Heshani Wijethunga: Coverage Probability of Confidence Intervals for Variance Components of Mixed Effects Models

Abstract.

Hierarchical, nested, and repeated measures data are commonly analyzed by mixed-effects models (MEMs), which are becoming a basic statistical tool in many scientific disciplines. These are extensions to traditional regression models that account for both fixed effects, which affect all observations equally, and random effects, which represent within-group or within-subject specific variations. MEMs are particularly helpful in research related to fields such as psychology, healthcare, education, economics, and environmental sciences, where the data on which the analysis is to be built exhibit multilevel dependencies.

There are three most commonly used R packages for mixed-effects modeling, namely lme4, nlme, and brms. The lme4 package is widely acknowledged as an efficient computational and scalable package for this use and is recommended for use with large datasets. While it handles LMMs (Linear mixed-effects models) and GLMMs (General Linear mixed-effects models) efficiently, it does not support modeling for within-group correlation structures or heteroscedasticity, which limits its use in longitudinal studies.

The thesis presents a simulation study to evaluate the use of MEMs to estimate variance components of hierarchical data. Linear mixed-effects models with random intercepts for groups are fitted in the context of the simulation using the lme4 package in R. Different values of the parameters, such as the number of groups, the number of observations per group, and the variance components for the error levels at the group and individual level in the simulation, are considered. The simulation results demonstrate that the coverage probabilities of error keep up well in most cases, while the coverage probabilities of the random intercept face greater risks of undercoverage in small groups or when the data are highly variable. When testing coverage levels, researchers should consider adding various groups to improve the accuracy of the models. However, it can be concluded that the coverage probability of the confidence interval for variance components of MEM may not always provide accurate inference for the random effects.