Basic PLR Models

Coverage

The simulations are based on the the make_plr_CCDDHNR2018-DGP with \(500\) observations.

DoubleML Version                           0.11.5.dev55
Script                         PLRATECoverageSimulation
Date                                   2026-08-10 13:51
Total Runtime (minutes)                      197.864018
Python Version                                   3.12.3
Config File              scripts/plm/plr_ate_config.yml

Partialling out

ⓘLearner l Learner m Bias CI Length Coverage Loss l Loss m
LGBM Regr. LGBM Regr. 0.043 0.175 0.907 1.205 1.087
LGBM Regr. LassoCV 0.039 0.190 0.952 1.205 1.008
LassoCV LGBM Regr. 0.073 0.165 0.594 1.128 1.086
LassoCV LassoCV 0.036 0.175 0.958 1.128 1.008
LassoCV RF Regr. 0.049 0.170 0.841 1.128 1.052
RF Regr. LassoCV 0.036 0.180 0.959 1.153 1.008
RF Regr. RF Regr. 0.035 0.170 0.947 1.153 1.052
Coverage for 95%-Confidence Interval over 1000 Repetitions
ⓘLearner l Learner m Bias CI Length Coverage Loss l Loss m
LGBM Regr. LGBM Regr. 0.043 0.146 0.822 1.205 1.087
LGBM Regr. LassoCV 0.039 0.159 0.902 1.205 1.008
LassoCV LGBM Regr. 0.073 0.139 0.473 1.128 1.086
LassoCV LassoCV 0.036 0.147 0.905 1.128 1.008
LassoCV RF Regr. 0.049 0.143 0.753 1.128 1.052
RF Regr. LassoCV 0.036 0.151 0.914 1.153 1.008
RF Regr. RF Regr. 0.035 0.143 0.897 1.153 1.052
Coverage for 90%-Confidence Interval over 1000 Repetitions

IV-type

For the IV-type score, the learners ml_l and ml_g are both set to the same type of learner (here Learner g).

ⓘLearner g Learner m Bias CI Length Coverage Loss g Loss m
LGBM Regr. LGBM Regr. 0.041 0.190 0.946 1.071 1.087
LGBM Regr. LassoCV 0.037 0.177 0.946 1.071 1.008
LassoCV LGBM Regr. 0.038 0.179 0.950 1.011 1.085
LassoCV LassoCV 0.035 0.167 0.947 1.009 1.008
LassoCV RF Regr. 0.037 0.155 0.921 1.010 1.052
RF Regr. LassoCV 0.035 0.168 0.946 1.017 1.008
RF Regr. RF Regr. 0.037 0.157 0.924 1.017 1.052
Coverage for 95%-Confidence Interval over 1000 Repetitions
ⓘLearner g Learner m Bias CI Length Coverage Loss g Loss m
LGBM Regr. LGBM Regr. 0.041 0.160 0.880 1.071 1.087
LGBM Regr. LassoCV 0.037 0.148 0.884 1.071 1.008
LassoCV LGBM Regr. 0.038 0.150 0.891 1.011 1.085
LassoCV LassoCV 0.035 0.140 0.896 1.009 1.008
LassoCV RF Regr. 0.037 0.130 0.854 1.010 1.052
RF Regr. LassoCV 0.035 0.141 0.897 1.017 1.008
RF Regr. RF Regr. 0.037 0.132 0.850 1.017 1.052
Coverage for 90%-Confidence Interval over 1000 Repetitions

Sensitivity

The simulations are based on the the make_confounded_plr_data-DGP with \(1000\) observations as highlighted in the Example Gallery. As the DGP is nonlinear, we will only use corresponding learners. Since the DGP includes unobserved confounders, we would expect a bias in the ATE estimates, leading to low coverage of the true parameter.

Both sensitivity parameters are set to \(cf_y=cf_d=0.1\), such that the robustness value \(RV\) should be approximately \(10\%\). Further, the corresponding confidence intervals are one-sided (since the direction of the bias is unkown), such that only one side should approximate the corresponding coverage level (here only the upper coverage is relevant since the bias is positive). Remark that for the coverage level the value of \(\rho\) has to be correctly specified, such that the coverage level will be generally (significantly) larger than the nominal level under the conservative choice of \(|\rho|=1\).

