dsm_var_prop {dsm}

Prediction variance propagation for DSMs

Description

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).

Usage

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

Arguments

dsm.obj

a model object fitted by 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 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.

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

Diagnostics

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.

Limitations

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).

Author(s)

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

References

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.