# Structural nested mean model

This study validates `StructuralNestedMean`, the linear structural nested mean model of Lewis and
Syrgkanis (2021). The estimator fits the blip coefficients by g-estimation with cross-fitted
nuisances. It also reports the reference mean `ey_reference` and the levels and contrasts of
declared static regimens. The page
[Structural dynamic effects](../structural-dynamic-effects.md) states the estimator, its
influence curve and its refusals.

The declared comparator is EconML 0.17.0 `DynamicDML` (`econml`) in a pinned container. Its runs
are a later change, so this page holds Python property evidence, with comparator runs pending.
The fast-tier parity fixture of `tests/canonical/econml_dynamic_dml` checks the point estimates
on one panel. That fixture is not a registered comparison.

## What was fitted

| setting | value |
| --- | --- |
| datasets | 1,000 samples of 2,000 rows for each of 11 scenarios, drawn from exact finite laws in `tests/studies/structural_nested_mean_laws.py` |
| fit | one `StructuralNestedMean` fit for each sample, with the blip features of its law |
| scenarios | `s2` (two binary nodes), `s3` (three binary nodes), `k` (two nodes of three levels), `c` (two doses), `h` (features that read $W$ and $A_1$), `p` (a past-treatment feature), `m` (a treatment that reads an earlier covariate), `l` (a feature that reads a time-varying covariate), `n` (nonlinear nuisances), `s2w` (known weights) and `s2c` (clusters of ten) |
| reported parameters | the blip coefficients, `ey_reference`, and the levels and contrasts of the declared static regimens. Law `l` reports the blips and `ey_reference` only |
| nuisances | a Gaussian `GLM` outcome regression and a `GLM` treatment regression at the declared interaction order of each law. Law `n` uses an early-stopped gradient booster for both roles |
| splitting | ten outer folds. Law `n` uses five |
| intervals | pointwise 95% Wald from the influence curve |
| initial estimate | not published. The estimator fits no fluctuation |

Each truth comes from an independent g-formula in `tests/discrete_law_structural.py`. Every law
except the negative controls satisfies the linear structural nested mean model with its declared
features. `tests/studies/canonical_structural_nested_mean.py` declares the laws, the learners,
the sizes and the reading rule before the run.

## Accuracy against known truth

<!-- generated: accuracy -->
| law | estimand | what was tested | implementation | bias (99% interval) | coverage | SE ratio | result |
| --- | --- | --- | --- | --- | --- | --- | --- |
| law C: two doses on -1, 0, 1, every conditional mean linear in the history | `ate_regimen[dose_high vs dose0]` | difference in mean outcome between the plans "assign dose 1 at the first node and -0.5 at the second" against "assign dose 0 at both nodes" | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.000916 to 0.0025 | 0.9460 | 0.9842 | pass |
| law C: two doses on -1, 0, 1, every conditional mean linear in the history | `ate_regimen[dose_mid vs dose0]` | difference in mean outcome between the plans "assign dose 0.5 at the first node and 0.25 at the second" against "assign dose 0 at both nodes" | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.000292 to 0.0012 | 0.9510 | 1.0201 | pass |
| law C: two doses on -1, 0, 1, every conditional mean linear in the history | `blip[A1:dose:intercept]` | blip of treatment A1 per unit dose | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.000620 to 0.0023 | 0.9410 | 1.0055 | pass |
| law C: two doses on -1, 0, 1, every conditional mean linear in the history | `blip[A2:dose:intercept]` | blip of treatment A2 per unit dose | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0011 to 0.0014 | 0.9450 | 0.9735 | pass |
| law C: two doses on -1, 0, 1, every conditional mean linear in the history | `ey_reference` | mean outcome with every treatment at its reference level | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0020 to 0.000479 | 0.9500 | 1.0080 | pass |
| law C: two doses on -1, 0, 1, every conditional mean linear in the history | `ey_regimen[dose_mid]` | mean outcome under the plan assign dose 0.5 at the first node and 0.25 at the second | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0017 to 0.0010 | 0.9460 | 0.9937 | pass |
| law H: blip features of the baseline at node 1 and of the baseline and the past treatment at node 2 | `ate_regimen[r10 vs r00]` | difference in mean outcome between the plans "assign treatment at the first node only" against "assign no treatment at both nodes" | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0028 to 0.0037 | 0.9490 | 1.0012 | pass |
| law H: blip features of the baseline at node 1 and of the baseline and the past treatment at node 2 | `ate_regimen[r11 vs r00]` | difference in mean outcome between the plans "assign treatment at both nodes" against "assign no treatment at both nodes" | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0022 to 0.0035 | 0.9570 | 1.0586 | pass |
| law H: blip features of the baseline at node 1 and of the baseline and the past treatment at node 2 | `blip[A1:1.0:W]` | blip of treatment A1 at level 1, coefficient of W | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0056 to 0.0045 | 0.9440 | 0.9655 | pass |
| law H: blip features of the baseline at node 1 and of the baseline and the past treatment at node 2 | `blip[A1:1.0:intercept]` | blip of treatment A1 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0034 to 0.0043 | 0.9520 | 0.9912 | pass |
| law H: blip features of the baseline at node 1 and of the baseline and the past treatment at node 2 | `blip[A2:1.0:A1]` | blip of treatment A2 at level 1, coefficient of A1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0044 to 0.0040 | 0.9450 | 0.9969 | pass |
| law H: blip features of the baseline at node 1 and of the baseline and the past treatment at node 2 | `blip[A2:1.0:W]` | blip of treatment A2 at level 1, coefficient of W | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0046 to 0.0044 | 0.9390 | 0.9304 | pass |
| law H: blip features of the baseline at node 1 and of the baseline and the past treatment at node 2 | `blip[A2:1.0:intercept]` | blip of treatment A2 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0029 to 0.0034 | 0.9390 | 0.9841 | pass |
| law H: blip features of the baseline at node 1 and of the baseline and the past treatment at node 2 | `ey_reference` | mean outcome with every treatment at its reference level | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0013 to 0.0023 | 0.9610 | 1.0382 | pass |
| law H: blip features of the baseline at node 1 and of the baseline and the past treatment at node 2 | `ey_regimen[r11]` | mean outcome under the plan assign treatment at both nodes | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0013 to 0.0035 | 0.9530 | 1.0447 | pass |
| law K: two nodes of three levels with unequal level effects | `ate_regimen[r12 vs r00]` | difference in mean outcome between the plans "assign level 1 at the first node and level 2 at the second" against "assign no treatment at both nodes" | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0051 to 0.0017 | 0.9540 | 1.0252 | pass |
| law K: two nodes of three levels with unequal level effects | `ate_regimen[r21 vs r00]` | difference in mean outcome between the plans "assign level 2 at the first node and level 1 at the second" against "assign no treatment at both nodes" | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0056 to 0.0017 | 0.9480 | 0.9631 | pass |
| law K: two nodes of three levels with unequal level effects | `blip[A1:1.0:intercept]` | blip of treatment A1 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0028 to 0.0024 | 0.9610 | 1.0246 | pass |
| law K: two nodes of three levels with unequal level effects | `blip[A1:2.0:intercept]` | blip of treatment A1 at level 2 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0041 to 0.0016 | 0.9490 | 0.9823 | pass |
| law K: two nodes of three levels with unequal level effects | `blip[A2:1.0:intercept]` | blip of treatment A2 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0032 to 0.0017 | 0.9380 | 0.9753 | pass |
| law K: two nodes of three levels with unequal level effects | `blip[A2:2.0:intercept]` | blip of treatment A2 at level 2 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0038 to 0.000822 | 0.9450 | 1.0075 | pass |
| law K: two nodes of three levels with unequal level effects | `ey_reference` | mean outcome with every treatment at its reference level | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0017 to 0.0023 | 0.9510 | 1.0094 | pass |
| law K: two nodes of three levels with unequal level effects | `ey_regimen[r12]` | mean outcome under the plan assign level 1 at the first node and level 2 at the second | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0040 to 0.0011 | 0.9520 | 1.0142 | pass |
| law L: the second blip depends on the second covariate, which the feature declares | `blip[A1:1.0:intercept]` | blip of treatment A1 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0020 to 0.0032 | 0.9430 | 0.9895 | pass |
| law L: the second blip depends on the second covariate, which the feature declares | `blip[A2:1.0:S2]` | blip of treatment A2 at level 1, coefficient of S2 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0043 to 0.0039 | 0.9570 | 1.0169 | pass |
| law L: the second blip depends on the second covariate, which the feature declares | `blip[A2:1.0:intercept]` | blip of treatment A2 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0035 to 0.0020 | 0.9610 | 1.0357 | pass |
| law L: the second blip depends on the second covariate, which the feature declares | `ey_reference` | mean outcome with every treatment at its reference level | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0014 to 0.0020 | 0.9510 | 1.0333 | pass |
| law M: the second treatment and the outcome read the first covariate | `ate_regimen[r11 vs r00]` | difference in mean outcome between the plans "assign treatment at both nodes" against "assign no treatment at both nodes" | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0037 to 0.0024 | 0.9540 | 1.0074 | pass |
| law M: the second treatment and the outcome read the first covariate | `blip[A1:1.0:intercept]` | blip of treatment A1 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0035 to 0.0013 | 0.9430 | 0.9917 | pass |
| law M: the second treatment and the outcome read the first covariate | `blip[A2:1.0:intercept]` | blip of treatment A2 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0019 to 0.0029 | 0.9410 | 1.0144 | pass |
| law M: the second treatment and the outcome read the first covariate | `ey_reference` | mean outcome with every treatment at its reference level | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0027 to 0.0022 | 0.9600 | 1.0082 | pass |
| law N: nonlinear nuisances on a nine-point baseline, fitted by a shallow booster | `ate_regimen[r11 vs r00]` | difference in mean outcome between the plans "assign treatment at both nodes" against "assign no treatment at both nodes" | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0051 to 0.0015 | 0.9360 | 0.9435 | pass |
| law N: nonlinear nuisances on a nine-point baseline, fitted by a shallow booster | `blip[A1:1.0:intercept]` | blip of treatment A1 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0028 to 0.0023 | 0.9470 | 0.9933 | pass |
| law N: nonlinear nuisances on a nine-point baseline, fitted by a shallow booster | `blip[A2:1.0:intercept]` | blip of treatment A2 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0037 to 0.000600 | 0.9430 | 0.9966 | pass |
| law N: nonlinear nuisances on a nine-point baseline, fitted by a shallow booster | `ey_reference` | mean outcome with every treatment at its reference level | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0026 to 0.0024 | 0.9410 | 0.9792 | pass |
| law P: the second blip depends on the first treatment | `ate_regimen[r11 vs r00]` | difference in mean outcome between the plans "assign treatment at both nodes" against "assign no treatment at both nodes" | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0020 to 0.0036 | 0.9520 | 1.0058 | pass |
| law P: the second blip depends on the first treatment | `blip[A1:1.0:intercept]` | blip of treatment A1 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.000616 to 0.0056 | 0.9560 | 1.0445 | pass |
| law P: the second blip depends on the first treatment | `blip[A2:1.0:A1]` | blip of treatment A2 at level 1, coefficient of A1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0067 to 0.0017 | 0.9420 | 0.9934 | pass |
| law P: the second blip depends on the first treatment | `blip[A2:1.0:intercept]` | blip of treatment A2 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0018 to 0.0035 | 0.9530 | 1.0108 | pass |
| law P: the second blip depends on the first treatment | `ey_reference` | mean outcome with every treatment at its reference level | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0029 to 0.000828 | 0.9610 | 1.0046 | pass |
| law P: the second blip depends on the first treatment | `ey_regimen[r01]` | mean outcome under the plan assign treatment at the second node only | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0024 to 0.0020 | 0.9460 | 1.0237 | pass |
| law S2: two binary nodes, a constant blip at each node | `ate_regimen[r11 vs r00]` | difference in mean outcome between the plans "assign treatment at both nodes" against "assign no treatment at both nodes" | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0020 to 0.0036 | 0.9500 | 0.9964 | pass |
| law S2: two binary nodes, a constant blip at each node | `blip[A1:1.0:intercept]` | blip of treatment A1 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0038 to 0.0010 | 0.9490 | 1.0019 | pass |
| law S2: two binary nodes, a constant blip at each node | `blip[A2:1.0:intercept]` | blip of treatment A2 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | 0.000165 to 0.0042 | 0.9590 | 1.0262 | pass |
| law S2: two binary nodes, a constant blip at each node | `ey_reference` | mean outcome with every treatment at its reference level | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0022 to 0.0013 | 0.9530 | 1.0002 | pass |
| law S2: two binary nodes, a constant blip at each node | `ey_regimen[r10]` | mean outcome under the plan assign treatment at the first node only | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0041 to 0.000395 | 0.9520 | 0.9937 | pass |
| law S2: two binary nodes, a constant blip at each node | `ey_regimen[r11]` | mean outcome under the plan assign treatment at both nodes | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0016 to 0.0023 | 0.9490 | 1.0031 | pass |
| law S2 in clusters of ten that share the baseline and an outcome intercept | `ate_regimen[r11 vs r00]` | difference in mean outcome between the plans "assign treatment at both nodes" against "assign no treatment at both nodes" | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0060 to 0.0049 | 0.9600 | 1.0286 | pass |
| law S2 in clusters of ten that share the baseline and an outcome intercept | `blip[A1:1.0:intercept]` | blip of treatment A1 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0045 to 0.0047 | 0.9540 | 1.0047 | pass |
| law S2 in clusters of ten that share the baseline and an outcome intercept | `ey_reference` | mean outcome with every treatment at its reference level | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0082 to 0.0043 | 0.9550 | 1.0301 | pass |
| law S2 in clusters of ten that share the baseline and an outcome intercept | `ey_regimen[r11]` | mean outcome under the plan assign treatment at both nodes | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0092 to 0.0042 | 0.9470 | 1.0054 | pass |
| law S2 with the known weight 0.5 + 1.5 W, target the reweighted population | `ate_regimen[r11 vs r00]` | difference in mean outcome between the plans "assign treatment at both nodes" against "assign no treatment at both nodes" | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0015 to 0.0050 | 0.9590 | 1.0406 | pass |
| law S2 with the known weight 0.5 + 1.5 W, target the reweighted population | `blip[A1:1.0:intercept]` | blip of treatment A1 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0024 to 0.0032 | 0.9540 | 1.0273 | pass |
| law S2 with the known weight 0.5 + 1.5 W, target the reweighted population | `ey_reference` | mean outcome with every treatment at its reference level | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0027 to 0.0017 | 0.9470 | 0.9781 | pass |
| law S2 with the known weight 0.5 + 1.5 W, target the reweighted population | `ey_regimen[r11]` | mean outcome under the plan assign treatment at both nodes | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.000868 to 0.0034 | 0.9600 | 1.0570 | pass |
| law S3: three binary nodes with a path from each treatment to the later ones | `ate_regimen[r101 vs r000]` | difference in mean outcome between the plans "assign treatment at the first and third nodes only" against "assign no treatment at the three nodes" | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0039 to 0.0023 | 0.9430 | 0.9829 | pass |
| law S3: three binary nodes with a path from each treatment to the later ones | `ate_regimen[r111 vs r000]` | difference in mean outcome between the plans "assign treatment at the three nodes" against "assign no treatment at the three nodes" | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0033 to 0.0029 | 0.9470 | 0.9867 | pass |
| law S3: three binary nodes with a path from each treatment to the later ones | `blip[A1:1.0:intercept]` | blip of treatment A1 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0041 to 0.0012 | 0.9580 | 0.9528 | pass |
| law S3: three binary nodes with a path from each treatment to the later ones | `blip[A2:1.0:intercept]` | blip of treatment A2 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0018 to 0.0031 | 0.9460 | 0.9796 | pass |
| law S3: three binary nodes with a path from each treatment to the later ones | `blip[A3:1.0:intercept]` | blip of treatment A3 at level 1 | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0015 to 0.0028 | 0.9560 | 1.0208 | pass |
| law S3: three binary nodes with a path from each treatment to the later ones | `ey_reference` | mean outcome with every treatment at its reference level | `cleverly` structural nested mean model, g-estimation with GLM nuisances (a shallow booster on law N) | -0.0018 to 0.0020 | 0.9460 | 0.9671 | pass |
<!-- /generated -->

