The impact of ignoring a level of nesting structure in multilevel growth mixture model: a Monte Carlo study

The number of longitudinal studies has increased steadily in various social science disciplines over the last decade. Growth Mixture Modeling (GMM) has emerged among the new approaches for analyzing longitudinal data. It can be viewed as a combination of Hierarchical Linear Modeling, Latent Growth Curve Modeling and Finite Mixture Modeling. The combination of both continuous and categorical latent variables makes GMM a flexible analysis procedure. However, when researchers analyze their data using GMM, some may assume that the units are independent of each other even though it may not always be the case. The purpose of this dissertation was to examine the impact of ignoring a higher nesting structure in Multilevel Growth Mixture Modeling on the accuracy of classification of individuals and the accuracy on tests of significance (i.e., Type I error rate and statistical power) of the parameter estimates for the model in each subpopulation. Two simulation studies were conducted. In the first study, the impact of misspecifying the multilevel mixture model is investigated by ignoring a level of nesting structure in cross-sectional data. In the second study, longitudinal clustered data (e.g., repeated measures nested within units and units nested within clusters) are analyzed correctly and with a misspecification ignoring the highest level of the nesting structure. Results indicate that ignoring a higher level nesting structure results in lower classification accuracy, less accurate fixed effect estimates, inflation of lower-level variance estimates, and less accurate standard error estimates, the latter result which in turn affects the accuracy of tests of significance for the fixed effects. The magnitude of the intra-class correlation (ICC) coefficient has a substantial impact when a higher level nesting structure is ignored; the higher the ICC, the more variance at the highest level is ignored, and the worse the performance of the model. The implication for applied researchers is that it is important to model the multilevel data structure in (growth) mixture modeling. In addition, researchers should be cautious in interpreting their results if ignoring a higher level nesting structure is inevitable. Limitations concerning appropriate use of latent class analysis in growth modeling include unknown effects of incorrect estimation of the number of latent classes, non-normal distribution effects, and different growth patterns within-group and between-group.