fit_IVDML: Fitting Double Machine Learning Models with Instrumental Variables and Potentially Heterogeneous Treatment Effect

Description

This function is used to fit a Double Machine Learning (DML) model with Instrumental Variables (IV) with the goal to perform inference on potentially heterogeneous treatment effects. The model under study is \(Y = \beta(A)D + g(X) + \epsilon\), where the error \(\epsilon\) is potentially correlated with the treatment \(D\), but there is an IV \(Z\) satisfying \(\mathbb E[\epsilon|Z,X] = 0\). The object of interest is the treatment effect \(\beta\) of the treatment \(D\) on the response \(Y\). The treatment effect \(\beta\) is either constant or can depend on the univariate quantity \(A\), which is typically a component of the covariates \(X\).

Usage

fit_IVDML(
  Y,
  D,
  Z,
  X = NULL,
  A = NULL,
  ml_method,
  ml_par = list(),
  A_deterministic_X = TRUE,
  K_dml = 5,
  iv_method = c("linearIV", "mlIV"),
  S_split = 1
)

Value

An object of class IVDML, containing:

results_splits: A list of S_split lists of cross-fitted residuals from the different sample splits.
A: The argument A of the function.
ml_method: The argument ml_method of the function.
A_deterministic_X: The argument A_deterministic_X of the function.
iv_method: The argument iv_method of the function. The treatment effect estimates, standard errors and confidence intervals can be calculated from the IVDML object using the functions coef.IVDML(), se(), standard_confint(), robust_confint().

Arguments

Y

Numeric vector. Response variable.

D

Numeric vector. Treatment variable.

Z

Matrix, vector, or data frame. Instrumental variables.

X

Matrix, vector, or data frame. Additional covariates (default: NULL).

A

Numeric vector. Variable with respect to which treatment effect heterogeneity is considered. Usually equal to a column of X and in this case it can also be specified later (default: NULL).

ml_method

Character. Machine learning method to use. Options are "gam", "xgboost", and "randomForest".

ml_par

List. Parameters for the machine learning method:

If ml_method == "gam", can specify ind_lin_Z and ind_lin_X for components of Z and X to be modeled linearly.
If ml_method == "xgboost", can specify max_nrounds, k_cv, early_stopping_rounds, and vectors eta and max_depth.
If ml_method == "randomForest", can specify num.trees, num_mtry (number of different mtry values to try out) or a vector mtry, a vector max.depth, num_min.node.size (number of different min.node.size values to try out) or a vector min.node.size.
To specify different parameters for the different nuisance function regressions, ml_par should be a list of lists: ml_par_D_XZ (parameters for nuisance function \(\mathbb E[D|Z, X]\), needed for iv_method "mlIV" and "mlIV_direct"), ml_par_D_X (parameters for nuisance function \(\mathbb E[D|X]\), needed for iv_method "linearIV", "mlIV" and "mlIV_direct"), ml_par_f_X (parameters for nuisance function \(\mathbb E[\widehat{\mathbb E}[D|Z, X]|X]\), needed for iv_method "mlIV"), ml_par_Y_X (parameters for nuisance function \(\mathbb E[Y|X]\), needed for iv_method "linearIV", "mlIV" and "mlIV_direct"), ml_par_Z_X (parameters for nuisance function \(\mathbb E[Z|X]\), needed for iv_method "linearIV").

A_deterministic_X

Logical. Whether A is a deterministic function of X (default: TRUE).

K_dml

Integer. Number of cross-fitting folds (default: 5).

iv_method

Character vector. Instrumental variables estimation method. Options: "linearIV", "mlIV", "mlIV_direct" (default: c("linearIV", "mlIV")). "linearIV" corresponds to using instruments linearly and "mlIV" corresponds to using machine learning instruments. "mlIV_direct" is a variant of "mlIV" that uses the same estimate of \(\mathbb E[D|X]\) for both the residuals \(X - \mathbb E[D|X]\) and \(\mathbb E[D|Z, X] - \mathbb E[D|X]\), whereas "mlIV" uses a two-stage estimate of \(\mathbb E[\widehat{\mathbb E}[D|Z, X]|X]\) for the residuals \(\mathbb E[D|Z, X] - \mathbb E[D|X]\).

S_split

Integer. Number of sample splits for cross-fitting (default: 1).

References

Cyrill Scheidegger, Zijian Guo and Peter Bühlmann. Inference for heterogeneous treatment effects with efficient instruments and machine learning. Preprint, arXiv:2503.03530, 2025.

Examples

Run this code

set.seed(1)
Z <- rnorm(100)
X <- Z + rnorm(100)
H <- rnorm(100)
D <- Z^2 + sin(X) + H + rnorm(100)
A <- X
Y <- tanh(A) * D + cos(X) - H + rnorm(100)
fit <- fit_IVDML(Y = Y, D = D, Z = Z, X = X, A = A, ml_method = "gam")
coef(fit, iv_method = "mlIV", a = 0, A = A, kernel_name = "boxcar", bandwidth = 0.2)