## Agreement with the canonical implementation

Python property evidence, with comparator runs pending. The EconML `DynamicDML` runs have not run
on the declared draws, so this study publishes no paired verdict. `equivalence.csv` records no
row. The change that registers the comparator runs adds the paired verdicts.

## Theory properties

<!-- generated: properties -->
| property | cell | role | what was tested | what must hold | measured | result |
| --- | --- | --- | --- | --- | --- | --- |
| `blip_feature_control` | `lu_ate_r01__too_few_features` | control | law L fitted without its second-covariate feature: contrast of regimen r01 against the reference regimen: the structural fit with the second-node blip feature the law needs left out | the bias interval must lie beyond the margin on the side of the computed gap | bias 0.1363 to 0.1395, margin 0.0070 | pass |
| `blip_feature_control` | `lu_ate_r10__too_few_features` | control | law L fitted without its second-covariate feature: contrast of regimen r10 against the reference regimen: the structural fit with the second-node blip feature the law needs left out | the bias interval must lie beyond the margin on the side of the computed gap | bias 0.1634 to 0.1676, margin 0.0091 | pass |
| `blip_feature_control` | `lu_ey_r11__too_few_features` | control | law L fitted without its second-covariate feature: mean outcome under regimen r11: the structural fit with the second-node blip feature the law needs left out | the bias interval must lie beyond the margin on the side of the computed gap | bias -0.0264 to -0.0228, margin 0.0078 | pass |
| `blip_feature_control` | `vb_ate_r01__too_few_features` | control | law P fitted with a baseline-only second feature: contrast of regimen r01 against the reference regimen: the structural fit with the second-node blip feature the law needs left out | the bias interval must lie beyond the margin on the side of the computed gap | bias 0.6202 to 0.6240, margin 0.0081 | pass |
| `blip_feature_control` | `vb_ate_r10__too_few_features` | control | law P fitted with a baseline-only second feature: contrast of regimen r10 against the reference regimen: the structural fit with the second-node blip feature the law needs left out | the bias interval must lie beyond the margin on the side of the computed gap | bias 0.7864 to 0.7907, margin 0.0093 | pass |
| `blip_feature_control` | `vb_ate_r11__too_few_features` | control | law P fitted with a baseline-only second feature: contrast of regimen r11 against the reference regimen: the structural fit with the second-node blip feature the law needs left out | the bias interval must lie beyond the margin on the side of the computed gap | bias -0.0916 to -0.0871, margin 0.0099 | pass |
| `blip_feature_control` | `vb_ey_r11__too_few_features` | control | law P fitted with a baseline-only second feature: mean outcome under regimen r11: the structural fit with the second-node blip feature the law needs left out | the bias interval must lie beyond the margin on the side of the computed gap | bias -0.3234 to -0.3199, margin 0.0075 | pass |
| `interval_calibration` | `c_ate_dose_high__correctly_specified` | positive | law C, two doses with linear conditional means: contrast of regimen dose_high against the reference regimen: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9468 to 0.9591, SE ratio 0.9773 to 1.0181 | pass |
| `interval_calibration` | `c_ate_dose_high__noise_control` | control | law C, two doses with linear conditional means: contrast of regimen dose_high against the reference regimen: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8244 to 0.8459, SE ratio 0.6940 to 0.7226 | pass |
| `interval_calibration` | `c_ate_dose_high__shrunken_se_control` | control | law C, two doses with linear conditional means: contrast of regimen dose_high against the reference regimen: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8165 to 0.8384, SE ratio 0.6845 to 0.7129 | pass |
| `interval_calibration` | `c_ate_dose_mid__correctly_specified` | positive | law C, two doses with linear conditional means: contrast of regimen dose_mid against the reference regimen: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9414 to 0.9543, SE ratio 0.9785 to 1.0194 | pass |
| `interval_calibration` | `c_ate_dose_mid__noise_control` | control | law C, two doses with linear conditional means: contrast of regimen dose_mid against the reference regimen: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8171 to 0.8390, SE ratio 0.6886 to 0.7169 | pass |
| `interval_calibration` | `c_ate_dose_mid__shrunken_se_control` | control | law C, two doses with linear conditional means: contrast of regimen dose_mid against the reference regimen: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8132 to 0.8352, SE ratio 0.6851 to 0.7133 | pass |
| `interval_calibration` | `c_blip_a1__correctly_specified` | positive | law C, two doses with linear conditional means: blip of the first treatment: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9407 to 0.9537, SE ratio 0.9782 to 1.0185 | pass |
| `interval_calibration` | `c_blip_a1__noise_control` | control | law C, two doses with linear conditional means: blip of the first treatment: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8246 to 0.8460, SE ratio 0.6931 to 0.7220 | pass |
| `interval_calibration` | `c_blip_a1__shrunken_se_control` | control | law C, two doses with linear conditional means: blip of the first treatment: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8137 to 0.8357, SE ratio 0.6852 to 0.7130 | pass |
| `interval_calibration` | `c_blip_a2__correctly_specified` | positive | law C, two doses with linear conditional means: blip of the second treatment: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9401 to 0.9531, SE ratio 0.9787 to 1.0195 | pass |
| `interval_calibration` | `c_blip_a2__noise_control` | control | law C, two doses with linear conditional means: blip of the second treatment: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8215 to 0.8431, SE ratio 0.6847 to 0.7129 | pass |
| `interval_calibration` | `c_blip_a2__shrunken_se_control` | control | law C, two doses with linear conditional means: blip of the second treatment: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8210 to 0.8426, SE ratio 0.6856 to 0.7136 | pass |
| `interval_calibration` | `c_ey0__correctly_specified` | positive | law C, two doses with linear conditional means: mean outcome with every treatment at its reference: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9451 to 0.9576, SE ratio 0.9857 to 1.0271 | pass |
| `interval_calibration` | `c_ey0__noise_control` | control | law C, two doses with linear conditional means: mean outcome with every treatment at its reference: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8299 to 0.8511, SE ratio 0.7028 to 0.7315 | pass |
| `interval_calibration` | `c_ey0__shrunken_se_control` | control | law C, two doses with linear conditional means: mean outcome with every treatment at its reference: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8239 to 0.8454, SE ratio 0.6899 to 0.7185 | pass |
| `interval_calibration` | `c_ey_dose_mid__correctly_specified` | positive | law C, two doses with linear conditional means: mean outcome under regimen dose_mid: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9452 to 0.9577, SE ratio 0.9859 to 1.0257 | pass |
| `interval_calibration` | `c_ey_dose_mid__noise_control` | control | law C, two doses with linear conditional means: mean outcome under regimen dose_mid: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8302 to 0.8514, SE ratio 0.6979 to 0.7274 | pass |
| `interval_calibration` | `c_ey_dose_mid__shrunken_se_control` | control | law C, two doses with linear conditional means: mean outcome under regimen dose_mid: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8198 to 0.8415, SE ratio 0.6900 to 0.7183 | pass |
| `interval_calibration` | `h_ate_r10__correctly_specified` | positive | law H, blip features of the baseline and the past treatment: contrast of regimen r10 against the reference regimen: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9361 to 0.9496, SE ratio 0.9598 to 0.9992 | pass |
| `interval_calibration` | `h_ate_r10__noise_control` | control | law H, blip features of the baseline and the past treatment: contrast of regimen r10 against the reference regimen: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8098 to 0.8320, SE ratio 0.6780 to 0.7056 | pass |
| `interval_calibration` | `h_ate_r10__shrunken_se_control` | control | law H, blip features of the baseline and the past treatment: contrast of regimen r10 against the reference regimen: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8116 to 0.8337, SE ratio 0.6716 to 0.6996 | pass |
| `interval_calibration` | `h_ate_r11__correctly_specified` | positive | law H, blip features of the baseline and the past treatment: contrast of regimen r11 against the reference regimen: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9417 to 0.9545, SE ratio 0.9711 to 1.0114 | pass |
| `interval_calibration` | `h_ate_r11__noise_control` | control | law H, blip features of the baseline and the past treatment: contrast of regimen r11 against the reference regimen: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8164 to 0.8382, SE ratio 0.6806 to 0.7092 | pass |
| `interval_calibration` | `h_ate_r11__shrunken_se_control` | control | law H, blip features of the baseline and the past treatment: contrast of regimen r11 against the reference regimen: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8116 to 0.8337, SE ratio 0.6795 to 0.7076 | pass |
| `interval_calibration` | `h_blip_a1_l1__correctly_specified` | positive | law H, blip features of the baseline and the past treatment: blip of the first treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9389 to 0.9521, SE ratio 0.9611 to 1.0007 | pass |
| `interval_calibration` | `h_blip_a1_l1__noise_control` | control | law H, blip features of the baseline and the past treatment: blip of the first treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8155 to 0.8374, SE ratio 0.6849 to 0.7136 | pass |
| `interval_calibration` | `h_blip_a1_l1__shrunken_se_control` | control | law H, blip features of the baseline and the past treatment: blip of the first treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8069 to 0.8292, SE ratio 0.6727 to 0.7008 | pass |
| `interval_calibration` | `h_blip_a1_l1_w__correctly_specified` | positive | law H, blip features of the baseline and the past treatment: blip of the first treatment at level 1, slope on the baseline W: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9423 to 0.9551, SE ratio 0.9870 to 1.0280 | pass |
| `interval_calibration` | `h_blip_a1_l1_w__noise_control` | control | law H, blip features of the baseline and the past treatment: blip of the first treatment at level 1, slope on the baseline W: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8332 to 0.8542, SE ratio 0.7037 to 0.7332 | pass |
| `interval_calibration` | `h_blip_a1_l1_w__shrunken_se_control` | control | law H, blip features of the baseline and the past treatment: blip of the first treatment at level 1, slope on the baseline W: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8189 to 0.8407, SE ratio 0.6907 to 0.7196 | pass |
| `interval_calibration` | `h_blip_a2_l1__correctly_specified` | positive | law H, blip features of the baseline and the past treatment: blip of the second treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9415 to 0.9544, SE ratio 0.9778 to 1.0192 | pass |
| `interval_calibration` | `h_blip_a2_l1__noise_control` | control | law H, blip features of the baseline and the past treatment: blip of the second treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8246 to 0.8460, SE ratio 0.6906 to 0.7191 | pass |
| `interval_calibration` | `h_blip_a2_l1__shrunken_se_control` | control | law H, blip features of the baseline and the past treatment: blip of the second treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8202 to 0.8419, SE ratio 0.6845 to 0.7129 | pass |
| `interval_calibration` | `h_blip_a2_l1_a1__correctly_specified` | positive | law H, blip features of the baseline and the past treatment: blip of the second treatment at level 1, slope on the first treatment: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9433 to 0.9560, SE ratio 0.9766 to 1.0168 | pass |
| `interval_calibration` | `h_blip_a2_l1_a1__noise_control` | control | law H, blip features of the baseline and the past treatment: blip of the second treatment at level 1, slope on the first treatment: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8316 to 0.8527, SE ratio 0.7058 to 0.7348 | pass |
| `interval_calibration` | `h_blip_a2_l1_a1__shrunken_se_control` | control | law H, blip features of the baseline and the past treatment: blip of the second treatment at level 1, slope on the first treatment: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8157 to 0.8376, SE ratio 0.6839 to 0.7119 | pass |
| `interval_calibration` | `h_blip_a2_l1_w__correctly_specified` | positive | law H, blip features of the baseline and the past treatment: blip of the second treatment at level 1, slope on the baseline W: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9435 to 0.9562, SE ratio 0.9788 to 1.0191 | pass |
| `interval_calibration` | `h_blip_a2_l1_w__noise_control` | control | law H, blip features of the baseline and the past treatment: blip of the second treatment at level 1, slope on the baseline W: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8198 to 0.8415, SE ratio 0.6878 to 0.7163 | pass |
| `interval_calibration` | `h_blip_a2_l1_w__shrunken_se_control` | control | law H, blip features of the baseline and the past treatment: blip of the second treatment at level 1, slope on the baseline W: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8162 to 0.8381, SE ratio 0.6853 to 0.7142 | pass |
| `interval_calibration` | `h_ey0__correctly_specified` | positive | law H, blip features of the baseline and the past treatment: mean outcome with every treatment at its reference: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9422 to 0.9550, SE ratio 0.9799 to 1.0199 | pass |
| `interval_calibration` | `h_ey0__noise_control` | control | law H, blip features of the baseline and the past treatment: mean outcome with every treatment at its reference: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8258 to 0.8473, SE ratio 0.6893 to 0.7176 | pass |
| `interval_calibration` | `h_ey0__shrunken_se_control` | control | law H, blip features of the baseline and the past treatment: mean outcome with every treatment at its reference: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8208 to 0.8425, SE ratio 0.6857 to 0.7142 | pass |
| `interval_calibration` | `h_ey_r11__correctly_specified` | positive | law H, blip features of the baseline and the past treatment: mean outcome under regimen r11: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9403 to 0.9534, SE ratio 0.9709 to 1.0096 | pass |
