simulate_gau: Simulate Gaussian antedependence series

In antedep: Antedependence Models for Longitudinal Data

Simulate Gaussian antedependence series

Description

Generate longitudinal continuous data from a Gaussian antedependence (AD) model of order 0, 1, or 2 using a conditional regression on predecessors.

Usage

simulate_gau(
  n_subjects,
  n_time,
  order = 1L,
  mu = NULL,
  phi = NULL,
  sigma = NULL,
  blocks = NULL,
  tau = 0,
  seed = NULL
)

Arguments

n_subjects	number of subjects
n_time	number of time points
order	antedependence order, 0, 1 or 2
mu	mean parameter; NULL, scalar, or length n_time
phi	dependence parameter; ignored when order = 0. For order = 1, NULL, scalar, or length n_time. For order = 2, NULL or a 2 by n_time matrix.
sigma	innovation standard deviation; NULL, scalar, or length n_time
blocks	integer vector of length n_subjects indicating block membership for each subject; if NULL, no block effect is applied
tau	group effect vector indexed by block; tau[1] is forced to 0. If scalar x, it is expanded to c(0, x, ..., x) with length equal to the number of blocks
seed	optional random seed for reproducibility

Details

For order = 0, each time point is generated independently as Y[, t] = mu[t] + tau[block] + eps, with eps ~ N(0, sigma[t]^2).

For order = 1, for t >= 2: ⁠Y[, t] = m_t + phi[t] * (Y[, t - 1] - m_{t-1}) + eps_t⁠, where m_t = mu[t] + tau[block] and eps_t ~ N(0, sigma[t]^2).

For order = 2, for t >= 3: ⁠Y[, t] = m_t + phi[1, t] * (Y[, t - 1] - m_{t-1}) + phi[2, t] * (Y[, t - 2] - m_{t-2}) + eps_t⁠.

If blocks is provided, each subject s belongs to a block and receives a mean shift tau[blocks[s]]. tau[1] is forced to 0.

Value

numeric matrix with dimension n_subjects by n_time

Examples

y <- simulate_gau(
  n_subjects = 20,
  n_time = 6,
  order = 1,
  phi = 0.4,
  seed = 42
)
dim(y)

antedep documentation built on April 25, 2026, 1:06 a.m.