DoubleML Version                                       0.11.5.dev55
Script                          PLRATESensitivityCoverageSimulation
Date                                               2026-08-10 14:25
Total Runtime (minutes)                                  232.292545
Python Version                                               3.12.3
Config File              scripts/plm/plr_ate_sensitivity_config.yml

Partialling out

ⓘLearner l Learner m Bias Bias (Lower) Bias (Upper) Coverage Coverage (Lower) Coverage (Upper) RV RVa
LGBM Regr. LGBM Regr. 0.759 1.459 0.262 0.317 1.000 0.994 0.104 0.031
LGBM Regr. LassoCV 1.331 2.059 0.608 0.073 1.000 0.752 0.173 0.077
LassoCV LGBM Regr. 0.915 2.437 0.638 0.827 1.000 1.000 0.061 0.005
LassoCV LassoCV 4.847 6.377 3.317 0.000 1.000 0.001 0.282 0.208
LassoCV RF Regr. 1.672 3.352 0.309 0.104 1.000 1.000 0.099 0.033
RF Regr. LassoCV 2.194 3.454 0.937 0.014 1.000 0.565 0.167 0.095
RF Regr. RF Regr. 1.612 2.951 0.382 0.049 1.000 0.974 0.118 0.054
Coverage for 95%-Confidence Interval over 1000 Repetitions
ⓘLearner l Learner m Bias Bias (Lower) Bias (Upper) Coverage Coverage (Lower) Coverage (Upper) RV RVa
LGBM Regr. LGBM Regr. 0.759 1.459 0.262 0.196 1.000 0.968 0.104 0.045
LGBM Regr. LassoCV 1.331 2.059 0.608 0.034 1.000 0.524 0.173 0.097
LassoCV LGBM Regr. 0.915 2.437 0.638 0.583 1.000 1.000 0.061 0.013
LassoCV LassoCV 4.847 6.377 3.317 0.000 1.000 0.000 0.282 0.224
LassoCV RF Regr. 1.672 3.352 0.309 0.037 1.000 1.000 0.099 0.047
RF Regr. LassoCV 2.194 3.454 0.937 0.004 1.000 0.310 0.167 0.111
RF Regr. RF Regr. 1.612 2.951 0.382 0.016 1.000 0.924 0.118 0.068
Coverage for 90%-Confidence Interval over 1000 Repetitions

IV-type

For the IV-type score, the learners ml_l and ml_g are both set to the same type of learner (here Learner g).

ⓘLearner g Learner m Bias Bias (Lower) Bias (Upper) Coverage Coverage (Lower) Coverage (Upper) RV RVa
LGBM Regr. LGBM Regr. 0.775 1.473 0.280 0.549 1.000 0.998 0.106 0.020
LGBM Regr. LassoCV 1.474 2.208 0.745 0.044 1.000 0.578 0.188 0.091
LassoCV LGBM Regr. 1.026 2.534 0.577 0.899 1.000 1.000 0.069 0.004
LassoCV LassoCV 4.849 6.379 3.320 0.000 1.000 0.001 0.283 0.208
LassoCV RF Regr. 1.729 3.382 0.321 0.098 1.000 1.000 0.104 0.038
RF Regr. LassoCV 2.507 3.765 1.249 0.005 1.000 0.274 0.188 0.116
RF Regr. RF Regr. 1.631 2.964 0.398 0.045 1.000 0.961 0.120 0.055
Coverage for 95%-Confidence Interval over 1000 Repetitions
ⓘLearner g Learner m Bias Bias (Lower) Bias (Upper) Coverage Coverage (Lower) Coverage (Upper) RV RVa
LGBM Regr. LGBM Regr. 0.775 1.473 0.280 0.383 1.000 0.987 0.106 0.034
LGBM Regr. LassoCV 1.474 2.208 0.745 0.016 1.000 0.334 0.188 0.112
LassoCV LGBM Regr. 1.026 2.534 0.577 0.742 1.000 0.999 0.069 0.011
LassoCV LassoCV 4.849 6.379 3.320 0.000 1.000 0.000 0.283 0.225
LassoCV RF Regr. 1.729 3.382 0.321 0.026 1.000 0.993 0.104 0.052
RF Regr. LassoCV 2.507 3.765 1.249 0.000 1.000 0.146 0.188 0.132
RF Regr. RF Regr. 1.631 2.964 0.398 0.018 1.000 0.898 0.120 0.070
Coverage for 90%-Confidence Interval over 1000 Repetitions

Tuning

The simulations are based on the the make_plr_CCDDHNR2018-DGP with \(500\) observations. This is only an example as the untuned version just relies on the default configuration.

DoubleML Version                                   0.12.dev0
Script                        PLRATETuningCoverageSimulation
Date                                        2025-12-03 21:40
Total Runtime (minutes)                            50.322924
Python Version                                        3.12.9
Config File              scripts/plm/plr_ate_tune_config.yml

Partialling out

ⓘLearner l Learner m Tuned Bias CI Length Coverage Loss l Loss m
LGBM Regr. LGBM Regr. False 0.046 0.175 0.868 1.236 1.117
LGBM Regr. LGBM Regr. True 0.038 0.172 0.916 1.169 1.065
Coverage for 95%-Confidence Interval over 500 Repetitions
ⓘLearner l Learner m Tuned Bias CI Length Coverage Loss l Loss m
LGBM Regr. LGBM Regr. False 0.046 0.147 0.794 1.236 1.117
LGBM Regr. LGBM Regr. True 0.038 0.145 0.862 1.169 1.065
Coverage for 90%-Confidence Interval over 500 Repetitions