2. Inference

2.1. Weights-based inference

The default inference uses the representation of effect estimates as weighted averages of outcomes. It combines the expectation of conditional variance with the variance of conditional expectation, conditioning on forest weights. Conditional moments are estimated by k-nearest neighbors (default) or Nadaraya-Watson kernel regression.

With p_cond_var=False, variance is estimated directly from weighted outcomes rather than conditional moments. See Lechner and Mareckova, Comprehensive Causal Machine Learning for the theoretical context and its assumptions.

2.2. Bootstrap inference

The weight-based bootstrap resamples observations or clusters and renormalizes weights. It does not retrain an entire forest in every replication. p_se_boot_ate, p_se_boot_gate, p_se_boot_iate and p_se_boot_qiate control the corresponding inference.

Use p_cluster_std with var_cluster_name for clustered inference; see Sampling weights and clustering. When efficiency improvements are enabled through gen_ate_eff, gen_gate_eff, gen_iate_eff or gen_qiate_eff, the variance calculation depends on the type of treatment effect being estimated. See Estimation of treatment effects for details.

2.3. Parameters

Parameter	Purpose
p_cond_var	Use conditional moments (default True).
p_knn	Use k-nearest neighbors (True) or Nadaraya-Watson (False).
p_se_boot_ate, p_se_boot_gate	Weight-based bootstrap for average and group effects.
p_se_boot_iate, p_se_boot_qiate	Weight-based bootstrap for individual and quantile effects.
p_ci_level	Pointwise confidence level used in effect plots.

See the API for details.

2.3.1. Example

from mcf.example_data import example_data
from mcf.mcf_main import ModifiedCausalForest

# Generate example data using the built-in function `example_data()`
training_df, prediction_df, name_dict = example_data()

my_mcf = ModifiedCausalForest(
    var_y_name="outcome",
    var_d_name="treat",
    var_x_name_ord=["x_cont0", "x_cont1", "x_ord1"],
    # Bootstrap of standard errors for ATE
    p_se_boot_ate=None,
    # Conditional mean & variances are used
    p_cond_var=True,
    # Specifies k-NN method
    p_knn=True
)

my_mcf.train(training_df)
results = my_mcf.predict(prediction_df)