| `interval_calibration` | `h_ey_r11__noise_control` | control | law H, blip features of the baseline and the past treatment: mean outcome under regimen r11: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8192 to 0.8409, SE ratio 0.6844 to 0.7134 | pass |
| `interval_calibration` | `h_ey_r11__shrunken_se_control` | control | law H, blip features of the baseline and the past treatment: mean outcome under regimen r11: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8123 to 0.8343, SE ratio 0.6795 to 0.7069 | pass |
| `interval_calibration` | `k_ate_r12__correctly_specified` | positive | law K, two nodes of three levels: contrast of regimen r12 against the reference regimen: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9441 to 0.9567, SE ratio 0.9819 to 1.0231 | pass |
| `interval_calibration` | `k_ate_r12__noise_control` | control | law K, two nodes of three levels: contrast of regimen r12 against the reference regimen: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8207 to 0.8424, SE ratio 0.6900 to 0.7188 | pass |
| `interval_calibration` | `k_ate_r12__shrunken_se_control` | control | law K, two nodes of three levels: contrast of regimen r12 against the reference regimen: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8211 to 0.8428, SE ratio 0.6876 to 0.7160 | pass |
| `interval_calibration` | `k_ate_r21__correctly_specified` | positive | law K, two nodes of three levels: contrast of regimen r21 against the reference regimen: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9407 to 0.9537, SE ratio 0.9813 to 1.0223 | pass |
| `interval_calibration` | `k_ate_r21__noise_control` | control | law K, two nodes of three levels: contrast of regimen r21 against the reference regimen: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8234 to 0.8449, SE ratio 0.6944 to 0.7224 | pass |
| `interval_calibration` | `k_ate_r21__shrunken_se_control` | control | law K, two nodes of three levels: contrast of regimen r21 against the reference regimen: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8215 to 0.8431, SE ratio 0.6867 to 0.7161 | pass |
| `interval_calibration` | `k_blip_a1_l1__correctly_specified` | positive | law K, two nodes of three levels: blip of the first treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9450 to 0.9575, SE ratio 0.9839 to 1.0243 | pass |
| `interval_calibration` | `k_blip_a1_l1__noise_control` | control | law K, two nodes of three levels: blip of the first treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8150 to 0.8369, SE ratio 0.6801 to 0.7078 | pass |
| `interval_calibration` | `k_blip_a1_l1__shrunken_se_control` | control | law K, two nodes of three levels: blip of the first treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8205 to 0.8421, SE ratio 0.6887 to 0.7175 | pass |
| `interval_calibration` | `k_blip_a1_l2__correctly_specified` | positive | law K, two nodes of three levels: blip of the first treatment at level 2: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9434 to 0.9561, SE ratio 0.9841 to 1.0228 | pass |
| `interval_calibration` | `k_blip_a1_l2__noise_control` | control | law K, two nodes of three levels: blip of the first treatment at level 2: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8225 to 0.8441, SE ratio 0.6921 to 0.7214 | pass |
| `interval_calibration` | `k_blip_a1_l2__shrunken_se_control` | control | law K, two nodes of three levels: blip of the first treatment at level 2: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8185 to 0.8403, SE ratio 0.6884 to 0.7160 | pass |
| `interval_calibration` | `k_blip_a2_l1__correctly_specified` | positive | law K, two nodes of three levels: blip of the second treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9462 to 0.9585, SE ratio 0.9866 to 1.0276 | pass |
| `interval_calibration` | `k_blip_a2_l1__noise_control` | control | law K, two nodes of three levels: blip of the second treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8221 to 0.8437, SE ratio 0.6860 to 0.7157 | pass |
| `interval_calibration` | `k_blip_a2_l1__shrunken_se_control` | control | law K, two nodes of three levels: blip of the second treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8176 to 0.8395, SE ratio 0.6906 to 0.7190 | pass |
| `interval_calibration` | `k_blip_a2_l2__correctly_specified` | positive | law K, two nodes of three levels: blip of the second treatment at level 2: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9421 to 0.9549, SE ratio 0.9790 to 1.0208 | pass |
| `interval_calibration` | `k_blip_a2_l2__noise_control` | control | law K, two nodes of three levels: blip of the second treatment at level 2: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8290 to 0.8503, SE ratio 0.6963 to 0.7251 | pass |
| `interval_calibration` | `k_blip_a2_l2__shrunken_se_control` | control | law K, two nodes of three levels: blip of the second treatment at level 2: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8253 to 0.8468, SE ratio 0.6857 to 0.7147 | pass |
| `interval_calibration` | `k_ey0__correctly_specified` | positive | law K, two nodes of three levels: mean outcome with every treatment at its reference: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9394 to 0.9525, SE ratio 0.9695 to 1.0097 | pass |
| `interval_calibration` | `k_ey0__noise_control` | control | law K, two nodes of three levels: mean outcome with every treatment at its reference: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8146 to 0.8365, SE ratio 0.6783 to 0.7060 | pass |
| `interval_calibration` | `k_ey0__shrunken_se_control` | control | law K, two nodes of three levels: mean outcome with every treatment at its reference: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8125 to 0.8346, SE ratio 0.6785 to 0.7070 | pass |
| `interval_calibration` | `k_ey_r12__correctly_specified` | positive | law K, two nodes of three levels: mean outcome under regimen r12: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9426 to 0.9554, SE ratio 0.9882 to 1.0291 | pass |
| `interval_calibration` | `k_ey_r12__noise_control` | control | law K, two nodes of three levels: mean outcome under regimen r12: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8264 to 0.8477, SE ratio 0.6940 to 0.7230 | pass |
| `interval_calibration` | `k_ey_r12__shrunken_se_control` | control | law K, two nodes of three levels: mean outcome under regimen r12: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8215 to 0.8431, SE ratio 0.6916 to 0.7202 | pass |
| `interval_calibration` | `l_blip_a1_l1__correctly_specified` | positive | law L, the second blip reads the second covariate, which the feature declares: blip of the first treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9439 to 0.9565, SE ratio 0.9911 to 1.0326 | pass |
| `interval_calibration` | `l_blip_a1_l1__noise_control` | control | law L, the second blip reads the second covariate, which the feature declares: blip of the first treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8251 to 0.8465, SE ratio 0.6924 to 0.7214 | pass |
| `interval_calibration` | `l_blip_a1_l1__shrunken_se_control` | control | law L, the second blip reads the second covariate, which the feature declares: blip of the first treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8285 to 0.8498, SE ratio 0.6938 to 0.7234 | pass |
| `interval_calibration` | `l_blip_a2_l1__correctly_specified` | positive | law L, the second blip reads the second covariate, which the feature declares: blip of the second treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9413 to 0.9542, SE ratio 0.9782 to 1.0188 | pass |
| `interval_calibration` | `l_blip_a2_l1__noise_control` | control | law L, the second blip reads the second covariate, which the feature declares: blip of the second treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8206 to 0.8423, SE ratio 0.6884 to 0.7178 | pass |
| `interval_calibration` | `l_blip_a2_l1__shrunken_se_control` | control | law L, the second blip reads the second covariate, which the feature declares: blip of the second treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8176 to 0.8395, SE ratio 0.6847 to 0.7131 | pass |
| `interval_calibration` | `l_blip_a2_l1_s2__correctly_specified` | positive | law L, the second blip reads the second covariate, which the feature declares: blip of the second treatment at level 1, slope on the second covariate: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9411 to 0.9541, SE ratio 0.9878 to 1.0296 | pass |
| `interval_calibration` | `l_blip_a2_l1_s2__noise_control` | control | law L, the second blip reads the second covariate, which the feature declares: blip of the second treatment at level 1, slope on the second covariate: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8269 to 0.8482, SE ratio 0.6981 to 0.7268 | pass |
| `interval_calibration` | `l_blip_a2_l1_s2__shrunken_se_control` | control | law L, the second blip reads the second covariate, which the feature declares: blip of the second treatment at level 1, slope on the second covariate: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8261 to 0.8475, SE ratio 0.6911 to 0.7206 | pass |
| `interval_calibration` | `l_ey0__correctly_specified` | positive | law L, the second blip reads the second covariate, which the feature declares: mean outcome with every treatment at its reference: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9393 to 0.9524, SE ratio 0.9602 to 1.0003 | pass |
| `interval_calibration` | `l_ey0__noise_control` | control | law L, the second blip reads the second covariate, which the feature declares: mean outcome with every treatment at its reference: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8244 to 0.8459, SE ratio 0.6892 to 0.7176 | pass |
| `interval_calibration` | `l_ey0__shrunken_se_control` | control | law L, the second blip reads the second covariate, which the feature declares: mean outcome with every treatment at its reference: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8128 to 0.8348, SE ratio 0.6721 to 0.7005 | pass |
| `interval_calibration` | `m_ate_r11__correctly_specified` | positive | law M, the second treatment and the outcome read the first covariate: contrast of regimen r11 against the reference regimen: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9428 to 0.9556, SE ratio 0.9797 to 1.0197 | pass |
| `interval_calibration` | `m_ate_r11__noise_control` | control | law M, the second treatment and the outcome read the first covariate: contrast of regimen r11 against the reference regimen: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8162 to 0.8381, SE ratio 0.6886 to 0.7174 | pass |
| `interval_calibration` | `m_ate_r11__shrunken_se_control` | control | law M, the second treatment and the outcome read the first covariate: contrast of regimen r11 against the reference regimen: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8189 to 0.8407, SE ratio 0.6855 to 0.7132 | pass |
| `interval_calibration` | `m_blip_a1_l1__correctly_specified` | positive | law M, the second treatment and the outcome read the first covariate: blip of the first treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9472 to 0.9594, SE ratio 0.9888 to 1.0299 | pass |
| `interval_calibration` | `m_blip_a1_l1__noise_control` | control | law M, the second treatment and the outcome read the first covariate: blip of the first treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8278 to 0.8491, SE ratio 0.6932 to 0.7239 | pass |
| `interval_calibration` | `m_blip_a1_l1__shrunken_se_control` | control | law M, the second treatment and the outcome read the first covariate: blip of the first treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8201 to 0.8418, SE ratio 0.6921 to 0.7205 | pass |
| `interval_calibration` | `m_blip_a2_l1__correctly_specified` | positive | law M, the second treatment and the outcome read the first covariate: blip of the second treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9415 to 0.9544, SE ratio 0.9721 to 1.0129 | pass |
| `interval_calibration` | `m_blip_a2_l1__noise_control` | control | law M, the second treatment and the outcome read the first covariate: blip of the second treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8175 to 0.8393, SE ratio 0.6828 to 0.7114 | pass |
| `interval_calibration` | `m_blip_a2_l1__shrunken_se_control` | control | law M, the second treatment and the outcome read the first covariate: blip of the second treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8165 to 0.8384, SE ratio 0.6801 to 0.7088 | pass |
| `interval_calibration` | `m_ey0__correctly_specified` | positive | law M, the second treatment and the outcome read the first covariate: mean outcome with every treatment at its reference: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9402 to 0.9532, SE ratio 0.9738 to 1.0148 | pass |
| `interval_calibration` | `m_ey0__noise_control` | control | law M, the second treatment and the outcome read the first covariate: mean outcome with every treatment at its reference: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8144 to 0.8364, SE ratio 0.6883 to 0.7173 | pass |
| `interval_calibration` | `m_ey0__shrunken_se_control` | control | law M, the second treatment and the outcome read the first covariate: mean outcome with every treatment at its reference: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8169 to 0.8387, SE ratio 0.6818 to 0.7099 | pass |
| `interval_calibration` | `n_ate_r11__correctly_specified` | positive | law N, nonlinear nuisances fitted by a shallow booster: contrast of regimen r11 against the reference regimen: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9451 to 0.9576, SE ratio 0.9719 to 1.0117 | pass |
| `interval_calibration` | `n_ate_r11__noise_control` | control | law N, nonlinear nuisances fitted by a shallow booster: contrast of regimen r11 against the reference regimen: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8193 to 0.8410, SE ratio 0.6919 to 0.7210 | pass |
| `interval_calibration` | `n_ate_r11__shrunken_se_control` | control | law N, nonlinear nuisances fitted by a shallow booster: contrast of regimen r11 against the reference regimen: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8125 to 0.8346, SE ratio 0.6799 to 0.7074 | pass |
| `interval_calibration` | `n_blip_a1_l1__correctly_specified` | positive | law N, nonlinear nuisances fitted by a shallow booster: blip of the first treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9377 to 0.9510, SE ratio 0.9632 to 1.0038 | pass |
| `interval_calibration` | `n_blip_a1_l1__noise_control` | control | law N, nonlinear nuisances fitted by a shallow booster: blip of the first treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8166 to 0.8385, SE ratio 0.6816 to 0.7104 | pass |
| `interval_calibration` | `n_blip_a1_l1__shrunken_se_control` | control | law N, nonlinear nuisances fitted by a shallow booster: blip of the first treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8162 to 0.8381, SE ratio 0.6740 to 0.7029 | pass |
