Analyzing individual growth with clustered longitudinal data: A comparison between model-based and design-based multilevel approaches

To prevent biased estimates of intraindividual growth and interindividual variability when working with clustered longitudinal data (e.g., repeated measures nested within students; students nested within schools), individual dependency should be considered. A Monte Carlo study was conducted to examine to what extent two model-based approaches (multilevel latent growth curve model - MLGCM, and maximum model - MM) and one design-based approach (design-based latent growth curve model - D-LGCM) could produce unbiased and efficient parameter estimates of intraindividual growth and interindividual variability given clustered longitudinal data. The solutions of a single-level latent growth curve model (SLGCM) were also provided to demonstrate the consequences of ignoring individual dependency. Design factors considered in the present simulation study were as follows: number of clusters (NC = 10, 30, 50, 100, 150, 200, and 500) and cluster size (CS = 5, 10, and 20). According to our results, when intraindividual growth is of interest, researchers are free to implement MLGCM, MM, or D-LGCM. With regard to interindividual variability, MLGCM and MM were capable of producing accurate parameter estimates and SEs. However, when D-LGCM and SLGCM were applied, parameter estimates of interindividual variability were not comprised exclusively of the variability in individual (e.g., students) growth but instead were the combined variability of individual and cluster (e.g., school) growth, which cannot be interpreted. The take-home message is that D-LGCM does not qualify as an alternative approach to analyzing clustered longitudinal data if interindividual variability is of interest.