Poisson-Gamma family for count/effort ratios

Two-process model where the numerator follows a Poisson distribution and the denominator (effort/exposure) follows a Gamma distribution. This is the natural family for CPUE-type data.

Use cases:

• Catch per unit effort (CPUE)

• Observations per hour

• Events per continuous exposure

Usage

ratiod_poisson_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_poisson_gamma()
print(fam)
#> tulpaRatio family: poisson_gamma 
#> Poisson numerator, Gamma denominator (CPUE-type) 
#> 
#> Numerator:  poisson(log)
#> Denominator: gamma (log) 

# Simulate CPUE data
set.seed(123)
n <- 60
df <- data.frame(
  catch = rpois(n, lambda = 8),
  effort_hours = rgamma(n, shape = 4, rate = 1),
  depth = rnorm(n),
  season = factor(rep(c("spring", "summer", "fall"), each = n/3)),
  vessel = factor(rep(1:6, each = n/6))
)

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