| `interval_calibration` | `n_blip_a2_l1__correctly_specified` | positive | law N, nonlinear nuisances fitted by a shallow booster: blip of the second treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9293 to 0.9434, SE ratio 0.9434 to 0.9830 | pass |
| `interval_calibration` | `n_blip_a2_l1__noise_control` | control | law N, nonlinear nuisances fitted by a shallow booster: blip of the second treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8013 to 0.8239, SE ratio 0.6637 to 0.6912 | pass |
| `interval_calibration` | `n_blip_a2_l1__shrunken_se_control` | control | law N, nonlinear nuisances fitted by a shallow booster: blip of the second treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.7971 to 0.8198, SE ratio 0.6604 to 0.6878 | pass |
| `interval_calibration` | `n_ey0__correctly_specified` | positive | law N, nonlinear nuisances fitted by a shallow booster: mean outcome with every treatment at its reference: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9407 to 0.9537, SE ratio 0.9788 to 1.0202 | pass |
| `interval_calibration` | `n_ey0__noise_control` | control | law N, nonlinear nuisances fitted by a shallow booster: mean outcome with every treatment at its reference: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8267 to 0.8481, SE ratio 0.6958 to 0.7239 | pass |
| `interval_calibration` | `n_ey0__shrunken_se_control` | control | law N, nonlinear nuisances fitted by a shallow booster: mean outcome with every treatment at its reference: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8183 to 0.8401, SE ratio 0.6851 to 0.7142 | pass |
| `interval_calibration` | `p_ate_r11__correctly_specified` | positive | law P, the second blip reads the first treatment: contrast of regimen r11 against the reference regimen: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9381 to 0.9514, SE ratio 0.9723 to 1.0138 | pass |
| `interval_calibration` | `p_ate_r11__noise_control` | control | law P, the second blip reads the first treatment: contrast of regimen r11 against the reference regimen: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8207 to 0.8424, SE ratio 0.6852 to 0.7135 | pass |
| `interval_calibration` | `p_ate_r11__shrunken_se_control` | control | law P, the second blip reads the first treatment: contrast of regimen r11 against the reference regimen: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8188 to 0.8406, SE ratio 0.6808 to 0.7097 | pass |
| `interval_calibration` | `p_blip_a1_l1__correctly_specified` | positive | law P, the second blip reads the first treatment: blip of the first treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9439 to 0.9565, SE ratio 0.9697 to 1.0107 | pass |
| `interval_calibration` | `p_blip_a1_l1__noise_control` | control | law P, the second blip reads the first treatment: blip of the first treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8240 to 0.8455, SE ratio 0.6913 to 0.7211 | pass |
| `interval_calibration` | `p_blip_a1_l1__shrunken_se_control` | control | law P, the second blip reads the first treatment: blip of the first treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8124 to 0.8345, SE ratio 0.6788 to 0.7078 | pass |
| `interval_calibration` | `p_blip_a2_l1__correctly_specified` | positive | law P, the second blip reads the first treatment: blip of the second treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9406 to 0.9536, SE ratio 0.9696 to 1.0091 | pass |
| `interval_calibration` | `p_blip_a2_l1__noise_control` | control | law P, the second blip reads the first treatment: blip of the second treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8155 to 0.8374, SE ratio 0.6876 to 0.7162 | pass |
| `interval_calibration` | `p_blip_a2_l1__shrunken_se_control` | control | law P, the second blip reads the first treatment: blip of the second treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8127 to 0.8347, SE ratio 0.6780 to 0.7068 | pass |
| `interval_calibration` | `p_blip_a2_l1_a1__correctly_specified` | positive | law P, the second blip reads the first treatment: blip of the second treatment at level 1, slope on the first treatment: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9385 to 0.9517, SE ratio 0.9732 to 1.0128 | pass |
| `interval_calibration` | `p_blip_a2_l1_a1__noise_control` | control | law P, the second blip reads the first treatment: blip of the second treatment at level 1, slope on the first treatment: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8171 to 0.8390, SE ratio 0.6877 to 0.7164 | pass |
| `interval_calibration` | `p_blip_a2_l1_a1__shrunken_se_control` | control | law P, the second blip reads the first treatment: blip of the second treatment at level 1, slope on the first treatment: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8124 to 0.8345, SE ratio 0.6813 to 0.7095 | pass |
| `interval_calibration` | `p_ey0__correctly_specified` | positive | law P, the second blip reads the first treatment: mean outcome with every treatment at its reference: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9406 to 0.9536, SE ratio 0.9731 to 1.0134 | pass |
| `interval_calibration` | `p_ey0__noise_control` | control | law P, the second blip reads the first treatment: mean outcome with every treatment at its reference: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8091 to 0.8313, SE ratio 0.6791 to 0.7072 | pass |
| `interval_calibration` | `p_ey0__shrunken_se_control` | control | law P, the second blip reads the first treatment: mean outcome with every treatment at its reference: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8152 to 0.8371, SE ratio 0.6808 to 0.7104 | pass |
| `interval_calibration` | `p_ey_r01__correctly_specified` | positive | law P, the second blip reads the first treatment: mean outcome under regimen r01: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9384 to 0.9516, SE ratio 0.9787 to 1.0190 | pass |
| `interval_calibration` | `p_ey_r01__noise_control` | control | law P, the second blip reads the first treatment: mean outcome under regimen r01: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8139 to 0.8359, SE ratio 0.6873 to 0.7152 | pass |
| `interval_calibration` | `p_ey_r01__shrunken_se_control` | control | law P, the second blip reads the first treatment: mean outcome under regimen r01: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8159 to 0.8378, SE ratio 0.6851 to 0.7134 | pass |
| `interval_calibration` | `s2_ate_r11__correctly_specified` | positive | law S2, two binary nodes: contrast of regimen r11 against the reference regimen: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9415 to 0.9544, SE ratio 0.9783 to 1.0198 | pass |
| `interval_calibration` | `s2_ate_r11__noise_control` | control | law S2, two binary nodes: contrast of regimen r11 against the reference regimen: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8237 to 0.8452, SE ratio 0.6920 to 0.7210 | pass |
| `interval_calibration` | `s2_ate_r11__shrunken_se_control` | control | law S2, two binary nodes: contrast of regimen r11 against the reference regimen: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8161 to 0.8380, SE ratio 0.6848 to 0.7141 | pass |
| `interval_calibration` | `s2_blip_a1_l1__correctly_specified` | positive | law S2, two binary nodes: blip of the first treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9430 to 0.9557, SE ratio 0.9825 to 1.0238 | pass |
| `interval_calibration` | `s2_blip_a1_l1__noise_control` | control | law S2, two binary nodes: blip of the first treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8233 to 0.8448, SE ratio 0.6986 to 0.7274 | pass |
| `interval_calibration` | `s2_blip_a1_l1__shrunken_se_control` | control | law S2, two binary nodes: blip of the first treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8207 to 0.8424, SE ratio 0.6881 to 0.7159 | pass |
| `interval_calibration` | `s2_blip_a2_l1__correctly_specified` | positive | law S2, two binary nodes: blip of the second treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9437 to 0.9563, SE ratio 0.9761 to 1.0167 | pass |
| `interval_calibration` | `s2_blip_a2_l1__noise_control` | control | law S2, two binary nodes: blip of the second treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8203 to 0.8420, SE ratio 0.6856 to 0.7138 | pass |
| `interval_calibration` | `s2_blip_a2_l1__shrunken_se_control` | control | law S2, two binary nodes: blip of the second treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8144 to 0.8364, SE ratio 0.6832 to 0.7119 | pass |
| `interval_calibration` | `s2_ey0__correctly_specified` | positive | law S2, two binary nodes: mean outcome with every treatment at its reference: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9439 to 0.9565, SE ratio 0.9711 to 1.0112 | pass |
| `interval_calibration` | `s2_ey0__noise_control` | control | law S2, two binary nodes: mean outcome with every treatment at its reference: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8147 to 0.8367, SE ratio 0.6897 to 0.7182 | pass |
| `interval_calibration` | `s2_ey0__shrunken_se_control` | control | law S2, two binary nodes: mean outcome with every treatment at its reference: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8143 to 0.8363, SE ratio 0.6797 to 0.7080 | pass |
| `interval_calibration` | `s2_ey_r10__correctly_specified` | positive | law S2, two binary nodes: mean outcome under regimen r10: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9448 to 0.9574, SE ratio 0.9760 to 1.0154 | pass |
| `interval_calibration` | `s2_ey_r10__noise_control` | control | law S2, two binary nodes: mean outcome under regimen r10: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8102 to 0.8324, SE ratio 0.6762 to 0.7038 | pass |
| `interval_calibration` | `s2_ey_r10__shrunken_se_control` | control | law S2, two binary nodes: mean outcome under regimen r10: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8120 to 0.8341, SE ratio 0.6836 to 0.7112 | pass |
| `interval_calibration` | `s2_ey_r11__correctly_specified` | positive | law S2, two binary nodes: mean outcome under regimen r11: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9400 to 0.9530, SE ratio 0.9750 to 1.0165 | pass |
| `interval_calibration` | `s2_ey_r11__noise_control` | control | law S2, two binary nodes: mean outcome under regimen r11: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8210 to 0.8426, SE ratio 0.6900 to 0.7186 | pass |
| `interval_calibration` | `s2_ey_r11__shrunken_se_control` | control | law S2, two binary nodes: mean outcome under regimen r11: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8142 to 0.8362, SE ratio 0.6825 to 0.7111 | pass |
| `interval_calibration` | `s2c_ate_r11__correctly_specified` | positive | law S2 in clusters of ten that share the baseline and an outcome intercept: contrast of regimen r11 against the reference regimen: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9435 to 0.9562, SE ratio 0.9828 to 1.0243 | pass |
| `interval_calibration` | `s2c_ate_r11__noise_control` | control | law S2 in clusters of ten that share the baseline and an outcome intercept: contrast of regimen r11 against the reference regimen: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8198 to 0.8415, SE ratio 0.6891 to 0.7184 | pass |
| `interval_calibration` | `s2c_ate_r11__shrunken_se_control` | control | law S2 in clusters of ten that share the baseline and an outcome intercept: contrast of regimen r11 against the reference regimen: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8199 to 0.8417, SE ratio 0.6883 to 0.7166 | pass |
| `interval_calibration` | `s2c_blip_a1_l1__correctly_specified` | positive | law S2 in clusters of ten that share the baseline and an outcome intercept: blip of the first treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9398 to 0.9529, SE ratio 0.9729 to 1.0137 | pass |
| `interval_calibration` | `s2c_blip_a1_l1__noise_control` | control | law S2 in clusters of ten that share the baseline and an outcome intercept: blip of the first treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8118 to 0.8339, SE ratio 0.6796 to 0.7080 | pass |
| `interval_calibration` | `s2c_blip_a1_l1__shrunken_se_control` | control | law S2 in clusters of ten that share the baseline and an outcome intercept: blip of the first treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8185 to 0.8403, SE ratio 0.6807 to 0.7095 | pass |
| `interval_calibration` | `s2c_ey0__correctly_specified` | positive | law S2 in clusters of ten that share the baseline and an outcome intercept: mean outcome with every treatment at its reference: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9385 to 0.9517, SE ratio 0.9761 to 1.0160 | pass |
| `interval_calibration` | `s2c_ey0__noise_control` | control | law S2 in clusters of ten that share the baseline and an outcome intercept: mean outcome with every treatment at its reference: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8139 to 0.8359, SE ratio 0.6806 to 0.7083 | pass |
| `interval_calibration` | `s2c_ey0__shrunken_se_control` | control | law S2 in clusters of ten that share the baseline and an outcome intercept: mean outcome with every treatment at its reference: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8141 to 0.8361, SE ratio 0.6830 to 0.7111 | pass |
| `interval_calibration` | `s2c_ey_r11__correctly_specified` | positive | law S2 in clusters of ten that share the baseline and an outcome intercept: mean outcome under regimen r11: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9394 to 0.9525, SE ratio 0.9774 to 1.0198 | pass |
| `interval_calibration` | `s2c_ey_r11__noise_control` | control | law S2 in clusters of ten that share the baseline and an outcome intercept: mean outcome under regimen r11: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8224 to 0.8440, SE ratio 0.6919 to 0.7204 | pass |
| `interval_calibration` | `s2c_ey_r11__shrunken_se_control` | control | law S2 in clusters of ten that share the baseline and an outcome intercept: mean outcome under regimen r11: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8161 to 0.8380, SE ratio 0.6843 to 0.7138 | pass |
| `interval_calibration` | `s2w_ate_r11__correctly_specified` | positive | law S2 with the known weight 0.5 + 1.5 W: contrast of regimen r11 against the reference regimen: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9430 to 0.9557, SE ratio 0.9708 to 1.0115 | pass |
| `interval_calibration` | `s2w_ate_r11__noise_control` | control | law S2 with the known weight 0.5 + 1.5 W: contrast of regimen r11 against the reference regimen: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8151 to 0.8370, SE ratio 0.6863 to 0.7146 | pass |
| `interval_calibration` | `s2w_ate_r11__shrunken_se_control` | control | law S2 with the known weight 0.5 + 1.5 W: contrast of regimen r11 against the reference regimen: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8194 to 0.8412, SE ratio 0.6794 to 0.7081 | pass |
| `interval_calibration` | `s2w_blip_a1_l1__correctly_specified` | positive | law S2 with the known weight 0.5 + 1.5 W: blip of the first treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9401 to 0.9531, SE ratio 0.9796 to 1.0212 | pass |
