Weakly-informative priors for cover-hurdle Laplace fits

Builds an opt-in fixed-effect prior for cover() models fit with a Laplace method. The cover hurdle has two arms with their own coefficients – an occurrence arm (Bernoulli presence) and a positive-cover arm (beta or lognormal) – each with an intercept and a slope bucket. The penalty is the quadratic + sum((beta_j - mu_j)^2 / (2 sd_j^2)) added to each arm's negative log-likelihood, the same mechanism occu_priors() uses.

Usage

cover_priors(
  occ_intercept = list(mean = 0, sd = 2),
  occ_slope = list(mean = 0, sd = 2.5),
  pos_intercept = list(mean = 0, sd = 3),
  pos_slope = list(mean = 0, sd = 2.5)
)

Arguments

occ_intercept

Prior on the occurrence (presence) intercept, logit scale. list(mean, sd). Default list(mean = 0, sd = 2).

occ_slope

Prior on occurrence slopes. Default list(mean = 0, sd = 2.5).

pos_intercept

Prior on the positive-cover intercept (logit scale for "beta", log scale for "lognormal"). Default list(mean = 0, sd = 3).

pos_slope

Prior on positive-cover slopes. Default list(mean = 0, sd = 2.5).

Value

A cover_priors object, ready to pass to tobs(..., priors = ...).

Details

Cover priors are opt-in: without priors, a cover fit is unpenalised. The main use is regularising perfect separation in the occurrence arm at small N. Set any sd = Inf to drop that component.

Coverage

Applied on the separate-Laplace path (method = "laplace" / "laplace_sla") when the formula has no spatial term. Both arms are penalised: the occurrence and lognormal-positive arms through tulpa::tulpa_laplace(), and the beta-positive arm through tulpa::tulpa_laplace_beta(). The joint nested-Laplace path (method = "nested_laplace" / "nested_laplace_sla", used for spatial cover formulas) also threads the priors, as a per-arm beta_prior_mean / beta_prior_prec on the joint engine's occurrence and positive responses. The separate-Laplace path keeps rejecting a prior alongside a spatial term (that solver carries its own); add the spatial term through the nested-Laplace path to combine the two.

See also

occu_priors()

Examples

# regularise the occurrence arm, leave the positive arm unpenalised
priors <- cover_priors(pos_intercept = list(mean = 0, sd = Inf),
                       pos_slope     = list(mean = 0, sd = Inf))
priors

# \donttest{
sim <- simulate_cover(N = 150, seed = 1)
fit <- tobs(cover ~ x, data = sim$data,
            family = cover(response = "lognormal"),
            method = "laplace", priors = priors)
coef(fit)
# }