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
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))
)
# \donttest{
# Fit model
fit <- tratio(
sp_count | total_count ~ habitat + (1 | site),
data = df,
family = ratiod_negbin_negbin(),
control = list(iter = 400, chains = 1, seed = 1)
)
summary(fit)
#> ratio model summary
#> ===================
#>
#> Inference: Exact (Tier 1) via hmc
#> Family: negbin_negbin
#>
#> Fixed effects (numerator):
#> parameter mean sd 2.5% 97.5% rhat ess_bulk
#> num:(Intercept) 2.615 0.112 2.427 2.872 1.046 58
#> num:habitatgrassland -0.017 0.157 -0.394 0.264 1.040 47
#>
#> Fixed effects (denominator):
#> parameter mean sd 2.5% 97.5% rhat ess_bulk
#> denom:(Intercept) 4.669 0.106 4.493 4.96 1.000 38
#> denom:habitatgrassland -0.032 0.163 -0.344 0.37 1.002 31
#>
#> Variance components:
#> parameter mean sd 2.5% 97.5% rhat ess_bulk
#> phi_denom 5.786 1.031 4.200 8.142 0.998 133
#> phi_num 6.350 1.689 3.655 10.368 1.008 124
#> sigma_re 0.111 0.084 0.003 0.302 1.025 17
#>
#> Diagnostics:
#> Divergences: 0
#> Avg. acceptance: 0.883
#> Chains: 1
#> Iterations: 400
#> Warmup: 200
#> R-hat > 1.01 for 3 parameter(s), largest 1.046 (num:(Intercept)).
#> Bulk ESS < 100 for 5 parameter(s), smallest 17 (sigma_re).
#> Run longer chains or reparameterise before using these estimates.
# }