4. CBGATEs and BGATEs

Balanced Group Average Treatment Effects (BGATEs) compare group effects using a common distribution of selected covariates. For a heterogeneity variable \(Z\) and balancing variables \(W\), define

\[\operatorname{BGATE}(m,l;z,F_W) = \int E[Y^m-Y^l\mid Z=z,W=w]\,dF_W(w).\]

\(F_W\) describes the distribution of the balancing variables in the prediction data remaining after data preparation and common-support checks. The same distribution is used for all groups, so their effects are compared using a common covariate distribution.

CBGATEs balance all other features. A causal moderation interpretation requires additional assumptions, not balancing alone; see Bearth and Lechner, Causal Machine Learning for Moderation Effects.

4.1. Implementation

• BGATEs use selected balancing covariates and nearest-neighbor reconstruction at the heterogeneity evaluation values. Set p_bgate=True and select var_x_name_balance_bgate.

• CBGATEs duplicate reference covariate rows and set the heterogeneity variable at each evaluation value. This balances all remaining features.

Both methods use the previously trained forest. p_bgate_sample_share controls the size of the reference sample, which is reused at each evaluation value of the heterogeneity variable. Minimum sample-size requirements can increase the number of observations used and the computation time.

See p_bgate_sample_share in the API for the exact sampling rule.

4.2. Parameters

Parameter	Purpose
p_bgate, p_cbgate	Enable BGATE and CBGATE estimation, respectively.
var_x_name_balance_bgate	Variables used for BGATE balancing. Defaults to the other heterogeneity variables.
p_gates_no_evalu_points	Number of evaluation points when no stored evaluation values are available.
p_bgate_sample_share	Controls reference-sample subsampling for BGATE and CBGATE estimation.

See the API for defaults and detailed parameter descriptions.

4.2.1. Examples

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"],
    var_z_name_cont=["x_cont0", "x_cont1"],
    # Variables to balance the GATEs on
    var_x_name_balance_bgate=["x_cont0", "x_cont1"],
    # Estimate a balanced GATE in selected features
    p_bgate=True,
    # Random samples to speed up the programme
    p_bgate_sample_share = None
)

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

my_mcf = ModifiedCausalForest(
    var_y_name="outcome",
    var_d_name="treat",
    var_x_name_ord=["x_cont0", "x_ord1"],
    var_x_name_unord=["x_unord0"],
    var_z_name_cont=["x_cont0"],
    # Estimate a GATE that is balanced in all other features
    p_cbgate=True
)

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