Statistical Analysis of Repeated Measures Data: A Simulation Study Comparing Ordinary Least Squares, Linear Mixed-Effects, and Cluster-Robust Estimators

Abstract Repeated measures designs are widely utilized across biomedical and psychological research, yet the inferential consequences of ignoring clustering remain pervasive. Following the ADEMP protocol, this Monte Carlo simulation evaluates three analytical strategies: Naive Ordinary Least Squares (OLS), Linear Mixed-Effects Models (LMM) with Satterthwaite degrees of freedom, and Cluster-Robust Variance Estimation using the small-sample bias-reduced CR2 adjustment. We evaluated 24 factorial scenarios crossing cluster counts (J∈{10,30,100}), intraclass correlation coefficients ("ICC"∈{0.10,0.50}), covariate structures (between- vs. within-subject), and effect sizes across 2,000 replications each (48,000 datasets), alongside an empirical re-analysis of the classic sleep deprivation benchmark. While all estimators yield unbiased point estimates, Naive OLS exhibits severe inferential failure: for between-subject covariates at "ICC"=0.50, standard errors are deflated by over 40% ("SE Ratio"≈0.55"-" 0.58), reducing 95% confidence interval coverage to 71.8%–74.2% and inflating Type I error rates to 26.0%–28.0% (nominal α=0.05). Conversely, for within-subject covariates, Naive OLS overestimates standard errors ("SE Ratio"≈1.39"-" 1.47), yielding conservative coverage (99.2%–99.4%) and deflated Type I error rates (0.6%–1.2%). Both LMM and CR2 estimators preserve nominal coverage (94.4%–96.0%) and controlled Type I error rates (4.3%–5.8%) even at J=10. In the empirical application, CR2 matched the standard error of a maximal random-slope model ("SE"=1.546) without requiring parametric random-effects specification, illustrating design-based robustness.