Draft

Basic IRM Models

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                       0.9.0
Script                   irm_ate_coverage.py
Date                     2024-09-09 08:23:16
Total Runtime (seconds)          3577.371852
Python Version                        3.12.5
Table 1: 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 0.148 0.715 0.960
Random Forest Logistic Regression 0.150 0.617 0.878
Random Forest Random Forest 0.150 0.743 0.953
Table 2: 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 0.148 0.600 0.927
Random Forest Logistic Regression 0.150 0.518 0.796
Random Forest Random Forest 0.150 0.623 0.897

ATTE Coverage

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

DoubleML Version                        0.9.0
Script                   irm_atte_coverage.py
Date                      2024-09-09 08:23:18
Total Runtime (seconds)           3582.448247
Python Version                         3.12.5
Table 3: Coverage for 95.0%-Confidence Interval over 1000 Repetitions
Learner g Learner m Bias CI Length Coverage
Lasso Logistic Regression 0.135 0.635 0.941
Lasso Random Forest 0.180 0.870 0.956
Random Forest Logistic Regression 0.150 0.658 0.922
Random Forest Random Forest 0.182 0.896 0.945
Table 4: 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 0.180 0.730 0.893
Random Forest Logistic Regression 0.150 0.552 0.869
Random Forest Random Forest 0.182 0.752 0.902

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 \(|\rho|=1\).

ATE

DoubleML Version                          0.9.0
Script                   irm_ate_sensitivity.py
Date                        2024-09-09 09:57:25
Total Runtime (seconds)             9228.398559
Python Version                           3.12.5
Table 5: 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
Table 6: 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                           0.9.0
Script                   irm_atte_sensitivity.py
Date                         2024-09-09 10:03:27
Total Runtime (seconds)              9588.962258
Python Version                            3.12.5
Table 7: 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 0.065 0.259 0.826 0.982 1.000 0.105 0.012
LGBM Logistic Regr. 0.131 0.065 0.259 0.834 0.984 1.000 0.098 0.011
Linear Reg. LGBM 0.125 0.065 0.244 0.858 0.986 1.000 0.099 0.010
Linear Reg. Logistic Regr. 0.074 0.095 0.175 0.976 0.998 1.000 0.058 0.002
Table 8: 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 0.065 0.259 0.702 0.950 1.000 0.105 0.024
LGBM Logistic Regr. 0.131 0.065 0.259 0.714 0.964 1.000 0.098 0.022
Linear Reg. LGBM 0.125 0.065 0.244 0.754 0.962 1.000 0.099 0.020
Linear Reg. Logistic Regr. 0.074 0.095 0.175 0.948 0.996 1.000 0.058 0.004