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"
)(integer(1))
The number of observations to simulate.
(integer(1))
The number of covariates.
(numeric(1))
The value of the causal parameter.
(numeric(1))
The value of the parameter \(R_d^2\).
(numeric(1))
The value of the parameter \(R_y^2\).
(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".
Belloni, A., Chernozhukov, V., Fernández-Val, I. and Hansen, C. (2017). Program Evaluation and Causal Inference With High-Dimensional Data. Econometrica, 85: 233-298.