Check whether the Generalised Gamma is likely identifiable from a dataset

The Generalised Gamma (GG, dist_type = 5) has three parameters: location (\(\mu\)), scale (\(\sigma\)/phi), and shape (\(Q\)/kappa). All datasets share a single (\(\sigma\), \(Q\)) pair, so the GG is only identifiable when datasets consistently imply the same distributional shape. If different studies show widely different coefficients of variation (CV = SD/mean), the sampler cannot find a coherent (\(\sigma\), \(Q\)) and will exhibit poor mixing or divergences.

Two fast, pre-fit checks are applied:

CV spread: Computes the CV for every dataset using moment approximations (same logic as update_phi_prior()). If max(CV) / min(CV) > cv_spread_threshold the CVs are too inconsistent to identify the extra GG parameter.
Information richness: The \(Q\) parameter encodes tail behaviour beyond mean and variance. Datasets that supply only summary statistics (mean + SD, median + IQR, median + range) provide at most two moments and give weak leverage on \(Q\). If the fraction of datasets with frequency-table or interval-censored data (summary types 4 and 5) is below min_rich_fraction, the shape is too poorly constrained.

Usage

should_attempt_gg(
  datasets,
  cv_spread_threshold = 2.5,
  min_rich_fraction = 0.3,
  verbose = TRUE
)

Arguments

datasets: A named list of datasets in the format accepted by prepare_stan_data_from_datasets().
cv_spread_threshold: Numeric scalar (default 2.5). Maximum tolerated ratio of the largest to the smallest per-dataset CV. Increase to be more permissive, decrease to be stricter.
min_rich_fraction: Numeric scalar in (0, 1] (default 0.30). Minimum fraction of datasets that must be frequency-table or interval-censored (summary types 4 / 5). Set to 0 to disable this check.
verbose: Logical (default TRUE). Print a one-line verdict with the reason a check failed.

Value

TRUE if both checks pass (GG fitting is worth attempting), FALSE otherwise.

Examples

if (FALSE) { # \dontrun{
should_attempt_gg(datasets_SARS)    # expected: FALSE
should_attempt_gg(datasets_Mpox)
} # }