simulate_data_nonlinear: Simulate data with linear confounding and non-linear causal...

In SDModels: Spectrally Deconfounded Models

Simulate data with linear confounding and non-linear causal effect

Description

Simulation 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.

Usage

simulate_data_nonlinear(q, p, n, m, K = 2, eff = NULL, fixEff = 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
K	number of fourier basis functions K K \in \mathbb{N}, e.g. complexity of causal function
eff	the number of affected covariates in X by the confounding, if NULL all covariates are affected
fixEff	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.

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
beta	the parameter vector for the function f(X), see f_four
H	the matrix of confounding covariates

Author(s)

Markus Ulmer

See Also

f_four

Examples

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

SDModels documentation built on April 11, 2025, 5:50 p.m.