R/simData.R
simulate_data_nonlinear.RdSimulation of data from a confounded non-linear model. 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 function on the fourier basis with a subset of size m covariates \(X_j\) having a causal effect on \(Y\). $$f(x_i) = \sum_{j = 1}^p 1_{j \in js} \sum_{k = 1}^K (\beta_{j, k}^{(1)} \cos(0.2 k x_j) + \beta_{j, k}^{(2)} \sin(0.2 k x_j))$$ \(E\), \(\nu\) 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 \(\nu\) which is drawn from a normal distribution with standard deviation 0.1. The parameters \(\beta\) are drawn from a uniform distribution between -1 and 1.
simulate_data_nonlinear(q, p, n, m, K = 2, eff = NULL, fixEff = FALSE)number of confounding covariates in H
number of covariates in X
number of observations
number of covariates with a causal effect on Y
number of fourier basis functions K \(K \in \mathbb{N}\), e.g. complexity of causal function
the number of affected covariates in X by the confounding, if NULL all covariates are affected
if eff is smaller than p: If fixEff = TRUE, the causal parents are always affected by confounding if fixEff = FALSE, affected covariates are chosen completely at random.
a list containing the simulated data:
a matrix of covariates
a vector of responses
a vector of the true function f(X)
the indices of the causal covariates in X
the parameter vector for the function f(X), see f_four
the matrix of confounding covariates
set.seed(42)
# simulation of confounded data
sim_data <- simulate_data_nonlinear(q = 2, p = 150, n = 100, m = 2)
X <- sim_data$X
Y <- sim_data$Y