Negative binomial - Gamma family for overdispersed count/effort ratios

Two-process model where the numerator follows a negative binomial distribution and the denominator (effort/exposure) follows a Gamma distribution. This fills the gap between Poisson-Gamma (equidispersed counts) and NegBin-NegBin (integer denominator): use it when counts are overdispersed and effort is continuous.

Use cases:

• Overdispersed catch per unit effort (CPUE)

• Overdispersed observations per continuous exposure

• Any ratio of overdispersed counts over continuous positive effort

Usage

ratiod_negbin_gamma(link_num = "log", link_denom = "log")

Arguments

link_num

Link function for count rate (default: "log")

link_denom

Link function for effort mean (default: "log")

Value

A ratiod_family object

Examples

# Create family object
fam <- ratiod_negbin_gamma()
print(fam)
#> tulpaRatio family: negbin_gamma 
#> Negative binomial numerator, Gamma denominator (overdispersed CPUE-type) 
#> 
#> Numerator:  neg_binomial_2(log)
#> Denominator: gamma (log) 

# Simulate overdispersed CPUE data
set.seed(123)
n <- 60
df <- data.frame(
  catch = rnbinom(n, size = 5, mu = 8),
  effort_hours = rgamma(n, shape = 4, rate = 1),
  depth = rnorm(n),
  vessel = factor(rep(1:6, each = n/6))
)

if (FALSE) { # \dontrun{
# Fit model (slow, not run on CRAN)
fit <- tratio(
  catch | effort_hours ~ depth + (1 | vessel),
  data = df,
  family = ratiod_negbin_gamma(),
  control = list(iter = 200, warmup = 100, chains = 1)
)
} # }