| `interval_calibration` | `s2w_blip_a1_l1__noise_control` | control | law S2 with the known weight 0.5 + 1.5 W: blip of the first treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8217 to 0.8434, SE ratio 0.6879 to 0.7171 | pass |
| `interval_calibration` | `s2w_blip_a1_l1__shrunken_se_control` | control | law S2 with the known weight 0.5 + 1.5 W: blip of the first treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8189 to 0.8407, SE ratio 0.6854 to 0.7142 | pass |
| `interval_calibration` | `s2w_ey0__correctly_specified` | positive | law S2 with the known weight 0.5 + 1.5 W: mean outcome with every treatment at its reference: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9443 to 0.9569, SE ratio 0.9811 to 1.0212 | pass |
| `interval_calibration` | `s2w_ey0__noise_control` | control | law S2 with the known weight 0.5 + 1.5 W: mean outcome with every treatment at its reference: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8293 to 0.8505, SE ratio 0.7022 to 0.7307 | pass |
| `interval_calibration` | `s2w_ey0__shrunken_se_control` | control | law S2 with the known weight 0.5 + 1.5 W: mean outcome with every treatment at its reference: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8171 to 0.8390, SE ratio 0.6865 to 0.7154 | pass |
| `interval_calibration` | `s2w_ey_r11__correctly_specified` | positive | law S2 with the known weight 0.5 + 1.5 W: mean outcome under regimen r11: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9400 to 0.9530, SE ratio 0.9733 to 1.0129 | pass |
| `interval_calibration` | `s2w_ey_r11__noise_control` | control | law S2 with the known weight 0.5 + 1.5 W: mean outcome under regimen r11: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8153 to 0.8373, SE ratio 0.6849 to 0.7122 | pass |
| `interval_calibration` | `s2w_ey_r11__shrunken_se_control` | control | law S2 with the known weight 0.5 + 1.5 W: mean outcome under regimen r11: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8133 to 0.8353, SE ratio 0.6809 to 0.7084 | pass |
| `interval_calibration` | `s3_ate_r101__correctly_specified` | positive | law S3, three binary nodes with a path from each treatment to the later ones: contrast of regimen r101 against the reference regimen: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9422 to 0.9550, SE ratio 0.9852 to 1.0253 | pass |
| `interval_calibration` | `s3_ate_r101__noise_control` | control | law S3, three binary nodes with a path from each treatment to the later ones: contrast of regimen r101 against the reference regimen: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8225 to 0.8441, SE ratio 0.6922 to 0.7207 | pass |
| `interval_calibration` | `s3_ate_r101__shrunken_se_control` | control | law S3, three binary nodes with a path from each treatment to the later ones: contrast of regimen r101 against the reference regimen: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8212 to 0.8429, SE ratio 0.6894 to 0.7185 | pass |
| `interval_calibration` | `s3_ate_r111__correctly_specified` | positive | law S3, three binary nodes with a path from each treatment to the later ones: contrast of regimen r111 against the reference regimen: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9418 to 0.9547, SE ratio 0.9850 to 1.0262 | pass |
| `interval_calibration` | `s3_ate_r111__noise_control` | control | law S3, three binary nodes with a path from each treatment to the later ones: contrast of regimen r111 against the reference regimen: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8284 to 0.8497, SE ratio 0.7008 to 0.7298 | pass |
| `interval_calibration` | `s3_ate_r111__shrunken_se_control` | control | law S3, three binary nodes with a path from each treatment to the later ones: contrast of regimen r111 against the reference regimen: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8214 to 0.8430, SE ratio 0.6895 to 0.7180 | pass |
| `interval_calibration` | `s3_blip_a1_l1__correctly_specified` | positive | law S3, three binary nodes with a path from each treatment to the later ones: blip of the first treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9414 to 0.9543, SE ratio 0.9838 to 1.0237 | pass |
| `interval_calibration` | `s3_blip_a1_l1__noise_control` | control | law S3, three binary nodes with a path from each treatment to the later ones: blip of the first treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8238 to 0.8453, SE ratio 0.6937 to 0.7229 | pass |
| `interval_calibration` | `s3_blip_a1_l1__shrunken_se_control` | control | law S3, three binary nodes with a path from each treatment to the later ones: blip of the first treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8233 to 0.8448, SE ratio 0.6881 to 0.7172 | pass |
| `interval_calibration` | `s3_blip_a2_l1__correctly_specified` | positive | law S3, three binary nodes with a path from each treatment to the later ones: blip of the second treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9414 to 0.9543, SE ratio 0.9727 to 1.0132 | pass |
| `interval_calibration` | `s3_blip_a2_l1__noise_control` | control | law S3, three binary nodes with a path from each treatment to the later ones: blip of the second treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8144 to 0.8364, SE ratio 0.6822 to 0.7098 | pass |
| `interval_calibration` | `s3_blip_a2_l1__shrunken_se_control` | control | law S3, three binary nodes with a path from each treatment to the later ones: blip of the second treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8112 to 0.8334, SE ratio 0.6812 to 0.7091 | pass |
| `interval_calibration` | `s3_blip_a3_l1__correctly_specified` | positive | law S3, three binary nodes with a path from each treatment to the later ones: blip of the third treatment at level 1: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9368 to 0.9502, SE ratio 0.9590 to 0.9981 | pass |
| `interval_calibration` | `s3_blip_a3_l1__noise_control` | control | law S3, three binary nodes with a path from each treatment to the later ones: blip of the third treatment at level 1: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8184 to 0.8402, SE ratio 0.6850 to 0.7135 | pass |
| `interval_calibration` | `s3_blip_a3_l1__shrunken_se_control` | control | law S3, three binary nodes with a path from each treatment to the later ones: blip of the third treatment at level 1: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8124 to 0.8345, SE ratio 0.6713 to 0.6992 | pass |
| `interval_calibration` | `s3_ey0__correctly_specified` | positive | law S3, three binary nodes with a path from each treatment to the later ones: mean outcome with every treatment at its reference: both nuisances are correctly specified | SE ratio and coverage intervals both inside their calibration bands | coverage 0.9425 to 0.9552, SE ratio 0.9896 to 1.0301 | pass |
| `interval_calibration` | `s3_ey0__noise_control` | control | law S3, three binary nodes with a path from each treatment to the later ones: mean outcome with every treatment at its reference: a declared scale of independent noise is added to each estimate | the SE-ratio interval must fall below the calibration band | coverage 0.8187 to 0.8404, SE ratio 0.6816 to 0.7099 | pass |
| `interval_calibration` | `s3_ey0__shrunken_se_control` | control | law S3, three binary nodes with a path from each treatment to the later ones: mean outcome with every treatment at its reference: the reported standard errors are multiplied by a declared factor below one | the SE-ratio interval must fall below the calibration band | coverage 0.8264 to 0.8477, SE ratio 0.6925 to 0.7213 | pass |
| `positivity_reporting` | `sp_ate_r01__weak_positivity` | diagnostic | law SP, treatment logits multiplied by three, weak positivity: contrast of regimen r01 against the reference regimen: the structural fit on a law with weak positivity, correct blip features | reported with no verdict | bias -0.0067 to 0.0011, coverage 0.9342 to 0.9694, SE ratio 1.0149 | reported |
| `positivity_reporting` | `sp_ate_r10__weak_positivity` | diagnostic | law SP, treatment logits multiplied by three, weak positivity: contrast of regimen r10 against the reference regimen: the structural fit on a law with weak positivity, correct blip features | reported with no verdict | bias -0.0053 to 0.0032, coverage 0.9226 to 0.9611, SE ratio 1.0023 | reported |
| `positivity_reporting` | `sp_ate_r11__weak_positivity` | diagnostic | law SP, treatment logits multiplied by three, weak positivity: contrast of regimen r11 against the reference regimen: the structural fit on a law with weak positivity, correct blip features | reported with no verdict | bias -0.0043 to 0.0019, coverage 0.9484 to 0.9790, SE ratio 1.0475 | reported |
| `positivity_reporting` | `sp_blip_a1_l1__weak_positivity` | diagnostic | law SP, treatment logits multiplied by three, weak positivity: blip of the first treatment at level 1: the structural fit on a law with weak positivity, correct blip features | reported with no verdict | bias -0.0074 to 0.0041, coverage 0.9272 to 0.9644, SE ratio 1.0124 | reported |
| `positivity_reporting` | `sp_blip_a1_l1_w__weak_positivity` | diagnostic | law SP, treatment logits multiplied by three, weak positivity: blip of the first treatment at level 1, slope on the baseline W: the structural fit on a law with weak positivity, correct blip features | reported with no verdict | bias -0.0045 to 0.0078, coverage 0.9400 to 0.9734, SE ratio 1.0355 | reported |
| `positivity_reporting` | `sp_blip_a2_l1__weak_positivity` | diagnostic | law SP, treatment logits multiplied by three, weak positivity: blip of the second treatment at level 1: the structural fit on a law with weak positivity, correct blip features | reported with no verdict | bias -0.0053 to 0.0019, coverage 0.9330 to 0.9685, SE ratio 1.0085 | reported |
| `positivity_reporting` | `sp_blip_a2_l1_a1__weak_positivity` | diagnostic | law SP, treatment logits multiplied by three, weak positivity: blip of the second treatment at level 1, slope on the first treatment: the structural fit on a law with weak positivity, correct blip features | reported with no verdict | bias -0.0034 to 0.0086, coverage 0.9226 to 0.9611, SE ratio 1.0002 | reported |
| `positivity_reporting` | `sp_blip_a2_l1_w__weak_positivity` | diagnostic | law SP, treatment logits multiplied by three, weak positivity: blip of the second treatment at level 1, slope on the baseline W: the structural fit on a law with weak positivity, correct blip features | reported with no verdict | bias -0.0081 to 0.0044, coverage 0.9214 to 0.9602, SE ratio 0.9599 | reported |
| `positivity_reporting` | `sp_ey0__weak_positivity` | diagnostic | law SP, treatment logits multiplied by three, weak positivity: mean outcome with every treatment at its reference: the structural fit on a law with weak positivity, correct blip features | reported with no verdict | bias -0.0021 to 0.0027, coverage 0.9460 to 0.9774, SE ratio 1.0360 | reported |
| `positivity_reporting` | `sp_ey_r11__weak_positivity` | diagnostic | law SP, treatment logits multiplied by three, weak positivity: mean outcome under regimen r11: the structural fit on a law with weak positivity, correct blip features | reported with no verdict | bias -0.0032 to 0.0014, coverage 0.9318 to 0.9677, SE ratio 0.9978 | reported |
| `power` | `lu_f10__model_check` | positive | law L fitted without its second-covariate feature, ten outer folds, n = 2,000: the same check on a law whose second blip reads a covariate the structural model omits | rejection lower bound clears the minimum power | rejection 1, 0.9739 to 1 | pass |
| `power` | `lu_f2__model_check` | positive | law L fitted without its second-covariate feature, two outer folds, n = 2,000: the same check on a law whose second blip reads a covariate the structural model omits | rejection lower bound clears the minimum power | rejection 1, 0.9739 to 1 | pass |
| `root_n_and_efficiency` | `c_ate_dose_high__n_2000` | positive | law C, two doses with linear conditional means: contrast of regimen dose_high against the reference regimen: bias, coverage and SE calibration at n = 2,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.000130, coverage 0.9353 to 0.9702, SE ratio 1.0263 | pass |
| `root_n_and_efficiency` | `c_ate_dose_high__n_500` | positive | law C, two doses with linear conditional means: contrast of regimen dose_high against the reference regimen: bias, coverage and SE calibration at n = 500 | bias inside the margin, coverage clears the floor, SE ratio inside the band | bias 0.0013, coverage 0.9318 to 0.9677, SE ratio 1.0034 | pass |
| `root_n_and_efficiency` | `c_ate_dose_high__n_8000` | positive | law C, two doses with linear conditional means: contrast of regimen dose_high against the reference regimen: bias, coverage and SE calibration at n = 8,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.000026, coverage 0.9295 to 0.9661, SE ratio 0.9993 | pass |
| `root_n_and_efficiency` | `h_ate_r11__n_2000` | positive | law H, blip features of the baseline and the past treatment: contrast of regimen r11 against the reference regimen: bias, coverage and SE calibration at n = 2,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.0012, coverage 0.9295 to 0.9661, SE ratio 1.0002 | pass |
| `root_n_and_efficiency` | `h_ate_r11__n_500` | positive | law H, blip features of the baseline and the past treatment: contrast of regimen r11 against the reference regimen: bias, coverage and SE calibration at n = 500 | bias inside the margin, coverage clears the floor, SE ratio inside the band | bias -0.0011, coverage 0.9342 to 0.9694, SE ratio 1.0080 | pass |
| `root_n_and_efficiency` | `h_ate_r11__n_8000` | positive | law H, blip features of the baseline and the past treatment: contrast of regimen r11 against the reference regimen: bias, coverage and SE calibration at n = 8,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.000050, coverage 0.9157 to 0.9560, SE ratio 0.9524 | pass |
| `root_n_and_efficiency` | `k_ate_r12__n_1000` | positive | law K, two nodes of three levels: contrast of regimen r12 against the reference regimen: bias, coverage and SE calibration at n = 1,000 | bias inside the margin, coverage clears the floor, SE ratio inside the band | bias -0.0025, coverage 0.9180 to 0.9577, SE ratio 0.9661 | pass |
| `root_n_and_efficiency` | `k_ate_r12__n_16000` | positive | law K, two nodes of three levels: contrast of regimen r12 against the reference regimen: bias, coverage and SE calibration at n = 16,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.000616, coverage 0.9353 to 0.9702, SE ratio 1.0416 | pass |
| `root_n_and_efficiency` | `k_ate_r12__n_4000` | positive | law K, two nodes of three levels: contrast of regimen r12 against the reference regimen: bias, coverage and SE calibration at n = 4,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.000052, coverage 0.9157 to 0.9560, SE ratio 0.9549 | pass |
| `root_n_and_efficiency` | `n_ate_r11__n_2000` | positive | law N, nonlinear nuisances fitted by a shallow booster: contrast of regimen r11 against the reference regimen: bias, coverage and SE calibration at n = 2,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.0030, coverage 0.9226 to 0.9611, SE ratio 0.9816 | pass |
