Does your covariance structure choice matter? Evidence from a systematic Monte Carlo study with mixed

Stata’s mixed command offers three common random-effects covariance structures (independent, exchangeable, unstructured) with little guidance on which to choose or what a wrong choice actually costs. This study analyzes results from a systematic Monte Carlo study varying the true correlation among random effects, the heterogeneity of their variances, cluster count and size, and the number of random effects to answer that question directly. Four findings carry direct implications for practice. Fixed-effect point estimates are robust to structure choice, but exchangeable can miscalibrate confidence-interval coverage even when its coefficients look unaffected, so a check comparing only point estimates can miss the problem. Independent biases the covariances by construction but leaves variances close to unbiased even under strong true correlation, so its cost is often smaller than assumed. Exchangeable can be actively misleading under heterogeneity, in one scenario reversing a covariance's sign entirely. Unstructured convergence degrades sharply as random effects grow relative to cluster count. The study derives concrete decision rules for when the extra unstructured parameters are worth fitting.