Basic IRM Models

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ATE Coverage

The simulations are based on the the make_irm_data-DGP with \(500\) observations. Due to the linearity of the DGP, Lasso and Logit Regression are nearly optimal choices for the nuisance estimation.

DoubleML Version                       0.8.2
Script                   irm_ate_coverage.py
Date                     2024-08-13 16:44:37
Total Runtime (seconds)          1115.591309
Python Version                        3.12.4
Coverage for 95.0%-Confidence Interval over 1000 Repetitions
Learner g Learner m Bias CI Length Coverage
Lasso Logistic Regression 0.123 0.557 0.935
Lasso Random Forest 0.147 0.720 0.956
Random Forest Logistic Regression 0.150 0.616 0.877
Random Forest Random Forest 0.152 0.750 0.947
Coverage for 90.0%-Confidence Interval over 1000 Repetitions
Learner g Learner m Bias CI Length Coverage
Lasso Logistic Regression 0.123 0.468 0.875
Lasso Random Forest 0.147 0.604 0.906
Random Forest Logistic Regression 0.150 0.517 0.796
Random Forest Random Forest 0.152 0.629 0.902

ATTE Coverage

As for the ATE, the simulations are based on the the make_irm_data-DGP with \(500\) observations.

DoubleML Version                        0.8.2
Script                   irm_atte_coverage.py
Date                      2024-08-13 17:15:42
Total Runtime (seconds)           1171.313816
Python Version                         3.12.4
Coverage for 95.0%-Confidence Interval over 1000 Repetitions
Learner g Learner m Bias CI Length Coverage
Lasso Logistic Regression 0.135 0.635 0.940
Lasso Random Forest 0.181 0.868 0.956
Random Forest Logistic Regression 0.150 0.656 0.924
Random Forest Random Forest 0.180 0.882 0.947
Coverage for 90.0%-Confidence Interval over 1000 Repetitions
Learner g Learner m Bias CI Length Coverage
Lasso Logistic Regression 0.135 0.533 0.888
Lasso Random Forest 0.181 0.729 0.895
Random Forest Logistic Regression 0.150 0.551 0.874
Random Forest Random Forest 0.180 0.740 0.892

Sensitivity

The simulations are based on the the ADD-DGP with \(10,000\) observations. As the DGP is nonlinear, we will only use corresponding learners. Since the DGP includes an unobserved confounder, we would expect a bias in the ATE estimates, leading to low coverage of the true parameter.

The confounding is set such that both sensitivity parameters are approximately \(cf_y=cf_d=0.1\), 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 lower 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 \(|\rho|=1\).

This is the init_notebook_mode cell from ITables v2.1.4
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ATE

DoubleML Version                          0.8.2
Script                   irm_ate_sensitivity.py
Date                        2024-08-14 22:52:08
Total Runtime (seconds)             9943.911803
Python Version                           3.12.4
Coverage for 95.0%-Confidence Interval over 500 Repetitions
Learner l Learner m Bias Bias (Lower) Bias (Upper) Coverage Coverage (Lower) Coverage (Upper) RV RVa
LGBM LGBM 0.179 0.043 0.322 0.318 0.998 1.000 0.124 0.034
LGBM Logistic Regr. 0.149 0.029 0.298 0.548 1.000 1.000 0.101 0.019
Linear Reg. LGBM 0.179 0.045 0.319 0.314 0.998 1.000 0.126 0.035
Linear Reg. Logistic Regr. 0.090 0.057 0.235 0.974 1.000 1.000 0.063 0.001
Coverage for 90.0%-Confidence Interval over 500 Repetitions
Learner l Learner m Bias Bias (Lower) Bias (Upper) Coverage Coverage (Lower) Coverage (Upper) RV RVa
LGBM LGBM 0.179 0.043 0.322 0.112 0.962 1.000 0.124 0.054
LGBM Logistic Regr. 0.149 0.029 0.298 0.292 1.000 1.000 0.101 0.035
Linear Reg. LGBM 0.179 0.045 0.319 0.122 0.964 1.000 0.126 0.055
Linear Reg. Logistic Regr. 0.090 0.057 0.235 0.860 1.000 1.000 0.063 0.007

ATTE

DoubleML Version                           0.8.2
Script                   irm_atte_sensitivity.py
Date                         2024-08-15 17:57:40
Total Runtime (seconds)              5941.642393
Python Version                            3.12.4
Coverage for 95.0%-Confidence Interval over 500 Repetitions
Learner l Learner m Bias Bias (Lower) Bias (Upper) Coverage Coverage (Lower) Coverage (Upper) RV RVa
LGBM LGBM 0.135 0.074 0.219 0.826 0.946 1.000 0.148 0.018
LGBM Logistic Regr. 0.131 0.071 0.218 0.834 0.962 1.000 0.139 0.016
Linear Reg. LGBM 0.125 0.070 0.208 0.858 0.964 1.000 0.135 0.014
Linear Reg. Logistic Regr. 0.074 0.074 0.140 0.976 0.996 1.000 0.081 0.002
Coverage for 90.0%-Confidence Interval over 500 Repetitions
Learner l Learner m Bias Bias (Lower) Bias (Upper) Coverage Coverage (Lower) Coverage (Upper) RV RVa
LGBM LGBM 0.135 0.074 0.219 0.702 0.866 1.000 0.148 0.035
LGBM Logistic Regr. 0.131 0.071 0.218 0.714 0.892 1.000 0.139 0.032
Linear Reg. LGBM 0.125 0.070 0.208 0.754 0.906 1.000 0.135 0.028
Linear Reg. Logistic Regr. 0.074 0.074 0.140 0.948 0.988 1.000 0.081 0.006