| `root_n_and_efficiency` | `n_ate_r11__n_500` | positive | law N, nonlinear nuisances fitted by a shallow booster: contrast of regimen r11 against the reference regimen: bias, coverage and SE calibration at n = 500 | bias inside the margin, coverage clears the floor, SE ratio inside the band | bias -0.0103, coverage 0.9365 to 0.9710, SE ratio 1.0121 | pass |
| `root_n_and_efficiency` | `n_ate_r11__n_8000` | positive | law N, nonlinear nuisances fitted by a shallow booster: contrast of regimen r11 against the reference regimen: bias, coverage and SE calibration at n = 8,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.000362, coverage 0.9389 to 0.9726, SE ratio 0.9997 | pass |
| `root_n_and_efficiency` | `n_blip_a1_l1__n_2000` | positive | law N, nonlinear nuisances fitted by a shallow booster: blip of the first treatment at level 1: bias, coverage and SE calibration at n = 2,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.0013, coverage 0.9342 to 0.9694, SE ratio 0.9887 | pass |
| `root_n_and_efficiency` | `n_blip_a1_l1__n_500` | positive | law N, nonlinear nuisances fitted by a shallow booster: blip of the first treatment at level 1: bias, coverage and SE calibration at n = 500 | bias inside the margin, coverage clears the floor, SE ratio inside the band | bias -0.0049, coverage 0.9168 to 0.9569, SE ratio 0.9746 | pass |
| `root_n_and_efficiency` | `n_blip_a1_l1__n_8000` | positive | law N, nonlinear nuisances fitted by a shallow booster: blip of the first treatment at level 1: bias, coverage and SE calibration at n = 8,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.000430, coverage 0.9389 to 0.9726, SE ratio 1.0050 | pass |
| `root_n_and_efficiency` | `n_blip_a2_l1__n_2000` | positive | law N, nonlinear nuisances fitted by a shallow booster: blip of the second treatment at level 1: bias, coverage and SE calibration at n = 2,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.0016, coverage 0.9168 to 0.9569, SE ratio 0.9849 | pass |
| `root_n_and_efficiency` | `n_blip_a2_l1__n_500` | positive | law N, nonlinear nuisances fitted by a shallow booster: blip of the second treatment at level 1: bias, coverage and SE calibration at n = 500 | bias inside the margin, coverage clears the floor, SE ratio inside the band | bias -0.0054, coverage 0.9214 to 0.9602, SE ratio 0.9824 | pass |
| `root_n_and_efficiency` | `n_blip_a2_l1__n_8000` | positive | law N, nonlinear nuisances fitted by a shallow booster: blip of the second treatment at level 1: bias, coverage and SE calibration at n = 8,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias 0.000068, coverage 0.9249 to 0.9627, SE ratio 0.9582 | pass |
| `root_n_and_efficiency` | `s2_ate_r11__n_2000` | positive | law S2, two binary nodes: contrast of regimen r11 against the reference regimen: bias, coverage and SE calibration at n = 2,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias 0.0010, coverage 0.9330 to 0.9685, SE ratio 1.0074 | pass |
| `root_n_and_efficiency` | `s2_ate_r11__n_500` | positive | law S2, two binary nodes: contrast of regimen r11 against the reference regimen: bias, coverage and SE calibration at n = 500 | bias inside the margin, coverage clears the floor, SE ratio inside the band | bias -0.000996, coverage 0.9180 to 0.9577, SE ratio 0.9991 | pass |
| `root_n_and_efficiency` | `s2_ate_r11__n_8000` | positive | law S2, two binary nodes: contrast of regimen r11 against the reference regimen: bias, coverage and SE calibration at n = 8,000 | bias inside the margin, coverage clears the floor, SE ratio inside the sanity band | bias -0.000274, coverage 0.9318 to 0.9677, SE ratio 1.0061 | pass |
| `root_n_rate` | `c_ate_dose_high__empirical_sd` | positive | law C, two doses with linear conditional means: contrast of regimen dose_high against the reference regimen: log empirical spread of the estimates regressed on log n across three sizes | slope interval inside the root-n band and excluding -1/4 | slope -0.5267 to -0.4699 | pass |
| `root_n_rate` | `c_ate_dose_high__reported_se` | positive | law C, two doses with linear conditional means: contrast of regimen dose_high against the reference regimen: the same regression applied to the mean reported standard error | slope interval inside the root-n band and excluding -1/4 | slope -0.5010 to -0.4985 | pass |
| `root_n_rate` | `h_ate_r11__empirical_sd` | positive | law H, blip features of the baseline and the past treatment: contrast of regimen r11 against the reference regimen: log empirical spread of the estimates regressed on log n across three sizes | slope interval inside the root-n band and excluding -1/4 | slope -0.5084 to -0.4500 | pass |
| `root_n_rate` | `h_ate_r11__reported_se` | positive | law H, blip features of the baseline and the past treatment: contrast of regimen r11 against the reference regimen: the same regression applied to the mean reported standard error | slope interval inside the root-n band and excluding -1/4 | slope -0.5011 to -0.4986 | pass |
| `root_n_rate` | `k_ate_r12__empirical_sd` | positive | law K, two nodes of three levels: contrast of regimen r12 against the reference regimen: log empirical spread of the estimates regressed on log n across three sizes | slope interval inside the root-n band and excluding -1/4 | slope -0.5560 to -0.4982 | pass |
| `root_n_rate` | `k_ate_r12__reported_se` | positive | law K, two nodes of three levels: contrast of regimen r12 against the reference regimen: the same regression applied to the mean reported standard error | slope interval inside the root-n band and excluding -1/4 | slope -0.5009 to -0.4992 | pass |
| `root_n_rate` | `n_ate_r11__empirical_sd` | positive | law N, nonlinear nuisances fitted by a shallow booster: contrast of regimen r11 against the reference regimen: log empirical spread of the estimates regressed on log n across three sizes | slope interval inside the root-n band and excluding -1/4 | slope -0.5305 to -0.4766 | pass |
| `root_n_rate` | `n_ate_r11__reported_se` | positive | law N, nonlinear nuisances fitted by a shallow booster: contrast of regimen r11 against the reference regimen: the same regression applied to the mean reported standard error | slope interval inside the root-n band and excluding -1/4 | slope -0.5094 to -0.5067 | pass |
| `root_n_rate` | `n_blip_a1_l1__empirical_sd` | positive | law N, nonlinear nuisances fitted by a shallow booster: blip of the first treatment at level 1: log empirical spread of the estimates regressed on log n across three sizes | slope interval inside the root-n band and excluding -1/4 | slope -0.5417 to -0.4858 | pass |
| `root_n_rate` | `n_blip_a1_l1__reported_se` | positive | law N, nonlinear nuisances fitted by a shallow booster: blip of the first treatment at level 1: the same regression applied to the mean reported standard error | slope interval inside the root-n band and excluding -1/4 | slope -0.5041 to -0.5014 | pass |
| `root_n_rate` | `n_blip_a2_l1__empirical_sd` | positive | law N, nonlinear nuisances fitted by a shallow booster: blip of the second treatment at level 1: log empirical spread of the estimates regressed on log n across three sizes | slope interval inside the root-n band and excluding -1/4 | slope -0.5313 to -0.4751 | pass |
| `root_n_rate` | `n_blip_a2_l1__reported_se` | positive | law N, nonlinear nuisances fitted by a shallow booster: blip of the second treatment at level 1: the same regression applied to the mean reported standard error | slope interval inside the root-n band and excluding -1/4 | slope -0.5132 to -0.5109 | pass |
| `root_n_rate` | `s2_ate_r11__empirical_sd` | positive | law S2, two binary nodes: contrast of regimen r11 against the reference regimen: log empirical spread of the estimates regressed on log n across three sizes | slope interval inside the root-n band and excluding -1/4 | slope -0.5318 to -0.4713 | pass |
| `root_n_rate` | `s2_ate_r11__reported_se` | positive | law S2, two binary nodes: contrast of regimen r11 against the reference regimen: the same regression applied to the mean reported standard error | slope interval inside the root-n band and excluding -1/4 | slope -0.5002 to -0.4978 | pass |
| `unclustered_se` | `s2c_ate_r11__unclustered` | diagnostic | law S2 in clusters of ten that share the baseline and an outcome intercept: contrast of regimen r11 against the reference regimen: the fit without the cluster column, on the clustered draws | the gated cells `s2c_ey0` and `s2c_ey_r11` need the SE-ratio interval below the calibration band, and the result column reads reported; the other cells state no verdict | SE ratio 0.9894 to 1.0324 | reported |
| `unclustered_se` | `s2c_blip_a1_l1__unclustered` | diagnostic | law S2 in clusters of ten that share the baseline and an outcome intercept: blip of the first treatment at level 1: the fit without the cluster column, on the clustered draws | the gated cells `s2c_ey0` and `s2c_ey_r11` need the SE-ratio interval below the calibration band, and the result column reads reported; the other cells state no verdict | SE ratio 0.9805 to 1.0210 | reported |
| `unclustered_se` | `s2c_ey0__unclustered` | diagnostic | law S2 in clusters of ten that share the baseline and an outcome intercept: mean outcome with every treatment at its reference: the fit without the cluster column, on the clustered draws | the gated cells `s2c_ey0` and `s2c_ey_r11` need the SE-ratio interval below the calibration band, and the result column reads reported; the other cells state no verdict | SE ratio 0.5006 to 0.5214 | reported |
| `unclustered_se` | `s2c_ey_r11__unclustered` | diagnostic | law S2 in clusters of ten that share the baseline and an outcome intercept: mean outcome under regimen r11: the fit without the cluster column, on the clustered draws | the gated cells `s2c_ey0` and `s2c_ey_r11` need the SE-ratio interval below the calibration band, and the result column reads reported; the other cells state no verdict | SE ratio 0.5491 to 0.5728 | reported |
| `warning_rate` | `h_f10__model_check` | positive | law H, structural model correct, ten outer folds, n = 1,000: the structural model check against the nonparametric contrasts, with the structural model correct; the rejection rate is published beside the verdict, and on the sparse-positivity law the covariance has few degrees of freedom, so the check can reject above its nominal level there | rejection upper bound at or below the type-I ceiling | rejection 0.0100, 0.0026 to 0.0259 | pass |
| `warning_rate` | `h_f2__model_check` | positive | law H, structural model correct, two outer folds, n = 1,000: the structural model check against the nonparametric contrasts, with the structural model correct; the rejection rate is published beside the verdict, and on the sparse-positivity law the covariance has few degrees of freedom, so the check can reject above its nominal level there | rejection upper bound at or below the type-I ceiling | rejection 0.0067, 0.0011 to 0.0208 | pass |
| `warning_rate` | `h_n2000_f10__model_check` | positive | law H, structural model correct, ten outer folds, n = 2,000: the structural model check against the nonparametric contrasts, with the structural model correct; the rejection rate is published beside the verdict, and on the sparse-positivity law the covariance has few degrees of freedom, so the check can reject above its nominal level there | rejection upper bound at or below the type-I ceiling | rejection 0.0183, 0.0072 to 0.0376 | pass |
| `warning_rate` | `h_n2000_f2__model_check` | positive | law H, structural model correct, two outer folds, n = 2,000: the structural model check against the nonparametric contrasts, with the structural model correct; the rejection rate is published beside the verdict, and on the sparse-positivity law the covariance has few degrees of freedom, so the check can reject above its nominal level there | rejection upper bound at or below the type-I ceiling | rejection 0.0217, 0.0094 to 0.0421 | pass |
| `warning_rate` | `s2_f10__model_check` | positive | law S2, structural model correct, ten outer folds, n = 1,000: the structural model check against the nonparametric contrasts, with the structural model correct; the rejection rate is published beside the verdict, and on the sparse-positivity law the covariance has few degrees of freedom, so the check can reject above its nominal level there | rejection upper bound at or below the type-I ceiling | rejection 0.0133, 0.0043 to 0.0307 | pass |
| `warning_rate` | `s2_f2__model_check` | positive | law S2, structural model correct, two outer folds, n = 1,000: the structural model check against the nonparametric contrasts, with the structural model correct; the rejection rate is published beside the verdict, and on the sparse-positivity law the covariance has few degrees of freedom, so the check can reject above its nominal level there | rejection upper bound at or below the type-I ceiling | rejection 0.0217, 0.0094 to 0.0421 | pass |
| `warning_rate` | `s2_n2000_f10__model_check` | positive | law S2, structural model correct, ten outer folds, n = 2,000: the structural model check against the nonparametric contrasts, with the structural model correct; the rejection rate is published beside the verdict, and on the sparse-positivity law the covariance has few degrees of freedom, so the check can reject above its nominal level there | rejection upper bound at or below the type-I ceiling | rejection 0.0300, 0.0150 to 0.0529 | pass |
| `warning_rate` | `s2_n2000_f2__model_check` | positive | law S2, structural model correct, two outer folds, n = 2,000: the structural model check against the nonparametric contrasts, with the structural model correct; the rejection rate is published beside the verdict, and on the sparse-positivity law the covariance has few degrees of freedom, so the check can reject above its nominal level there | rejection upper bound at or below the type-I ceiling | rejection 0.0383, 0.0210 to 0.0633 | pass |
| `warning_rate` | `sp_f10__model_check` | positive | law SP, treatment logits multiplied by three, ten outer folds, n = 2,000: the structural model check against the nonparametric contrasts, with the structural model correct; the rejection rate is published beside the verdict, and on the sparse-positivity law the covariance has few degrees of freedom, so the check can reject above its nominal level there | rejection upper bound at or below the type-I ceiling | rejection 0.0692, 0.0516 to 0.0902 | pass |
| `warning_rate` | `sp_f2__model_check` | positive | law SP, treatment logits multiplied by three, two outer folds, n = 2,000: the structural model check against the nonparametric contrasts, with the structural model correct; the rejection rate is published beside the verdict, and on the sparse-positivity law the covariance has few degrees of freedom, so the check can reject above its nominal level there | rejection upper bound at or below the type-I ceiling | rejection 0.0383, 0.0210 to 0.0633 | pass |
<!-- /generated -->

