Simulate INAD antedependence series

Generate longitudinal count data from an INAD model using a thinning operator and an innovation distribution.

Usage

simulate_inad(
  n_subjects,
  n_time,
  order = 1L,
  thinning = c("binom", "pois", "nbinom"),
  innovation = c("pois", "bell", "nbinom"),
  alpha = NULL,
  theta = NULL,
  nb_inno_size = 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

thinning

thinning operator, one of "binom", "pois", "nbinom"

innovation

innovation distribution, one of "pois", "bell", "nbinom"

alpha

thinning parameter or vector or matrix; if NULL, defaults are used depending on the order

theta

innovation parameter or vector; if NULL, defaults are used depending on the innovation type. For Poisson and negative binomial innovations, theta is the innovation mean parameter. For Bell innovations, theta is the Bell rate parameter, with innovation mean theta * exp(theta).

nb_inno_size

size (dispersion) parameter for negative binomial innovations when innovation = "nbinom"; must be positive. If NULL, defaults to 1. Larger values correspond to less overdispersion (approaching Poisson as size -> Inf).

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

integer matrix of counts with dimension n_subjects by n_time

Details

Time 1 observations are generated from the innovation distribution alone. For times 2 to n_time, counts are generated as thinning of previous counts plus independent innovations. When order = 0, all time points are generated from the innovation distribution and the thinning operator and alpha are ignored.

If blocks is provided, innovations include a block effect. For Poisson and negative binomial innovations, the innovation mean is theta[t] + tau[blocks[i]]. For Bell innovations, the innovation mean is theta[t] * exp(theta[t]) + tau[blocks[i]].

Examples

y <- simulate_inad(
  n_subjects = 20,
  n_time = 6,
  order = 1,
  thinning = "binom",
  innovation = "pois",
  alpha = 0.3,
  theta = 2,
  seed = 42
)
dim(y)
#> [1] 20  6