unmarked (version 1.2.5)

occu: Fit the MacKenzie et al. (2002) Occupancy Model

Description

This function fits the single season occupancy model of MacKenzie et al (2002).

Usage

occu(formula, data, knownOcc=numeric(0), linkPsi=c("logit", "cloglog"),
            starts, method="BFGS", se=TRUE, engine=c("C", "R", "TMB"),
            threads = 1, ...)

Value

unmarkedFitOccu object describing the model fit.

Arguments

formula

Double right-hand side formula describing covariates of detection and occupancy in that order.

data

An unmarkedFrameOccu object

knownOcc

Vector of sites that are known to be occupied. These should be supplied as row numbers of the y matrix, eg, c(3,8) if sites 3 and 8 were known to be occupied a priori.

linkPsi

Link function for the occupancy model. Options are "logit" for the standard occupancy model or "cloglog" for the complimentary log-log link, which relates occupancy to site-level abundance. See details.

starts

Vector of parameter starting values.

method

Optimization method used by optim.

se

Logical specifying whether or not to compute standard errors.

engine

Code to use for optimization. Either "C" for fast C++ code, "R" for native R code, or "TMB" for Template Model Builder. "TMB" is used automatically if your formula contains random effects.

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 threads=1 (the default), OpenMP is disabled.

...

Additional arguments to optim, such as lower and upper bounds

Author

Ian Fiske

Details

See unmarkedFrame and unmarkedFrameOccu for a description of how to supply data to the data argument.

occu fits the standard occupancy model based on zero-inflated binomial models (MacKenzie et al. 2006, Royle and Dorazio 2008). The occupancy state process (\(z_i\)) of site \(i\) is modeled as

$$z_i \sim Bernoulli(\psi_i)$$

The observation process is modeled as

$$y_{ij}|z_i \sim Bernoulli(z_i p_{ij})$$

By default, covariates of \(\psi_i\) and \(p_{ij}\) are modeled using the logit link according to the formula argument. The formula is a double right-hand sided formula like ~ detform ~ occform where detform is a formula for the detection process and occform is a formula for the partially observed occupancy state. See formula for details on constructing model formulae in R.

When linkPsi = "cloglog", the complimentary log-log link function is used for \(psi\) instead of the logit link. The cloglog link relates occupancy probability to the intensity parameter of an underlying Poisson process (Kery and Royle 2016). Thus, if abundance at a site is can be modeled as \(N_i ~ Poisson(\lambda_i)\), where \(log(\lambda_i) = \alpha + \beta*x\), then presence/absence data at the site can be modeled as \(Z_i ~ Binomial(\psi_i)\) where \(cloglog(\psi_i) = \alpha + \beta*x\).

References

Kery, Marc, and J. Andrew Royle. 2016. Applied Hierarchical Modeling in Ecology, Volume 1. Academic Press.

MacKenzie, D. I., J. D. Nichols, G. B. Lachman, S. Droege, J. Andrew Royle, and C. A. Langtimm. 2002. Estimating Site Occupancy Rates When Detection Probabilities Are Less Than One. Ecology 83: 2248-2255.

MacKenzie, D. I. et al. 2006. Occupancy Estimation and Modeling. Amsterdam: Academic Press.

Royle, J. A. and R. Dorazio. 2008. Hierarchical Modeling and Inference in Ecology. Academic Press.

See Also

unmarked, unmarkedFrameOccu, modSel, parboot

Examples

data(frogs)
pferUMF <- unmarkedFrameOccu(pfer.bin)
plot(pferUMF, panels=4)
# add some fake covariates for illustration
siteCovs(pferUMF) <- data.frame(sitevar1 = rnorm(numSites(pferUMF)))

# observation covariates are in site-major, observation-minor order
obsCovs(pferUMF) <- data.frame(obsvar1 = rnorm(numSites(pferUMF) * obsNum(pferUMF)))

(fm <- occu(~ obsvar1 ~ 1, pferUMF))

confint(fm, type='det', method = 'normal')
confint(fm, type='det', method = 'profile')

# estimate detection effect at obsvars=0.5
(lc <- linearComb(fm['det'],c(1,0.5)))

# transform this to probability (0 to 1) scale and get confidence limits
(btlc <- backTransform(lc))
confint(btlc, level = 0.9)

# Empirical Bayes estimates of proportion of sites occupied
re <- ranef(fm)
sum(bup(re, stat="mode"))