Description Usage Arguments Details Value Author(s) References See Also Examples

Fit the N-mixture model of Royle (2004)

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`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: "P", "NB", or "ZIP". |

`starts` |
vector of starting values |

`method` |
Optimization method used by |

`se` |
logical specifying whether or not to compute standard errors. |

`engine` |
Either "C", "R", or "TMB" to use fast C++ code, native R code, or TMB (required for random effects) during the optimization. |

`threads` |
Set the number of threads to use for optimization in C++, if
OpenMP is available on your system. Increasing the number of threads
may speed up optimization in some cases by running the likelihood
calculation in parallel. If |

`...` |
Additional arguments to optim, such as lower and upper bounds |

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, Kery et al 2005).

The latent abundance distribution, *f(N |
theta)* can be set as a Poisson, negative binomial, or zero-inflated
Poisson random
variable, depending on the setting of the `mixture`

argument,
`mixture = "P"`

, `mixture = "NB"`

, `mixture = "ZIP"`

respectively. For the first two distributions, the mean of *N_i* is
*lambda_i*. If *N_i ~ NB*, then an
additional parameter, *alpha*, describes dispersion (lower
*alpha* implies higher variance). For the ZIP distribution,
the mean is *lambda*(1-psi)*, where psi is the
zero-inflation parameter.

The detection process is modeled as binomial: *y_ij ~ Binomial(N_i, p_ij)*.

Covariates of *lamdba_i* use the log link and
covariates of *p_ij* use the logit link.

unmarkedFit object describing the model fit.

Ian Fiske and Richard Chandler

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

Kery, 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.

Johnson, N.L, A.W. Kemp, and S. Kotz. (2005) Univariate Discrete Distributions, 3rd ed. Wiley.

`unmarkedFramePCount`

, `pcountOpen`

,
`ranef`

, `parboot`

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## Not run:
# Simulate data
set.seed(35)
nSites <- 100
nVisits <- 3
x <- rnorm(nSites) # a covariate
beta0 <- 0
beta1 <- 1
lambda <- exp(beta0 + beta1*x) # expected counts at each site
N <- rpois(nSites, lambda) # latent abundance
y <- matrix(NA, nSites, nVisits)
p <- c(0.3, 0.6, 0.8) # detection prob for each visit
for(j in 1:nVisits) {
y[,j] <- rbinom(nSites, N, p[j])
}
# Organize data
visitMat <- matrix(as.character(1:nVisits), nSites, nVisits, byrow=TRUE)
umf <- unmarkedFramePCount(y=y, siteCovs=data.frame(x=x),
obsCovs=list(visit=visitMat))
summary(umf)
# Fit a model
fm1 <- pcount(~visit-1 ~ x, umf, K=50)
fm1
plogis(coef(fm1, type="det")) # Should be close to p
# Empirical Bayes estimation of random effects
(fm1re <- ranef(fm1))
plot(fm1re, subset=site %in% 1:25, xlim=c(-1,40))
sum(bup(fm1re)) # Estimated population size
sum(N) # Actual population size
# Real data
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))
## End(Not run)
``` |

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