Variance propogation for DSM models

Description

Rather than use a bootstrap to calculate the variance in a dsm model, use the clever variance propogation trick from Williams et al. (2011).

Usage

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dsm.var.prop(dsm.obj, pred.data, off.set, seglen.varname = "Effort",
  type.pred = "response")

Arguments

dsm.obj

an object returned from running dsm.

pred.data

either: a single prediction grid or list of prediction grids. Each grid should be a data.frame with the same columns as the original data.

off.set

a a vector or list of vectors with as many elements as there are in pred.data. Each vector is as long as the number of rows in the corresponding element of pred.data. These give the area associated with each prediction cell. If a single number is supplied it will be replicated for the length of pred.data.

seglen.varname

name for the column which holds the segment length (default value "Effort").

type.pred

should the predictions be on the "response" or "link" scale? (default "response").

Details

The idea is to refit the spatial model but including the Hessian of the offset as an extra term. Variance estimates using this new model can then be used to calculate the variance of abundance estimates which incorporate detection function uncertainty. Further mathematical details are given in the paper in the references below.

Many prediction grids can be supplied by supplying a list of data.frames to the function.

Note that this routine is only useful if a detection function has been used in the DSM.

Based on (much more general) code from Mark Bravington and Sharon Hedley.

Value

a list with elements

model the fitted model object
pred.var variance of each region given in pred.data.
bootstrap logical, always FALSE
pred.data as above
off.set as above
model the fitted model with the extra term
dsm.object the original model, as above
model.check simple check of subtracting the coefficients of the two models to see if there is a large difference
deriv numerically calculated Hessian of the offset

Author(s)

Mark V. Bravington, Sharon L. Hedley. Bugs added by David L. Miller.

References

Williams, R., Hedley, S.L., Branch, T.A., Bravington, M.V., Zerbini, A.N. and Findlay, K.P. (2011). Chilean Blue Whales as a Case Study to Illustrate Methods to Estimate Abundance and Evaluate Conservation Status of Rare Species. Conservation Biology 25(3), 526-535.

Examples

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## Not run: 
 library(Distance)
 library(dsm)

 # load the Gulf of Mexico dolphin data (see ?mexdolphins)
 data(mexdolphins)
 attach(mexdolphins)

 # fit a detection function and look at the summary
 hr.model <- ds(distdata, max(distdata$distance),
                key = "hr", adjustment = NULL)
 summary(hr.model)

 # fit a simple smooth of x and y
 mod1 <- dsm(N~s(x,y), hr.model, segdata, obsdata)

 # Calculate the variance
 mod1.var <- dsm.var.prop(mod1, preddata, off.set=preddata$area)

 # this will give a summary over the whole area in mexdolphins$preddata

# detach the data
detach("mexdolphins")

## End(Not run)

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