The property families draw from their own streams. The table above lists every cell. This section
states what each family tests.

| family | what it tests | size |
| --- | --- | --- |
| `interval_calibration` | coverage and SE ratio inside the calibration bands for every estimand of the 11 positive laws, and the bias inside 0.25 empirical SD. A shrunken-SE control and a noise control must fail the same bands | $n$ = 2,000, 8,000 replications |
| `root_n_and_efficiency` | bias, coverage and SE ratio at three sizes for one contrast of `s2`, `h`, `k` and `c`, and for the contrast and both blips of `n` | 500, 2,000 and 8,000 rows (`k`: 1,000, 4,000 and 16,000), 1,000 replications each |
| `root_n_rate` | the slope of the empirical SD and of the mean reported SE in $n$ for the same seven labels | the three sizes above |
| `warning_rate` | the rejection rate of `check_model` at the 5% level with the structural model correct, on `S2`, `H` and the weak-positivity law `SP` | $n$ = 1,000 and 2,000, two and ten folds, 600 replications (1,200 for `sp_f10`) |
| `power` | the rejection rate of `check_model` on the law `LU`, whose second blip reads a covariate that the fit leaves out | $n$ = 2,000, two and ten folds, 200 replications |
| `blip_feature_control` | the negative controls `LU` and `VB`. Each one fits too few blip features, so its regimen estimands miss the truth. A cell passes when its 99% bias interval lies beyond 0.25 SD on the side of the computed gap | $n$ = 2,000, 2,000 replications |
| `unclustered_se` | the clustered law `s2c` fitted without its cluster column. The role is `diagnostic`, so the table reads "reported" for all four cells. The two level estimands carry the cluster intercept, so their SE ratios fall below the band. Those two cells, `s2c_ey0__unclustered` and `s2c_ey_r11__unclustered`, carry a directional gate in `GATED_DIRECTIONS`, and both pass it. The blip and the contrast difference the intercept away, so they state no verdict | $n$ = 2,000, 8,000 replications |
| `positivity_reporting` | the fit on the law `SP`, whose treatment probabilities range from 0.05 to 0.94. The role is `diagnostic`, and no rule gates these cells | $n$ = 2,000, 1,000 replications |

