Informative Variance Priors for Bayesian Multilevel Modeling with Large and Small Samples

Music City Center 

Frequentist multilevel models (MLMs) often struggle with unstable variance estimates when the number of clusters (L2 units) is small, leading to imprecise inferences. Bayesian MLMs provide a solution by incorporating informative variance priors, which stabilize random effects and improve small-sample estimation. This study applies Bayesian MLM with strongly informative inverse-gamma priors to cross-sectional child trafficking data from Sierra Leone, examining individual- and household-level predictors of trafficking vulnerabilities while addressing challenges related to small L2 clusters and missing data.

Using R (brms) with Hamiltonian Monte Carlo in Stan, we specify variance priors based on empirical variance distributions, aligning prior mode with realistic estimates to reduce bias, improve precision, and yield narrower credible intervals. Model validation includes posterior predictive checks, prior sensitivity analyses, and Gelman-Rubin diagnostics.

Findings confirm that informative variance priors enhance small-sample estimation, improving inference for hierarchical data. Beyond methodology, this research provides policy-relevant insights for targeted interventions.

Bayesian

Multilevel modeling

Informative variance priors

Inverse-gamma

Hierarchical data

Small sample estimation 

Section on Bayesian Statistical Science