Generates data from a interactive regression (IRM) model. The data generating process is defined as

\(d_i = 1\left\lbrace \frac{\exp(c_d x_i' \beta)}{1+\exp(c_d x_i' \beta)} > v_i \right\rbrace,\)

\( y_i = \theta d_i + c_y x_i' \beta d_i + \zeta_i,\)

with \(v_i \sim \mathcal{U}(0,1)\), \(\zeta_i \sim \mathcal{N}(0,1)\) and covariates \(x_i \sim \mathcal{N}(0, \Sigma)\), where \(\Sigma\) is a matrix with entries \(\Sigma_{kj} = 0.5^{|j-k|}\). \(\beta\) is a dim_x-vector with entries \(\beta_j = \frac{1}{j^2}\) and the constancts \(c_y\) and \(c_d\) are given by

\( c_y = \sqrt{\frac{R_y^2}{(1-R_y^2) \beta' \Sigma \beta}},\)

\(c_d = \sqrt{\frac{(\pi^2 /3) R_d^2}{(1-R_d^2) \beta' \Sigma \beta}}.\)

The data generating process is inspired by a process used in the simulation experiment (see Appendix P) of Belloni et al. (2017).

make_irm_data(
  n_obs = 500,
  dim_x = 20,
  theta = 0,
  R2_d = 0.5,
  R2_y = 0.5,
  return_type = "DoubleMLData"
)

Arguments

n_obs

(integer(1))
The number of observations to simulate.

dim_x

(integer(1))
The number of covariates.

theta

(numeric(1))
The value of the causal parameter.

R2_d

(numeric(1))
The value of the parameter \(R_d^2\).

R2_y

(numeric(1))
The value of the parameter \(R_y^2\).

return_type

(character(1))
If "DoubleMLData", returns a DoubleMLData object. If "data.frame" returns a data.frame(). If "data.table" returns a data.table(). If "matrix" a named list() with entries X, y, d and z is returned. Every entry in the list is a matrix() object. Default is "DoubleMLData".

References

Belloni, A., Chernozhukov, V., Fernández-Val, I. and Hansen, C. (2017). Program Evaluation and Causal Inference With High-Dimensional Data. Econometrica, 85: 233-298.