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Calculate log-likelihood for Negative Binomial-distributed count data

Source: R/calc_log_likelihood_distributions.R
calc_log_likelihood_negbin.Rd

Computes the total log-likelihood for count data under the Negative Binomial distribution, using the gamma-function formulation. Each observation can be weighted.

Usage

calc_log_likelihood_negbin(
  observed,
  estimated,
  k = NULL,
  k_min = NULL,
  weights = NULL,
  eps_rel = 0.02,
  verbose = TRUE
)

Arguments

observed

Integer vector of observed non-negative counts (e.g., cases, deaths).

estimated

Numeric vector of expected values from the model (same length as observed).

k

Numeric scalar; dispersion parameter. If NULL, it is estimated via method of moments.

k_min

Deprecated and ignored; retained only so existing calls do not error. Dispersion is estimated by est_nb_dispersion and arrives already bounded. If k = Inf (Poisson limit), no flooring is applied.

weights

Optional numeric vector of non-negative weights, same length as observed. Default is NULL, which sets all weights to 1.

eps_rel

Positive scalar; the predicted mean of every cell is floored at max(1e-4, eps_rel * mean(observed)) before the density is evaluated. Default 0.02. This floor is the only thing standing between a zero prediction and log(0), and its SIZE sets how hard a spurious zero is punished, so it is channel-specific: see calc_model_likelihood (eps_rel_cases / eps_rel_deaths).

verbose

Logical; if TRUE, prints diagnostics including the (floored) dispersion and total log-likelihood.

Value

A scalar representing the total log-likelihood (numeric).

Details

If k is not supplied, it is estimated as \(k = \bar{x}^2 / (s^2 - \bar{x})\) from observed. If \(s^2 \le \bar{x}\), the function uses the Poisson limit (k = Inf).

Examples

# k is used as supplied
calc_log_likelihood_negbin(c(0, 5, 9), c(3, 4, 5))
#> Estimated k = 1.390 (from Var = 20.333, Mean = 4.667)
#> Negative Binomial log-likelihood (k=1.390): -7.50
#> [1] -7.498757
# Supply the dispersion k explicitly (used exactly as given)
calc_log_likelihood_negbin(c(0, 5, 9), c(3, 4, 5), k = 1.2)
#> Using provided k = 1.200
#> Negative Binomial log-likelihood (k=1.200): -7.51
#> [1] -7.513423