dsm (version 2.1.3)

dsm.var.prop: 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

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 po

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").

Value

• a list with elements ll{model the fitted model object pred.var covariances of the regions given in pred.data. Diagonal elements are the variances in order 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 . }

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.

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

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

library(Distance)
 library(dsm)

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

 # fit a detection function and look at the summary
 hr.model <- ds(mexdolphins$distdata, max(mexdolphins$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, mexdolphins$segdata, mexdolphins$obsdata)

 # Calculate the offset...
 off.set <- 444*1000*1000

 # Calculate the variance
 mod1.var <- dsm.var.prop(mod1, mexdolphins$pred, off.set)

 # summary over the whole area in mexdolphins$pred

 # Plot a map of the CV
 #   need to format the prediction data with split
 mod1.var.map <- dsm.var.prop(mod1,
                 split(mexdolphins$pred,1:nrow(mexdolphins$pred)), off.set)
 plot(mod1.var.map)