To ensure that uncertainty from the detection function is correctly propagated to the final variance estimate of abundance, this function uses a method first detailed in Williams et al (2011), further explanation is given in Bravington et al. (2021).
dsm_var_prop(
dsm.obj,
pred.data,
off.set,
seglen.varname = "Effort",
type.pred = "response"
)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
a model object fitted by dsm.
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.
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.
name for the column which holds the segment length
(default value "Effort").
should the predictions be on the "response" or "link"
scale? (default "response").
The summary output from the function includes a simply diagnostic that shows
the average probability of detection from the "original" fitted model (the
model supplied to this function; column Fitted.model) and the probability
of detection from the refitted model (used for variance propagation; column
Refitted.model) along with the standard error of the probability of
detection from the fitted model (Fitted.model.se), at the unique values of
any factor covariates used in the detection function (for continuous
covariates the 5%, 50% and 95% quantiles are shown). If there are large
differences between the probabilities of detection then there are
potentially problems with the fitted model, the variance propagation or
both. This can be because the fitted model does not account for enough of
the variability in the data and in refitting the variance model accounts for
this in the random effect.
Note that this routine is only useful if a detection function has been used
in the DSM. It cannot be used when the abundance.est or density.est
responses are used. Importantly this requires that if the detection function
has covariates, then these do not vary within a segment (so, for example
covariates like sex cannot be used).
Mark V. Bravington, Sharon L. Hedley. Bugs added by David L. Miller.
The idea is to refit the spatial model but including an extra random effect. This random effect has zero mean and hence to effect on point estimates. Its variance is the Hessian of the detection function. Variance estimates then 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 simply calls dsm_varprop. If you
don't require multiple prediction grids, the other routine will probably be
faster.
This routine is only useful if a detection function with covariates has been used in the DSM.
Bravington, M. V., Miller, D. L., & Hedley, S. L. (2021). Variance Propagation for Density Surface Models. Journal of Agricultural, Biological and Environmental Statistics. https://doi.org/10.1007/s13253-021-00438-2
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.