R: Fit the hierarchical distance sampling model of Royle et al....

distsamp {unmarked} | R Documentation

## Fit the hierarchical distance sampling model of Royle et al. (2004)

### Description

Fit the hierarchical distance sampling model of Royle et al. (2004) to line or point transect data recorded in discrete distance intervals.

### Usage

    distsamp(formula, data, keyfun=c("halfnorm", "exp",
      "hazard", "uniform"), output=c("density", "abund"),
      unitsOut=c("ha", "kmsq"), starts, method="BFGS", se=TRUE,
      engine=c("C", "R"), rel.tol=0.001, ...)

### Arguments

`formula` | Double right-hand formula describing detection covariates followed by abundance covariates. ~1 ~1 would be a null model.
`data` | object of class `unmarkedFrameDS`, containing response matrix, covariates, distance interval cut points, survey type ("line" or "point"), transect lengths (for survey = "line"), and units ("m" or "km") for cut points and transect lengths. See example for set up.
`keyfun` | One of the following detection functions: "halfnorm", "hazard", "exp", or "uniform." See details.
`output` | Model either "density" or "abund"
`unitsOut` | Units of density. Either "ha" or "kmsq" for hectares and square kilometers, respectively.
`starts` | Vector of starting values for parameters.
`method` | Optimization method used by `optim`.
`se` | logical specifying whether or not to compute standard errors.
`engine` | Use code written in C++ or R
`rel.tol` | Requested relative accuracy of the integral, see `integrate`
`...` | Additional arguments to optim, such as lower and upper bounds

### Details

Unlike conventional distance sampling, which uses the 'conditional on detection' likelihood formulation, this model is based upon the unconditional likelihood and allows for modeling both abundance and detection function parameters.

The latent transect-level abundance distribution f(N | theta) assumed to be Poisson with mean lambda (but see `gdistsamp` for alternatives).

The detection process is modeled as multinomial: y_ij ~ Multinomial(N_i, pi_i1, pi_i2, ..., pi_iJ), where pi_ij is the multinomial cell probability for transect i in distance class j. These are computed based upon a detection function g(x | sigma), such as the half-normal, negative exponential, or hazard rate.

Parameters lambda and sigma can be vectors affected by transect-specific covariates using the log link.

### Value

unmarkedFitDS object (child class of `unmarkedFit-class`) describing the model fit.

### Note

You cannot use obsCovs.

### Author(s)

Richard Chandler rbchan@uga.edu

### References

Royle, J. A., D. K. Dawson, and S. Bates (2004) Modeling abundance effects in distance sampling. Ecology 85, pp. 1591-1597.

Sillett, S. and Chandler, R.B. and Royle, J.A. and Kery, M. and Morrison, S.A. In Press. Hierarchical distance sampling models to estimate population size and habitat-specific abundance of an island endemic. Ecological Applications

### See Also

`unmarkedFrameDS`, `unmarkedFit-class` `fitList`, `formatDistData`, `parboot`, `sight2perpdist`, `detFuns`, `gdistsamp`, `ranef`. Also look at vignette("distsamp").

### Examples

    ## Line transect examples

    data(linetran)

    ltUMF <- with(linetran, {
       unmarkedFrameDS(y = cbind(dc1, dc2, dc3, dc4),
       siteCovs = data.frame(Length, area, habitat),
       dist.breaks = c(0, 5, 10, 15, 20),
       tlength = linetran$Length * 1000, survey = "line", unitsIn = "m")
       })

    ltUMF
    summary(ltUMF)
    hist(ltUMF)

    # Half-normal detection function. Density output (log scale). No covariates.
    (fm1 <- distsamp(~ 1 ~ 1, ltUMF))

    # Some methods to use on fitted model
    summary(fm1)
    backTransform(fm1, type="state")                # animals / ha
    exp(coef(fm1, type="state", altNames=TRUE))     # same
    backTransform(fm1, type="det")                  # half-normal SD
    hist(fm1, xlab="Distance (m)")	# Only works when there are no det covars
    # Empirical Bayes estimates of posterior distribution for N_i
    plot(ranef(fm1, K=50))

    # Effective strip half-width
    (eshw <- integrate(gxhn, 0, 20, sigma=10.9)$value)

    # Detection probability
    eshw / 20 # 20 is strip-width

    # Halfnormal. Covariates affecting both density and and detection.
    (fm2 <- distsamp(~area + habitat ~ habitat, ltUMF))

    # Hazard-rate detection function.
    (fm3 <- distsamp(~ 1 ~ 1, ltUMF, keyfun="hazard"))

    # Plot detection function.
    fmhz.shape <- exp(coef(fm3, type="det"))
    fmhz.scale <- exp(coef(fm3, type="scale"))
    plot(function(x) gxhaz(x, shape=fmhz.shape, scale=fmhz.scale), 0, 25,
    	xlab="Distance (m)", ylab="Detection probability")

    ## Point transect examples

    # Analysis of the Island Scrub-jay data.
    # See Sillett et al. (In press)

    data(issj)
    str(issj)

    jayumf <- unmarkedFrameDS(y=as.matrix(issj[,1:3]),
     siteCovs=data.frame(scale(issj[,c("elevation","forest","chaparral")])),
     dist.breaks=c(0,100,200,300), unitsIn="m", survey="point")

    (fm1jay <- distsamp(~chaparral ~chaparral, jayumf))

    ## Not run:

    data(pointtran)

    ptUMF <- with(pointtran, {
    	unmarkedFrameDS(y = cbind(dc1, dc2, dc3, dc4, dc5),
    	siteCovs = data.frame(area, habitat),
    	dist.breaks = seq(0, 25, by=5), survey = "point", unitsIn = "m")
    	})

    # Half-normal.
    (fmp1 <- distsamp(~ 1 ~ 1, ptUMF))
    hist(fmp1, ylim=c(0, 0.07), xlab="Distance (m)")

    # effective radius
    sig <- exp(coef(fmp1, type="det"))
    ea <- 2*pi * integrate(grhn, 0, 25, sigma=sig)$value # effective area
    sqrt(ea / pi) # effective radius

    # detection probability
    ea / (pi*25^2)

    ## End(Not run)

[Package unmarked version 1.0.0 Index]