r | Response | Method | Scenario 1 | Scenario 2 | Scenario 3 | |||
---|---|---|---|---|---|---|---|---|
 |  |  | \(\textrm{Bias}\) | RMSE | \(\textrm{Bias}\) | RMSE | \(\textrm{Bias}\) | RMSE |
1 | Linear | IPW | 0.040 | 0.42 | 0.217 | 0.55 | 0.179 | 0.50 |
 |  | PSM | 0.162 | 0.42 | 0.247 | 0.57 | 0.365 | 0.67 |
 |  | FM | 0.156 | 0.40 | 0.280 | 0.57 | 0.378 | 0.66 |
 |  | EBAL | -0.002 | 0.11 | -0.003 | 0.11 | -0.005 | 0.11 |
 |  | SBW | -0.003 | 0.10 | -0.004 | 0.11 | -0.005 | 0.11 |
 |  | EBCW | -0.002 | 0.11 | -0.003 | 0.11 | -0.004 | 0.11 |
 |  | \(\textrm{QReR}_{\textrm{M}}\) | -0.022 | 0.12 | -0.031 | 0.12 | -0.029 | 0.12 |
 | Nonlinear | IPW | 0.077 | 0.58 | 0.290 | 0.72 | 0.245 | 0.64 |
 | (Interaction) | PSM | 0.245 | 0.61 | 0.241 | 0.81 | 0.423 | 0.95 |
 |  | FM | 0.235 | 0.59 | 0.292 | 0.80 | 0.440 | 0.93 |
 |  | EBAL | 0.012 | 0.19 | -0.029 | 0.22 | -0.041 | 0.21 |
 |  | SBW | 0.011 | 0.19 | -0.042 | 0.22 | -0.056 | 0.22 |
 |  | EBCW | 0.012 | 0.19 | -0.029 | 0.22 | -0.040 | 0.21 |
 |  | \(\textrm{QReR}_{\textrm{M}}\) | -0.033 | 0.19 | -0.123 | 0.24 | -0.133 | 0.26 |
 | Nonlinear | IPW | 0.247 | 3.56 | 5.333 | 11.91 | -10.193 | 14.00 |
 | (Polynomial) | PSM | 0.097 | 3.54 | 5.217 | 9.40 | -8.803 | 10.90 |
 |  | FM | 0.124 | 3.53 | 5.134 | 9.29 | -8.872 | 11.00 |
 |  | EBAL | 0.092 | 2.72 | 4.925 | 8.51 | -8.850 | 10.62 |
 |  | SBW | 0.119 | 2.55 | 5.419 | 8.54 | -7.836 | 9.52 |
 |  | EBCW | 0.092 | 2.72 | 4.925 | 8.51 | -8.850 | 10.62 |
 |  | \(\textrm{QReR}_{\textrm{M}}\) | 0.025 | 2.04 | 4.875 | 7.01 | -6.112 | 7.56 |
2 | Linear | IPW | 0.024 | 0.35 | -0.565 | 0.96 | -1.154 | 1.42 |
 |  | PSM | 0.085 | 0.41 | -0.032 | 0.49 | -0.311 | 0.58 |
 |  | FM | 0.088 | 0.40 | -0.035 | 0.48 | -0.302 | 0.56 |
 |  | EBAL | 0.002 | 0.09 | 0.002 | 0.09 | 0.001 | 0.09 |
 |  | SBW | 0.001 | 0.09 | 0.001 | 0.09 | 0.000 | 0.09 |
 |  | EBCW | 0.002 | 0.09 | 0.002 | 0.09 | 0.001 | 0.09 |
 |  | \(\textrm{QReR}_{\textrm{M}}\) | -0.017 | 0.10 | -0.017 | 0.10 | -0.013 | 0.10 |
 | Nonlinear | IPW | 0.049 | 0.46 | -0.766 | 1.23 | -1.611 | 1.91 |
 | (Interaction) | PSM | 0.130 | 0.56 | -0.174 | 0.68 | -0.603 | 0.91 |
 |  | FM | 0.132 | 0.54 | -0.179 | 0.67 | -0.595 | 0.88 |
 |  | EBAL | 0.006 | 0.17 | -0.023 | 0.20 | -0.032 | 0.20 |
 |  | SBW | -0.052 | 0.17 | -0.104 | 0.22 | -0.121 | 0.23 |
 |  | EBCW | 0.006 | 0.17 | -0.023 | 0.20 | -0.032 | 0.20 |
 |  | \(\textrm{QReR}_{\textrm{M}}\) | -0.080 | 0.18 | -0.142 | 0.23 | -0.145 | 0.25 |
 | Nonlinear | IPW | 0.060 | 3.22 | 4.734 | 14.91 | -12.453 | 18.48 |
 | (Polynomial) | PSM | -0.105 | 2.72 | 5.280 | 9.50 | -8.156 | 10.14 |
 |  | FM | -0.064 | 2.66 | 5.230 | 9.45 | -8.279 | 10.20 |
 |  | EBAL | -0.056 | 2.20 | 5.098 | 8.74 | -8.151 | 10.08 |
 |  | SBW | -0.069 | 2.09 | 5.678 | 8.83 | -6.955 | 8.77 |
 |  | EBCW | -0.056 | 2.20 | 5.098 | 8.74 | -8.152 | 10.08 |
 |  | \(\textrm{QReR}_{\textrm{M}}\) | -0.261 | 1.63 | 4.810 | 6.81 | -4.825 | 6.26 |