Poisson-link model application

[BioCatFish]

Hi! I would like to get some clarification on data preparation for a model which estimates biomass. If I use a conventional delta-model which considers encounter probability and positive catch rates the model settings should be: ObsModel=c(2,0), "b_i"=as_units(catch_kg, "kg"), "a_i"=as_units(temp[,'area_swept_km2'],"km^2").

If apply poisson-link model is said that "Poisson-link model is derived by defining n_i as the predicted density of individuals or groups at sample i, where the number of observed individuals is assumed to follow a Poisson process with expectation n_i".

In this case should I input in the "b_i" both catches in kg and numbers of individuals caught?

Thanks.

[James-Thorson-NOAA]

Good question :) So the Poisson-linked delta models has two linear predictors (LPs) where LP-1 has units log(numbers) and LP-2 has units log(mass-per-number). The response is then exp(LP-1) * exp(LP-2), which has units mass. So short answer is b_i should have units mass.

happy to keep discussing here, but closing for now

[BioCatFish]

Thank you for the comment. This is what I was thinking. I'm just wondering how does VAST dinstinguish numbers and mass-per-number from biomass data having no information about numbers caught or average individual weight within a sample?

[James-Thorson-NOAA]

It's mainly a way of expressing that the mean-variance relationship is derived from a Poisson process. I wouldn't overinterpret the linear predictors themselves.

[BioCatFish]

Thanks James. So, using the Poisson-link model can interpret combined resulted covariate effects on 1st and 2nd linear predictors on final density just as their sum since the response is then exp(LP-1) * exp(LP-2)?

[James-Thorson-NOAA]

Yes, except it's the additive effect on log density , i.e., log(D) = LP-1 + LP-2 (re-iterating what you have above)