Maximum-likelihood fit of the multistate false-positive occupancy model

Fits the Miller et al. (2011) false-positive occupancy model with confirmed detections (y in {0, 1, 2}) by maximising the exact two-state 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 (occupancy psi, true detection p11, false-positive p10, certain-classification b) are site-level logit predictors.

Usage

fp_occu_laplace(
  y,
  site_idx,
  X_psi,
  X_p11,
  X_p10,
  X_b,
  sigma_beta = NULL,
  max_iter = 200L,
  tol = 1e-08,
  verbose = FALSE
)

Arguments

y

Integer vector of detection states (0/1/2), long form (valid visits only).

site_idx

Integer vector, same length as y, 1-based site index.

X_psi, X_p11, X_p10, X_b

Numeric [n_sites x p_arm] design matrices for the four arms.

sigma_beta

Optional Gaussian prior SD on the coefficients (a mild ridge for stability); NULL (default) is the unpenalised MLE.

max_iter

BFGS iteration budget (default 200).

tol

Convergence tolerance (optim reltol, default 1e-8).

verbose

Print convergence status.

Value

A list of class fp_occu_fit with beta_psi, beta_p11, beta_p10, beta_b, log_lik, vcov, H_obs, per-site posterior occupancy w1, and converged.

References

Miller, D. A. W., et al. (2011). Improving occupancy estimation when two types of observational error occur. Ecology 92, 1422-1428.