Simulate data with linear confounding and causal effect following a step-function

Source: R/simData.R

Simulation of data from a confounded non-linear model. Where the non-linear function is a random regression tree. The data generating process is given by: $$Y = f(X) + \delta^T H + \nu$$ $$X = \Gamma^T H + E$$ where \(f(X)\) is a random regression tree with \(m\) random splits of the data. Resulting in a random step-function with \(m+1\) levels, i.e. leaf-levels. $$f(x_i) = \sum_{k = 1}^K 1_{\{x_i \in R_k\}} c_k$$ \(E\), \(\nu\) are random error terms and \(H \in \mathbb{R}^{n \times q}\) is a matrix of random confounding covariates. \(\Gamma \in \mathbb{R}^{q \times p}\) and \(\delta \in \mathbb{R}^{q}\) are random coefficient vectors. For the simulation, all the above parameters are drawn from a standard normal distribution, except for \(\delta\) which is drawn from a normal distribution with standard deviation 10. The leaf levels \(c_k\) are drawn from a uniform distribution between -50 and 50.

simulate_data_step(q, p, n, m, make_tree = FALSE)

Arguments

q

number of confounding covariates in H

p

number of covariates in X

n

number of observations

m

number of covariates with a causal effect on Y

make_tree

Whether the random regression tree should be returned.

Value

a list containing the simulated data:

X

a matrix of covariates

Y

a vector of responses

f_X

a vector of the true function f(X)

j

the indices of the causal covariates in X

tree

If make_tree, the random regression tree of class Node from Glur2023Data.tree:StructureSDModels

References

Author

Markus Ulmer

Examples

set.seed(42)
# simulation of confounded data
sim_data <- simulate_data_step(q = 2, p = 15, n = 100, m = 2)
X <- sim_data$X
Y <- sim_data$Y