Simulate cover-hurdle data (lognormal positive part)

Generates synthetic data matching the cover(response = "lognormal") generative model:

Usage

simulate_cover(
  N = 200L,
  beta_occ = c(-0.5, 0.8),
  beta_pos = c(-1, 0.3),
  sigma_pos = 0.4,
  response = c("lognormal", "gaussian"),
  spatial_range = NULL,
  spatial_var = 1,
  seed = NULL
)

Arguments

N: Number of sites (default 200).
beta_occ: Length-2 occurrence coefficients (intercept, slope on x).
beta_pos: Length-2 log-cover coefficients (intercept, slope on x).
sigma_pos: Lognormal residual standard deviation (default 0.4).
response: Positive-arm likelihood: "lognormal" (default) or "gaussian".
spatial_range: Length scale of the exponential spatial field (in unit-square distance). NULL disables the spatial layer.
spatial_var: Marginal variance of the spatial field (default 1).
seed: Optional integer seed.

Value

A list with:

data: A data frame with cover, covariate x, and lon, lat.
y: data$cover (length-N numeric vector, for passing to tobs()).
coords: An N x 2 matrix of coordinates.
truth: A list with beta_occ, beta_pos, sigma_pos, p, mu, occur, spatial_occ, spatial_pos.

Details

eta_occ: = X %*% beta_occ + spatial_occ
eta_pos: = X %*% beta_pos + spatial_pos
p: = plogis(eta_occ)
occur: ~ Bernoulli(p)
log_cover: ~ Normal(eta_pos, sigma_pos^2) | occur = 1
cover: = exp(log_cover) when occur = 1, else 0

Both layers share the same design matrix by default (one continuous covariate plus an intercept). When spatial_range is supplied, a simple exponential-kernel Gaussian field on a random unit-square coordinate set is added to both linear predictors; the two layers see independently simulated draws of that field, which matches the two-independent-arm fit. The joint engine's shared field is a different generative model.

Examples

sim <- simulate_cover(N = 200, seed = 1)
head(sim$data)