Longitudinal Data Analysis Using Multilevel Linear Modeling (MLM): Fitting an Optimal Variance-Covariance Structure

This dissertation focuses on issues related to fitting an optimal variance-covariance structure in multilevel linear modeling framework with two Monte Carlo simulation studies. In the first study, the author evaluated the performance of common fit statistics such as Likelihood Ratio Test (LRT), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) and a new proposed method, standardized root mean square residual (SRMR), for selecting the correct within-subject covariance structure. Results from the simulated data suggested SRMR had the best performance in selecting the optimal covariance structure. A pharmaceutical example was also used to evaluate the performance of these fit statistics empirically. The LRT failed to decide which is a better model because LRT can only be used for nested models. SRMR, on the other hand, had congruent result as AIC and BIC and chose ARMA(1,1) as the optimal variance-covariance structure. In the second study, the author adopted a first-order autoregressive structure as the true within-subject V-C structure with variability in the intercept and slope (estimating [tau]00 and [tau]11 only) and investigated the consequence of misspecifying different levels/types of the V-C matrices simultaneously on the estimation and test of significance for the growth/fixed-effect and random-effect parameters, considering the size of the autoregressive parameter, magnitude of the fixed effect parameters, number of cases, and number of waves. The result of the simulation study showed that the commonly-used identity within-subject structure with unstructured between-subject matrix performed equally well as the true model in the evaluation of the criterion variables. On the other hand, other misspecified conditions, such as Under G & Over R conditions and Generally misspecified G & R conditions had biased standard error estimates for the fixed effect and lead to inflated Type I error rate or lowered statistical power. The two studies bridged the gap between the theory and practical application in the current literature. More research can be done to test the effectiveness of proposed SRMR in searching for the optimal V-C structure under different conditions and evaluate the impact of different types/levels of misspecification with various specifications of the within- and between- level V-C structures simultaneously.