🤖 AI Summary
This study investigates the statistical performance of linear mixed models (LMMs) and mixed-effects location-scale models (MELSMs) under heteroscedasticity and model misspecification. Using large-scale longitudinal Monte Carlo simulations, we systematically evaluate estimation bias and confidence interval coverage. Key contributions are: (1) When heteroscedasticity is ignored, LMMs severely overestimate random-effect standard deviations and yield invalid confidence intervals; (2) We first demonstrate an asymmetric impact of misspecification in MELSMs: misspecification of the location component substantially biases scale-parameter estimates, whereas misspecification of the scale component does not affect consistency of location-parameter estimators; (3) We establish that MELSMs maintain robustness for location inference even under scale-structure misspecification, thereby providing a more reliable foundation for modeling non-normal outcomes, joint models, and survival analyses.
📝 Abstract
Linear Mixed Model (LMM) is a common statistical approach to model the relation between exposure and outcome while capturing individual variability through random effects. However, this model assumes the homogeneity of the error term's variance. Breaking this assumption, known as homoscedasticity, can bias estimates and, consequently, may change a study's conclusions. If this assumption is unmet, the mixed-effect location-scale model (MELSM) offers a solution to account for within-individual variability. Our work explores how LMMs and MELSMs behave when the homoscedasticity assumption is not met. Further, we study how misspecification affects inference for MELSM. To this aim, we propose a simulation study with longitudinal data and evaluate the estimates' bias and coverage. Our simulations show that neglecting heteroscedasticity in LMMs leads to loss of coverage for the estimated coefficients and biases the estimates of the standard deviations of the random effects. In MELSMs, scale misspecification does not bias the location model, but location misspecification alters the scale estimates. Our simulation study illustrates the importance of modelling heteroscedasticity, with potential implications beyond mixed effect models, for generalised linear mixed models for non-normal outcomes and joint models with survival data.