Calculate log-likelihood for Beta-distributed proportions — calc_log_likelihood

Computes the total log-likelihood for proportion data under the Beta distribution. Supports either the mean-precision parameterization (default) or the standard shape parameterization. In both cases, a single global set of shape parameters is estimated from the data using the method of moments. Each observation can be weighted via weights.

Usage

calc_log_likelihood_beta(
  observed,
  estimated,
  mean_precision = TRUE,
  weights = NULL,
  verbose = TRUE
)

Arguments

observed: Numeric vector of observed values in (0, 1).
estimated: Numeric vector of model-predicted values in (0, 1).
mean_precision: Logical; if TRUE (default), use mean-precision parameterization. If FALSE, estimate shape parameters directly from the observed vector.
weights: Optional numeric vector of non-negative weights, same length as observed. Default is NULL, which sets all weights to 1.
verbose: Logical; if TRUE, prints shape parameter estimates and total log-likelihood.

Value

A scalar log-likelihood (numeric).

Details

When mean_precision = TRUE, the precision parameter $\phi$ is estimated as: $$ \phi = \frac{\mu (1 - \mu)}{\text{Var}(Y)} - 1 $$ Then: $$ \text{shape}_1 = \mu_t \phi, \quad \text{shape}_2 = (1 - \mu_t) \phi $$

When mean_precision = FALSE, a single global $\text{shape}_1$, $\text{shape}_2$ is estimated from the observed vector: $$ \text{shape}_1 = \left( \frac{1 - \mu}{\sigma^2} - \frac{1}{\mu} \right) \mu^2 $$ $$ \text{shape}_2 = \text{shape}_1 \left( \frac{1}{\mu} - 1 \right) $$

The total log-likelihood is then summed across observations, each multiplied by weights[i].

Examples

calc_log_likelihood_beta(c(0.2, 0.6, 0.4), c(0.25, 0.55, 0.35))
#> Mean–precision mode: estimated phi = 71.00
#> Beta log-likelihood: 4.77
#> [1] 4.770705