The calibration budget is the smallest multiple of 400 replications at which all 61 positive
calibration cells pass with a probability of at least 0.95. The rule takes the true SE ratio of
each cell from its pilot, shrunk toward the mean of its law. The probability is 0.952 at 8,000
replications. `tests/unit/test_structural_nested_mean_design.py` checks the rule.

The size cells of `SP` have about 8 degrees of freedom in the model-check covariance. These
cells measure the size of the check only. The `sp_f10` cell rejects at the rate in the measured
values below. Its 99% interval lies above the nominal 5% and below the
declared ceiling of 10%. The [model check](../structural-dynamic-effects.md#the-model-check)
section gives the pilot rates on `SP`.

## Fitting failures

Six fits of the calibration loop of law `m` raised a recordable error. Five reported a singular
`GLM` information matrix, and one reported a fitted probability at separation. Each lost fit
writes 12 cells: the 4 positive cells of `m` and their 8 controls. Each of those cells lost 6 of
8,000 replications. The declared failure bound of 0.01 allows 80 for each cell.

| item | value |
| --- | --- |
| records | `property-failures.csv`, one row for each lost fit |
| accounting | `property-failure-accounting.csv`. Every clause of the 12 cells holds at its worst case, and every cell reads `within bound` |
| witnesses | `property-failure-witnesses.csv`, the draw statistic of each lost replicate among the survivors of its cell |
| primary phase | no fit failed |

## Measured values

Names beginning `margin:` are thresholds declared before the run. Everything else is measured from
the committed results and checked at the precision printed.

| quantity | value | source |
| --- | --- | --- |
| `replicates` | 1000 | primary replications per scenario |
| `n` | 2000 | observations per primary replication |
| `independent_tests_total` | 61 | implementation-estimand tests against the truth |
| `independent_tests_passed` | 61 | of those, passing |
| `paired_tests_total` | 0 | paired comparisons with EconML `DynamicDML` |
| `paired_tests_passed` | 0 | of those, passing |
| `property_cells_total` | 237 | repeated-sampling property cells, reported cells excluded |
| `property_cells_passed` | 237 | cells whose own and family verdicts pass |
| `property_cells_reported` | 14 | cells reported with the `diagnostic` role: `positivity_reporting` and `unclustered_se`. Two of the 14, `s2c_ey0__unclustered` and `s2c_ey_r11__unclustered`, carry the directional gate and pass it. The 237 above do not count them |
| `max_standardized_bias` | 0.0883 | largest absolute primary bias in empirical standard deviations |
| `min_coverage` | 0.9360 | lowest measured primary-study coverage |
| `min_se_ratio_ci_lower` | 0.8769 | lowest bootstrap primary SE-ratio endpoint |
| `max_se_ratio_ci_upper` | 1.1279 | highest bootstrap primary SE-ratio endpoint |
| `properties[warning_rate/sp_f10__model_check]:rejection_rate` | 0.0692 | the rejection rate of the check on `SP` at ten folds |
| `properties[warning_rate/sp_f10__model_check]:rejection_ci_lower` | 0.0516 | its 99% lower bound |
| `properties[warning_rate/sp_f10__model_check]:rejection_ci_upper` | 0.0902 | its 99% upper bound |
| `properties[interval_calibration/m_ey0__correctly_specified]:failed_replicates` | 6 | replications that each cell of law `m` lost to a recorded fitting failure |
| `margin:alpha` | 0.0500 | nominal size of the reported intervals, and the family level of the rule |
| `margin:bootstrap_replicates` | 10000 | resamples behind every bootstrap interval |
| `margin:calibration_coverage_lower` | 0.9200 | calibration-cell coverage band, lower limit |
| `margin:calibration_coverage_upper` | 0.9800 | calibration-cell coverage band, upper limit |
| `margin:calibration_noninferiority` | 0.0500 | largest external-comparison calibration excess bound |
| `margin:calibration_se_ratio_lower` | 0.9300 | calibration-cell SE-ratio band, lower limit |
| `margin:calibration_se_ratio_upper` | 1.0700 | calibration-cell SE-ratio band, upper limit |
| `margin:confidence_level` | 0.9900 | confidence level of every Monte Carlo interval |
| `margin:coverage_floor` | 0.9000 | validity floor the coverage lower endpoint must clear |
| `margin:coverage_noninferiority` | -0.0250 | smallest external-comparison coverage difference bound |
| `margin:excluded_slope` | -0.2500 | slower rate a root-n interval must exclude |
| `margin:minimum_power` | 0.8000 | rejection lower bound a power cell must clear |
| `margin:nominal_coverage` | 0.9500 | nominal coverage those intervals claim |
| `margin:over_coverage_ceiling` | 0.9900 | above this, coverage is conservative rather than invalid |
| `margin:paired_difference` | 0.1500 | paired similarity margin, in pooled empirical standard deviations |
| `margin:rmse_noninferiority` | 1.1000 | largest external-comparison RMSE ratio bound |
| `margin:root_n_slope` | -0.5000 | contraction rate root-n asymptotics predict |
| `margin:root_n_slope_lower` | -0.6250 | accepted root-n slope band, lower limit |
| `margin:root_n_slope_upper` | -0.3750 | accepted root-n slope band, upper limit |
| `margin:se_ratio_sanity_lower` | 0.8000 | SE-ratio screen, lower limit |
| `margin:se_ratio_sanity_upper` | 1.2000 | SE-ratio screen, upper limit |
| `margin:standardized_bias` | 0.2500 | bias equivalence margin, in empirical standard deviations |
| `margin:type_i_ceiling` | 0.1000 | the rate a size cell must bound |
| `margin:shrunken_se_factor` | 0.7000 | factor the shrunken-SE control multiplies the standard error by |
| `margin:subject_failure_bound` | 0.0100 | declared share of replications a cell may lose to a recordable fitting failure |
| `margin:subject_failures_allowed` | 10 | the same bound, in primary replications |

## Limitations

| limit | what it means for use |
| --- | --- |
| the comparator runs are pending | the claim rests on exact truths, the exact-law witnesses and the controls. The EconML parity fixture covers the point estimate on one panel only |
| every positive law satisfies the linear structural nested mean model | the intervals are valid under that model. The controls `LU` and `VB` show the bias when a feature is missing. They do not bound it on another law |
| one size for the calibration cells | the calibration cells draw $n$ = 2,000. Seven labels have a three-size ladder |
| `GLM` nuisances on finite laws, and one booster | the `GLM` regressions are exact on each finite law. The booster of law `n` stops early on a validation split. No general proof gives its rate, and the claim that its rate suffices rests on a probe of law `n` at $n$ = 128,000 and 512,000. No support row covers a booster fit, because a row cannot name the booster settings |
| the model check rejects above its nominal level under weak positivity | on `SP` the check has about 8 degrees of freedom. The `sp_f10` cell rejects at 0.0692, with a 99% interval from 0.0516 to 0.0902. The interval lies above the nominal 5% and below the declared ceiling of 10%. The 99% interval of the `sp_f2` cell, 0.0210 to 0.0633, contains 5% |
| the weak-positivity cells gate nothing | `positivity_reporting` reports the fit on `SP` and states no verdict |
| six lost replications in the calibration of law `m` | each of the 12 cells of law `m` lost 6 of 8,000 replications to a singular `GLM` fit or a separated fit. The accounting holds every clause at its worst case |
| no censoring, survival outcome, rule or policy | the estimator refuses them. A feature that reads a time-varying covariate reports the blips and `ey_reference` only |
| clusters and weights at one setting each | `s2c` uses 200 clusters of ten and `s2w` uses known weights. The study covers no estimated weights and no fit below 40 clusters |

The causal interpretation requires consistency, sequential exchangeability and longitudinal
positivity. The [model](../structural-dynamic-effects.md#the-model) section states the model
assumption.

## Reproduction

The [fixture README](https://github.com/esbraun/cleverly-tmle/blob/main/tests/canonical/structural_nested_mean_study/README.md)
gives the regeneration commands. The
[manifest](https://github.com/esbraun/cleverly-tmle/blob/main/tests/canonical/structural_nested_mean_study/manifest.json)
records the pending comparator, the declared EconML sources, the seeds and the artifact hashes.