Simulate Gaussian antedependence series

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

Value

numeric matrix with dimension n_subjects by n_time

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.

Examples

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