Table 1 Simulation results (1000 simulated datasets, each with n patients) showing empirical rejection probabilities of the proposed resampling tests for a regression Random Forest. Correlations within the simulation model are given as the correlation between Y and Z (C(Y, Z)) and semipartial correlation between Y and Z (\(spC(Y,Z):=spC(Y,Z|X_1, \dots , X_5)\))
Simulation design | Rejection probability of \(\bf H_0^{(1)}\) | Rejection probability of \(\bf H_0^{(2)}\) | |||||
|---|---|---|---|---|---|---|---|
C(Y, Z) | spC(Y, Z) | n=500 | n=1000 | n=5000 | n=500 | n=1000 | n=5000 |
0.3 | 0 | 0.946 | 0.995 | 1.000 | 0.019 | 0.027 | 0.020 |
0.3 | 0.1 | 0.985 | 0.999 | 1.000 | 0.237 | 0.396 | 0.937 |
0.3 | 0.2 | 0.538 | 0.801 | 0.999 | 0.775 | 0.968 | 1.000 |
0.6 | 0.2 | 1.000 | 1.000 | 1.000 | 0.946 | 1.000 | 1.000 |
0.6 | 0.4 | 0.994 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
0.9 | 0.3 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
0.9 | 0.6 | 0.999 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |