Calculate an upper bound on catch counts for the censored Poisson family

Usage

get_censored_upper(prop_removed, n_catch, n_hooks, pstar = 0.95)

Arguments

prop_removed: The proportion of baits removed in each fishing event from any species. I.e., the proportion of hooks returning without bait for any reason.
n_catch: The observed catch counts on each fishing event of the target species.
n_hooks: The number of hooks deployed on each fishing event.
pstar: A single value between 0 <= pstar <= 1 specifying the breakdown point of observed catch counts as a result of hook competition.

Value

A numeric vector of upper bound catch counts of the target species to improve convergence of the censored method.

Details

pstar could be obtained via inspecting a GAM or other smoother fit with catch counts as the response, an offset for log(hook count), and proportion of baits removed for each fishing event as the predictor. Check when the curve drops off as the proportion bait removed increases.

Pass the returned vector to control = sdmTMBcontrol(censored_upper = ...) with family = censored_poisson() and the observed catch counts (n_catch) as the response. Fishing events with prop_removed below pstar get an upper bound equal to the observed catch and are therefore treated as uncensored. Alternatively, set censored_upper to NA for fishing events above pstar to use the right-censored likelihood without an upper bound.

The right-censored Poisson density can be written as:

  dcens_pois <- function(x, lambda) {
      1 - ppois(x - 1, lambda)
   }

and the right-censored Poisson density with an upper limit can be written as:

  dcens_pois_upper <- function(x, lambda, upper) {
    ppois(upper, lambda) - ppois(x - 1, lambda)
  }

In practice, these computations are done in log space for numerical stability.

References

Watson, J., Edwards, A.M., and Auger-Méthé, M. 2023. A statistical censoring approach accounts for hook competition in abundance indices from longline surveys. Canadian Journal of Fisheries and Aquatic Sciences. 80(3): 468–486. doi:10.1139/cjfas-2022-0159

Examples

dat <- structure(
  list(
    n_catch = c(
      78L, 63L, 15L, 6L, 7L, 11L, 37L, 99L, 34L, 100L, 77L, 79L,
      98L, 30L, 49L, 33L, 6L, 28L, 99L, 33L
    ),
    prop_removed = c(
      0.61, 0.81, 0.96, 0.69, 0.99, 0.98, 0.25, 0.95, 0.89, 1, 0.95, 0.95,
      0.94, 1, 0.95, 1, 0.84, 0.3, 1, 0.99
    ), n_hooks = c(
      140L, 140L, 140L, 140L, 140L, 140L, 140L, 140L, 140L, 140L, 140L, 140L,
      140L, 140L, 140L, 140L, 140L, 140L, 140L, 140L
    )
  ),
  class = "data.frame", row.names = c(NA, -20L)
)
upr <- get_censored_upper(dat$prop_removed, dat$n_catch, dat$n_hooks, pstar = 0.9)
upr
#>  [1]  78  63  28   6  39  34  37 109  34 140  87  89 105  70  59  73   6  28 139
#> [20]  65

plot(dat$n_catch, upr, xlab = "N catch", ylab = "N catch upper limit")
abline(0, 1, lty = 2)
above_pstar <- dat[dat$prop_removed > 0.9, ]
upr_pstar <- upr[dat$prop_removed > 0.9]
points(above_pstar$n_catch, upr_pstar, col = "red", pch = 20)
txt <- paste0(
  "Red indicates catch events\n",
  "with >= pstar proportion of hooks\n",
  "coming back without bait.\n\n",
  "The rest are fishing events < pstar\n",
  "('high-quality' events)."
)
text(10, 120, txt, adj = 0)