Generates data from a interactive regression (IRM) model.
Description
Generates data from a interactive regression (IRM) model.
The data generating process is defined as
di=1{1+exp(cdxi′β)exp(cdxi′β)>vi},
yi=θdi+cyxi′βdi+ζi,
with vi∼U(0,1), ζi∼N(0,1)
and covariates xi∼N(0,Σ), where Σ
is a matrix with entries Σkj=0.5∣j−k∣.
β is a dim_x-vector with entries βj=j21
and the constancts cy and cd are given by
cy=(1−Ry2)β′ΣβRy2,
cd=(1−Rd2)β′Σβ(π2/3)Rd2.
The data generating process is inspired by a process used in the simulation
experiment (see Appendix P) of Belloni et al. (2017).
(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 Rd2.
R2_y
(numeric(1))
The value of the parameter Ry2.
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.