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

occu {unmarked} | R Documentation

## 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"), ...)

### 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` | Either "C" or "R" to use fast C++ code or native R code during the optimization.
`...` | Additional arguments to optim, such as lower and upper bounds

### 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 ~ Bernoulli(psi_i)

The observation process is modeled as

y_ij | z_i ~ 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(λ_i), where log(λ_i) = α + β*x, then presence/absence data at the site can be modeled as Z_i ~ Binomial(ψ_i) where cloglog(ψ_i) = α + β*x.

### Value

unmarkedFitOccu object describing the model fit.

### Author(s)

Ian Fiske

### 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"))

[Package unmarked version 1.0.0 Index]