Maximum-likelihood fit of the Dail-Madsen open N-mixture

Fits the Dail-Madsen (2011) open-population N-mixture (Poisson initial abundance, binomial survival, Poisson recruitment, binomial detection) by maximising the exact HMM forward marginal likelihood with an analytic gradient (BFGS). The observed-information covariance is the inverse of the negative finite-difference Jacobian of the analytic gradient at the mode. All four arms (initial abundance lambda, detection p, survival omega, recruitment gamma) are site-level.

Usage

dyn_abun_laplace(
  y_flat,
  n_sites,
  T,
  J,
  K_max,
  X_lambda,
  X_p,
  X_omega,
  X_gamma,
  mixture = "poisson",
  log_r_init = NULL,
  max_iter = 300L,
  tol = 1e-08,
  verbose = FALSE
)

Arguments

y_flat: Integer vector, flattened detection counts (site-major, then season, then visit; -1 marks a missing visit).
n_sites, T, J: Sites, primary seasons, secondary visits per season.
K_max: Abundance-state truncation (states 0..K_max).
X_lambda, X_p, X_omega, X_gamma: Numeric [n_sites x p_arm] design matrices.
mixture: Initial-abundance distribution: "poisson" (default) or "negbin" (negative-binomial).
log_r_init: Optional starting value (log scale) for the negative-binomial size parameter r; used only when mixture = "negbin". Default NULL starts from log(2).
max_iter: BFGS iteration budget (default 300).
tol: Convergence tolerance (optim reltol, default 1e-8).
verbose: Print convergence status.

Value

A list of class dyn_abun_fit with beta_lambda, beta_p, beta_omega, beta_gamma, log_lik, vcov, H_obs, per-site mean_N1, and converged.

References

Dail, D., Madsen, L. (2011). Models for estimating abundance from repeated counts of an open metapopulation. Biometrics 67, 577-587.