Compute the realized mean informativeness
\(\widehat{I} = \sigma_\tau^2 / (\sigma_\tau^2 + \mathrm{GM}(\widehat{se}_j^2))\),
where GM is the geometric mean of the per-site sampling variances.
Higher \(\widehat{I}\) indicates more precise per-site estimates
relative to the between-site heterogeneity scale; a feasibility index
near 1 means each site's estimate alone identifies the latent effect.
Arguments
- se2_j
Numeric vector (length \(\ge 2\)). Per-site sampling variances \(\widehat{se}_j^2\). Must be strictly positive.
- sigma_tau
Numeric (\(\ge 0\)). Between-site SD.
0returns0(no heterogeneity → no informativeness to recover).- tau_j
Optional numeric vector matching
se2_jlength. Kept for signature compatibility with the S3 method; not used in the computation.
Details
This is the realized counterpart to the design-target \(I\) fed to
sim_meta or used in gen_se_direct. Under
the deterministic-grid direct-precision path, the realized and target
\(I\) match exactly; under the site-size-driven path or under a
custom se_fn, the realized value is what you read off the simulation.
tau_j is accepted for data-method signature compatibility (so
the same call shape works for multisitedgp_data objects and bare
numeric vectors) but does not enter the statistic.
References
Lee, J., Che, J., Rabe-Hesketh, S., Feller, A., & Miratrix, L. (2025). Improving the estimation of site-specific effects and their distribution in multisite trials. Journal of Educational and Behavioral Statistics, 50(5), 731–764. doi:10.3102/10769986241254286 .
See also
informativeness for the S3 generic with methods for
multisitedgp_data and numeric se2_j inputs;
compute_kappa for the precision constant input to the
site-size-driven path;
heterogeneity_ratio for the realized \(R\).
Other family-diagnostics:
bhattacharyya_coef(),
compute_kappa(),
compute_shrinkage(),
default_thresholds(),
feasibility_index(),
heterogeneity_ratio(),
informativeness(),
ks_distance(),
mean_shrinkage(),
realized_rank_corr(),
realized_rank_corr_marginal(),
scenario_audit()
Examples
se2 <- c(0.05, 0.08, 0.10)
compute_I(se2, sigma_tau = 0.20)
#> [1] 0.3518629