sdmTMB standard error and CV of index values

[seananderson]

Question by email:

I have been using sdmtMB to create an abundance estimate for insert species on the insert survey and I was wondering how sdmTMB computes the confidence intervals. Is it bootstrapping these or exponentiating the SE (standard error)? If it is the latter, can I extract this from the model output somehow? I ask because I am trying to come up with a CV for the estimate that will be comparable to the CV for the design-based estimate.

[seananderson]

sdmTMB uses TMB's generalized delta method (see ?TMB::sdreport) on the area-weighted sum of abundance/biomass to calculate the SE. The upper and lower 95% CIs are then +/- 1.96 the SE from log abundance or biomass followed by exp(). Where 1.96 is from qnorm(1 - (1 - 0.95)/2).

Those are available in the output of get_index() in the se column. Those are on log abundance. Assuming a lognormal variable, which we are, you can get a CV as: sqrt(exp(se^2) - 1). For small values, the SE of the log variable and the CV will be very similar.