Simulate SDR data — simulate_risdr

Simulates data from a sufficient dimension reduction model with an autoregressive covariance structure. The function returns the true orthonormal central subspace basis, which allows simulation studies to evaluate both prediction accuracy and subspace recovery.

Usage

simulate_risdr_data(
  n = 200,
  p = 50,
  d = 2,
  rho = 0.6,
  sigma = 1,
  signal_strength = 1,
  model = c("linear_quadratic", "symmetric", "interaction", "linear"),
  beta_type = c("coordinate", "random_sparse", "random_dense"),
  beta = NULL,
  seed = NULL
)

Arguments

n: Sample size.
p: Number of predictors.
d: Structural dimension.
rho: AR(1) correlation parameter.
sigma: Error standard deviation.
signal_strength: Multiplicative strength of the regression signal.
model: Data-generating model.
beta_type: Type of true central subspace basis.
beta: Optional user-supplied p by d central subspace basis. When supplied, its orthonormal basis is used and beta_type is ignored.
seed: Optional random seed.

Value

A list containing the simulated predictors, response, true basis, latent sufficient predictors, population covariance matrix, signal, error, and simulation settings.

Examples

simulated <- simulate_risdr_data(
  n = 60,
  p = 6,
  d = 2,
  rho = 0.4,
  seed = 2026
)

dim(simulated$X)
#> [1] 60  6
head(simulated$y)
#> [1]  0.6492720 -3.9456499 -1.6755412 -2.0225007  3.7572592  0.5424327
crossprod(simulated$beta)
#>       beta1 beta2
#> beta1     1     0
#> beta2     0     1