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\name{gdistsamp}
\alias{gdistsamp}
\title{
Fit the generalized distance sampling model of Chandler et al. (2011).
}
\description{
Extends the distance sampling model of Royle et al. (2004) to estimate
the probability of being available for detection. Also allows abundance
to be modeled using the negative binomial distribution.
}
\usage{
gdistsamp(lambdaformula, phiformula, pformula, data, keyfun =
c("halfnorm", "exp", "hazard", "uniform"), output = c("abund",
"density"), unitsOut = c("ha", "kmsq"), mixture = c("P", "NB", "ZIP"), K,
starts, method = "BFGS", se = TRUE, engine=c("C","R"), rel.tol=1e-4, threads=1, ...)
}
\arguments{
\item{lambdaformula}{
A right-hand side formula describing the abundance covariates.
}
\item{phiformula}{
A right-hand side formula describing the availability covariates.
}
\item{pformula}{
A right-hand side formula describing the detection function covariates.
}
\item{data}{
An object of class \code{unmarkedFrameGDS}
}
\item{keyfun}{
One of the following detection functions: "halfnorm", "hazard", "exp",
or "uniform." See details.
}
\item{output}{
Model either "density" or "abund"
}
\item{unitsOut}{
Units of density. Either "ha" or "kmsq" for hectares and square
kilometers, respectively.
}
\item{mixture}{
Either "P", "NB", or "ZIP" for the Poisson, negative binomial, or
zero-inflated Poisson models of abundance.
}
\item{K}{
An integer value specifying the upper bound used in the integration.
}
\item{starts}{
A numeric vector of starting values for the model parameters.
}
\item{method}{
Optimization method used by \code{\link{optim}}.
}
\item{se}{
logical specifying whether or not to compute standard errors.
}
\item{engine}{
Either "C" to use fast C++ code or "R" to use native R code during the
optimization.
}
\item{rel.tol}{relative accuracy for the integration of the detection function.
See \link{integrate}. You might try adjusting this if you get an error
message related to the integral. Alternatively, try providing
different starting values.}
\item{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 \code{threads=1} (the default), OpenMP is disabled.}
\item{\dots}{Additional arguments to optim, such as lower and upper
bounds}
}
\details{
This model extends the model of Royle et al. (2004) by estimating the
probability of being available for detection \eqn{\phi}{phi}. This
effectively relaxes the assumption that \eqn{g(0)=1}. In other words,
inividuals at a distance of 0 are not assumed to be detected with
certainty. To estimate this additional parameter, replicate distance
sampling data must be collected at each transect. Thus the data are
collected at i = 1, 2, ..., R transects on t = 1, 2, ..., T
occassions. As with the model of Royle et al. (2004), the detections
must be binned into distance classes. These data must be formatted in
a matrix with R rows, and JT columns where J is the number of distance
classses. See \code{\link{unmarkedFrameGDS}} for more information.
}
\note{
If you aren't interested in estimating phi, but you want to
use the negative binomial distribution, simply set numPrimary=1 when
formatting the data.
}
\value{
An object of class unmarkedFitGDS.
}
\references{
Royle, J. A., D. K. Dawson, and S. Bates. 2004. Modeling
abundance effects in distance sampling. \emph{Ecology}
85:1591-1597.
Chandler, R. B, J. A. Royle, and D. I. King. 2011. Inference about
density and temporary emigration in unmarked
populations. \emph{Ecology} 92:1429--1435.
}
\author{
Richard Chandler \email{rbchan@uga.edu}
}
\note{
You cannot use obsCovs, but you can use yearlySiteCovs (a confusing name
since this model isn't for multi-year data. It's just a hold-over
from the colext methods of formatting data upon which it is based.)
}
\seealso{
\code{\link{distsamp}}
}
\examples{
# Simulate some line-transect data
set.seed(36837)
R <- 50 # number of transects
T <- 5 # number of replicates
strip.width <- 50
transect.length <- 100
breaks <- seq(0, 50, by=10)
lambda <- 5 # Abundance
phi <- 0.6 # Availability
sigma <- 30 # Half-normal shape parameter
J <- length(breaks)-1
y <- array(0, c(R, J, T))
for(i in 1:R) {
M <- rpois(1, lambda) # Individuals within the 1-ha strip
for(t in 1:T) {
# Distances from point
d <- runif(M, 0, strip.width)
# Detection process
if(length(d)) {
cp <- phi*exp(-d^2 / (2 * sigma^2)) # half-normal w/ g(0)<1
d <- d[rbinom(length(d), 1, cp) == 1]
y[i,,t] <- table(cut(d, breaks, include.lowest=TRUE))
}
}
}
y <- matrix(y, nrow=R) # convert array to matrix
# Organize data
umf <- unmarkedFrameGDS(y = y, survey="line", unitsIn="m",
dist.breaks=breaks, tlength=rep(transect.length, R), numPrimary=T)
summary(umf)
# Fit the model
m1 <- gdistsamp(~1, ~1, ~1, umf, output="density", K=50)
summary(m1)
backTransform(m1, type="lambda")
backTransform(m1, type="phi")
backTransform(m1, type="det")
\dontrun{
# Empirical Bayes estimates of abundance at each site
re <- ranef(m1)
plot(re, layout=c(10,5), xlim=c(-1, 20))
}
}
\keyword{ models }
|
