unmarked (version 0.9-1)

pcount: Fit the N-mixture model of Royle (2004)

Description

Fit the N-mixture model of Royle (2004)

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. This should be set high enough so that it does not affect the parameter estimates. Note that computation time will increase with K.

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 N-mixture model of Royle (2004) to spatially replicated count data. See unmarkedFramePCount for a description of how to format data for pcount. 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.

See Also

unmarkedFramePCount, pcountOpen

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, K=30))
(fm.mallard.nb <- pcount(~ date + I(date^2) ~ length + elev, mixture = "NB", mallardUMF, K=30))