Negative binomial - Negative binomial family

Two-process model where both numerator and denominator follow negative binomial distributions. This is the core family for count-count ratios where both processes exhibit overdispersion.

Use cases:

• Species counts / total counts (relative abundance)

• Events / opportunities (both counts)

• Any ratio where numerator and denominator are overdispersed counts

Usage

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

Arguments

link_num

Link function for numerator (default: "log")

link_denom

Link function for denominator (default: "log")

Value

A ratiod_family object

Examples

# Create family object
fam <- ratiod_negbin_negbin()
print(fam)
#> tulpaRatio family: negbin_negbin 
#> Negative binomial numerator, negative binomial denominator 
#> 
#> Numerator:  neg_binomial_2(log)
#> Denominator: neg_binomial_2 (log) 

# Simulate data for relative abundance
set.seed(123)
n <- 60
df <- data.frame(
  sp_count = rnbinom(n, size = 5, mu = 15),
  total_count = rnbinom(n, size = 8, mu = 100),
  habitat = factor(rep(c("forest", "grassland"), each = n/2)),
  site = factor(rep(1:10, each = n/10))
)

if (FALSE) { # \dontrun{
# Fit model (slow, not run on CRAN)
fit <- tratio(
  sp_count | total_count ~ habitat + (1 | site),
  data = df,
  family = ratiod_negbin_negbin(),
  control = list(iter = 200, warmup = 100, chains = 1)
)
} # }