unmarked (version 0.8-5)

pcount: Fit the N-mixture point count model...

Description

Fit the N-mixture point count model

Usage

pcount(formula, data, K, mixture=c("P", "NB"), starts, method="BFGS",
    control=list(), se=TRUE)

Arguments

formula

Double right-hand side formula describing covariates of detection and abundance, in that order

data

an unmarkedFramePCount object supplying data to the model.

K

Integer upper index of integration for N-mixture.

mixture

character specifying mixture: either "P" or "NB".

starts

vector of starting values

method

Optimization method used by optim.

control

Other arguments passed to optim.

se

logical specifying whether or not to compute standard errors.

Value

• unmarkedFit object describing the model fit.

Details

This function fits binomial-Poisson mixture model for spatially replicated point count data.

See unmarkedFrame for a description of how to supply by creating and unmarkedFrame.

This function fits the latent N-mixture model for point count data (Royle 2004, Kéry et al 2005).

The latent abundance distribution, $f(N | \mathbf{\theta})$ can be set as either a Poisson or a negative binomial random variable, depending on the setting of the mixture argument. mixture = "P" or mixture = "NB" select the Poisson or negative binomial distribution respectively. The mean of $N_i$ is $\lambda_i$. If $N_i \sim NB$, then an additional parameter, $\alpha$, describes dispersion (lower $\alpha$ implies higher variance).

The detection process is modeled as binomial: $y_{ij} \sim Binomial(N_i, p_{ij})$.

Covariates of $\lambda_i$ use the log link and covariates of $p_{ij}$ use the logit link.

References

Royle, J. A. (2004) N-Mixture Models for Estimating Population Size from Spatially Replicated Counts. Biometrics 60, pp. 108--105.

Kéry, M., Royle, J. A., and Schmid, H. (2005) Modeling Avaian Abundance from Replicated Counts Using Binomial Mixture Models. Ecological Applications 15(4), pp. 1450--1461.

Examples

data(mallard)
mallardUMF <- unmarkedFramePCount(mallard.y, siteCovs = mallard.site,
obsCovs = mallard.obs)
(fm.mallard <- pcount(~ ivel+ date + I(date^2) ~ length + elev + forest, mallardUMF))
(fm.mallard.nb <- pcount(~ date + I(date^2) ~ length + elev, mixture = "NB", mallardUMF))