r1.overall_att, r2.overall_att, atol=1e-8
+        ), "ATT not scale-invariant for reg+cov+survey"
+        assert np.isclose(
+            r1.overall_se, r2.overall_se, atol=1e-8
+        ), f"SE not scale-invariant for reg+cov+survey: {r1.overall_se} vs {r2.overall_se}"
+
     def test_weighted_logit(self, staggered_survey_data, survey_design_weights_only):
         """Propensity scores should change with survey weights (IPW path)."""
         r_unw = CallawaySantAnna(estimation_method="ipw").fit(