In longitudinal studies, both repeated measures (RM) and hierarchical linear model (HLM) can be applied. Yet, it is not clearly determined which of RM and HLM should be applied in the balanced design of a longitudinal study. The purpose of this study was to explore the interrelation of HLM and RM in their theoretical development and to compare the two approaches to the evaluation of fixed effects in the balanced design of longitudinal data analysis. This was done through a Monte Carlo (MC) study of the empirical power of HLM and RM in three fixed effect tests: Two-group treatment effect, time effect and treatment-by-time interaction.
In this research, RM included traditional RM (TRM) and updated multivariate RM (UMRM). Two covariance structures examined under UMRM were UN and AR(1). Specifically, this paper compared the power of HLM, AR(1), UN and TRM in the three fixed effect tests within three factors: Effect sizes, sample sizes and G matrices. The results indicated that HLM, AR(1) and UN had similar power patterns but different from TRM. TRM was significantly more powerful than the other three in the treatment and time tests, but significantly less powerful than the three in the interaction test. Among HLM, AR(1) and UN, UN power seemed to rank the highest, AR(1) the second, and HLM the lowest, in all three tests under defined conditions. Nevertheless, the pairwise power differences of HLM, AR(1) and UN are not all significant.
Additionally, findings from Type I error rates, bootstrap bias, standard errors, confidence intervals and model fit statistics (AIC and BIC) were examined for the four models. Limitations, conclusions, recommendations for future study were also provided.