Linear Mixed-Effects Models for Dependent Data: Power and Accuracy in Parameter Estimation.

Abstract

Linear mixed-effects models have been increasingly used to analyze dependent data in psychological research. Despite their many advantages over ANOVA, critical issues in their analyses remain. Due to increasing random effects and model complexity, estimation computation is demanding, and convergence becomes challenging. Applied users need help choosing appropriate methods to estimate random effects. The present Monte Carlo simulation study investigated the impacts when the restricted maximum likelihood (REML) and Bayesian estimation models were misspecified in the estimation. We also compared the performance of Akaike information criterion (AIC) and deviance information criterion (DIC) in model selection. Results showed that models neglecting the existing random effects had inflated Type I errors, unacceptable coverage, and inaccurate R-squared measures of fixed and random effects variation. Furthermore, models with redundant random effects had convergence problems, lower statistical power, and inaccurate R-squared measures for Bayesian estimation. The convergence problem is more severe for REML, while reduced power and inaccurate R-squared measures were more severe for Bayesian estimation. Notably, DIC was better than AIC in identifying the true models (especially for models including person random intercept only), improving convergence rates, and providing more accurate effect size estimates, despite AIC having higher power than DIC with 10 items and the most complicated true model.