Multispecies (community) relative-abundance GLMM family

The community analogue of count(): a per-species GLMM on an observed count or continuous response with Gaussian community hyperpriors on the per-species coefficients (the spAbundance msAbund model). No detection and no latent state – the abundance counterpart of ms_occu() without the occupancy layer. Poisson / negative-binomial (log link) or Gaussian (identity). y is an n_sites x n_species matrix (or a named list of n_species count vectors), one value per site per species; species names the columns.

Usage

ms_count(response = c("poisson", "negbin", "gaussian", "binomial"))

Arguments

response: One of "poisson", "negbin", "gaussian", or "binomial". The binomial response is the community k-of-n GLMM (community svcPGBinom): supply the per-site (or per-site x species) trial count as trials = on tobs() (default 1, i.e. Bernoulli, which is the jsdm() response). With trials > 1 the community-mean intercept carries a small first-order-Laplace bias of order 1 / n_species (a few hundredths on the logit scale at 20 species, shrinking with more species; the slope and the trials = 1 case are unbiased) – the same character as the negative-binomial slope attenuation noted above.

Value

A tobs_family object.

Details

As with the other community Laplace-EM families (ms_occu(), ms_occu_cover()), the community means are recovered essentially unbiased for the Gaussian (identity link, exact Laplace) and Poisson responses; the negative-binomial slope carries a mild first-order-Laplace (PQL) attenuation of order the community variance (a few percent, shrinking with the number of species and observations per species). The community-mean Wald intervals are calibrated to the package rubric (pooled coverage at least 0.85).

method = "nuts" samples the exact joint posterior (community means, per-species deviations, and the community covariance) for all three responses – the negative binomial carrying a per-species dispersion random effect, the Gaussian a per-species free residual variance – which removes the Laplace-EM's negative-binomial attenuation and returns calibrated, non-Gaussian community intervals. A shared areal field or latent factors are available through method = "nested_laplace" / the latent() term; see the package overview for the spatial and factor variants.

Examples

# \donttest{
sim <- simulate_ms_count(N = 120, n_species = 8, seed = 1)
fit <- tobs(~ x, data = sim$data, family = ms_count(), y = sim$y,
            species = colnames(sim$y), method = "laplace")
summary(fit)
# }