Pool multiple imputation draws via Rubin's rules

Pools per-imputation block fits via Rubin's rules. When every draw also carries a per-coefficient skewness vector $gamma, the third cumulant is pooled by the law of total cumulants $$\kappa_3 = E[\kappa_3(X | k)] + 3\,\mathrm{Cov}(\mu_k, \sigma_k^2) + \kappa_3(\mu_k),$$ giving a pooled skewness $gamma alongside the usual $mean / $se. If any draw is missing $gamma, the third-cumulant path is skipped.

Usage

rubins_pool(draws)

Arguments

draws

List of K draws. Each draw is a named list of submodel results, each with beta (numeric vector), se (numeric vector), and optionally gamma (numeric vector, same length as beta).

Value

A named list of pooled submodel summaries, each with mean, se, V_within, V_between, V_total, K (number of draws that contributed), and when applicable gamma (pooled skewness) and kappa3 (pooled third cumulant).