N-mixture abundance family — abun • tulpaObs

Latent Poisson (or NB) abundance with binomial detection per visit (Royle 2004).

Usage

abun(K_max = NULL, mixture = c("poisson", "negbin", "zip", "zinb"))

Arguments

K_max: upper bound for the latent-abundance marginal sum (the exact integration over N is truncated at K_max). NULL (default) lets the engine pick max(y) + 100 (matching unmarked::pcount()); raise it if a fit warns that the posterior over N puts mass on the boundary.
mixture: latent-abundance distribution, both fitted via tulpa's closed-form marginal Laplace engine. "poisson" is the default; "negbin" (negative binomial, Var(N) = lambda + lambda^2 / r) adds an overdispersion parameter r. Non-spatially the log size log_r is estimated jointly with the coefficients and reported with an SE; on the areal-spatial path (method = "nested_laplace") r is integrated over the outer hyperparameter grid and reported as a posterior mean / sd. Named mixture (after unmarked::pcount()) to avoid collision with the model-type family argument of tobs().

Value

A tobs_family object.

Details

Royle's (2004) N-mixture model: latent abundance N_i ~ Poisson(lambda_i) with log lambda_i = X_lambda beta_lambda, and counts y_ij | N_i ~ Binomial(N_i, p_ij) with logit p_ij = X_p beta_p. The abundance formula is the tobs() formula; the per-visit detection formula is detection. The marginal likelihood integrates N out exactly, so the fit is a direct Laplace approximation (no EM): method = "laplace" (fixed effects) or method = "nested_laplace" (an areal icar() / bym2() / car() offset on the abundance arm).

Examples

# \donttest{
sim <- simulate_abun(N = 120, J = 4, n_abund_covs = 1, n_det_covs = 1, seed = 1)
fit <- tobs(~ abund_cov1, data = sim$data, family = abun(),
            detection = ~ det_cov1, y = sim$y, method = "laplace")
summary(fit)
# }