Description Usage Arguments Details Value Diagnostics Limitations Author(s) References

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).

1 2 3 4 5 6 7 | ```
dsm.var.prop(
dsm.obj,
pred.data,
off.set,
seglen.varname = "Effort",
type.pred = "response"
)
``` |

`dsm.obj` |
a model object returned from running |

`pred.data` |
either: a single prediction grid or list of prediction grids. Each grid should be a |

`off.set` |
a a vector or list of vectors with as many elements as there are in |

`seglen.varname` |
name for the column which holds the segment length (default value |

`type.pred` |
should the predictions be on the "response" or "link" scale? (default |

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.frame`

s 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.

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 |

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

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.

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.

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