nmixTTD {unmarked} | R Documentation |
Fit N-mixture Time-to-detection Models
Description
Fit N-mixture models with time-to-detection data.
Usage
nmixTTD(stateformula= ~1, detformula = ~1, data, K=100,
mixture = c("P","NB"), ttdDist = c("exp", "weibull"), starts, method="BFGS",
se=TRUE, engine = c("C", "R"), threads = 1, ...)
Arguments
stateformula |
Right-hand sided formula for the abundance at each site. |
detformula |
Right-hand sided formula for mean time-to-detection. |
data |
|
K |
The upper summation index used to numerically integrate out the latent abundance. This should be set high enough so that it does not affect the parameter estimates. Computation time will increase with K. |
mixture |
String specifying mixture distribution: "P" for Poisson or "NB" for negative binomial. |
ttdDist |
Distribution to use for time-to-detection; either
|
starts |
optionally, initial values for parameters in the optimization. |
method |
Optimization method used by |
se |
logical specifying whether or not to compute standard errors. |
engine |
Either "C" or "R" to use fast C++ code or native R code 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 |
Details
This model extends time-to-detection (TTD) occupancy models to estimate site
abundance using data from single or repeated visits. Latent abundance can be
modeled as Poisson (mixture="P"
) or negative binomial (mixture="NB"
).
Time-to-detection can be modeled as an exponential (ttdDist="exp"
) or
Weibull (ttdDist="weibull"
) random variable with rate parameter
and, for the Weibull, an additional shape parameter
. Note that
occuTTD
puts covariates on and not
, i.e.,
the expected time between events.
Assuming that there are independent individuals at a site, and all
individuals have the same individual detection rate, the expected
detection rate across all individuals
is equal to the the
individual-level detection rate
multipled by the number of individuals
present
.
In the case where there are no detections before the maximum sample time at
a site (surveyLength
) is reached, we are not sure if the site has
or if we just didn't wait long enough for a detection. We therefore
must censor (
the exponential or Weibull distribution at the maximum survey
length,
. Thus, assuming true abundance at site
is
, and an exponential distribution for the TTD
(parameterized
with the rate), then:
Note that when , the exponential rate
and the
scale is therefore
, and thus the value will be censored
at
.
Because in unmarked
values of NA
are typically used to indicate
missing values that were a result of the sampling structure (e.g., lost data),
we indicate a censored in
nmixTTD
instead by setting
in the
y
matrix provided to
unmarkedFrameOccuTTD
. You can provide either a single value of
to the
surveyLength
argument of unmarkedFrameOccuTTD
,
or provide a matrix, potentially with a unique value of for each
value of
y
. Note that in the latter case the value of y
that will
be interpreted by nmixTTD
as a censored observation (i.e., )
will differ between observations!
Value
unmarkedFitNmixTTD object describing model fit.
Author(s)
Ken Kellner contact@kenkellner.com
References
Strebel, N., Fiss, C., Kellner, K. F., Larkin, J. L., Kery, M., & Cohen, J (2021). Estimating abundance based on time-to-detection data. Methods in Ecology and Evolution 12: 909-920.
See Also
unmarked
, unmarkedFrameOccuTTD
Examples
## Not run:
# Simulate data
M = 1000 # Number of sites
nrep <- 3 # Number of visits per site
Tmax = 5 # Max duration of a visit
alpha1 = -1 # Covariate on rate
beta1 = 1 # Covariate on density
mu.lambda = 1 # Rate at alpha1 = 0
mu.dens = 1 # Density at beta1 = 0
covDet <- matrix(rnorm(M*nrep),nrow = M,ncol = nrep) #Detection covariate
covDens <- rnorm(M) #Abundance/density covariate
dens <- exp(log(mu.dens) + beta1 * covDens)
sum(N <- rpois(M, dens)) # Realized density per site
lambda <- exp(log(mu.lambda) + alpha1 * covDet) # per-individual detection rate
ttd <- NULL
for(i in 1:nrep) {
ttd <- cbind(ttd,rexp(M, N*lambda[,i])) # Simulate time to first detection per visit
}
ttd[N == 0,] <- 5 # Not observed where N = 0; ttd set to Tmax
ttd[ttd >= Tmax] <- 5 # Crop at Tmax
#Build unmarked frame
umf <- unmarkedFrameOccuTTD(y = ttd, surveyLength=5,
siteCovs = data.frame(covDens=covDens),
obsCovs = data.frame(covDet=as.vector(t(covDet))))
#Fit model
fit <- nmixTTD(~covDens, ~covDet, data=umf, K=max(N)+10)
#Compare to truth
cbind(coef(fit), c(log(mu.dens), beta1, log(mu.lambda), alpha1))
#Predict abundance/density values
head(predict(fit, type='state'))
## End(Not run)