Linear mixed models and latent growth curve models for group comparison studies contaminated by outliers.

Abstract

The linear mixed model (LMM) and latent growth model (LGM) are frequently applied to within-subject two-group comparison studies to investigate group differences in the time effect, supposedly due to differential group treatments. Yet, research about LMM and LGM in the presence of outliers (defined as observations with a very low probability of occurrence if assumed from a given distribution) is scarce. Moreover, when such research exists, it focuses on estimation properties (bias and efficiency), neglecting inferential characteristics (e.g., power and type-I error). We study power and type-I error rates of Wald-type and bootstrap confidence intervals (CIs), as well as coverage and length of CIs and mean absolute error (MAE) of estimates, associated with classical and robust estimations of LMM and LGM, applied to a within-subject two-group comparison design. We conduct a Monte Carlo simulation experiment to compare CIs and MAEs under different conditions: data (a) without contamination, (b) contaminated by within-subject outliers, (c) contaminated by between-subject outliers, and (d) both contaminated by within- and between-subject outliers. Results show that without contamination, methods perform similarly, except CIs based on S, a robust LMM estimator, which are slightly less close to nominal values in their coverage. However, in the presence of both within- and between-subject outliers, CIs based on robust estimators, especially S, performed better than those of classical methods. In particular, the percentile CI with the wild bootstrap applied to the robust LMM estimators outperformed all other methods, especially with between-subject outliers, when we found the classical Wald-type CI based on the t statistic with Satterthwaite approximation for LMM to be highly misleading. We provide R code to compute all methods presented here. (PsycInfo Database Record (c) 2024 APA, all rights reserved).