Investigating Sample Size Requirements of Multilevel Growth Mixture Models via Monte Carlo Simulations

• In Event: Interrogating Mixture Models in Pursuit of True Population Heterogeneity

Abstract

Given that individuals are often nested within clusters (e.g., students within schools) in social and behavioral sciences, multilevel growth mixture modeling (ML GMM) has been proposed to account for such nested data structures while estimating distinct growth trajectories (Muthén & Asparouhov, 2009; Palardy & Vermunt, 2010). However, methodological guidelines for ML GMM are still lacking, which might contribute to the scarcity of its applications. This study aims to fill this gap and provide sample size recommendations regarding two types of ML GMM, one that estimates the number of latent classes at the individual level (or level 1) only (ML GMM-L1), and one that estimates latent classes at both the individual level and the cluster level (or level 2) (ML GMM-L1L2). Note that for the latter, the number of level-2 latent classes is estimated based on the average growth trajectory for each cluster.
ML GMM-L1 has been demonstrated (Muthén & Asparouhov, 2009) and evaluated via Monte Carlo simulations (Chen et al., 2010, 2017). For instance, Chen et al. (2010) observed the overall adequate performance of the model across all sample sizes (30, 50, and 80 clusters crossed with cluster sizes of 20 and 40). Chen et al. (2017) found that BIC performed well in identifying the correct number of classes (2 or 3), except for small sample sizes. However, sample size requirements have not been evaluated comprehensively, taking into account various class separation levels and sample sizes. The performance of ML GMM-L1L2 has not been investigated so its sample size requirements remain unknown.
To systematically evaluate sample size requirements of ML GMM, design factors included the number of time points (4, 8), number of level-1 latent classes (2, 3), number of level-2 latent classes (2, 3; for ML GMM-L1L2), class separation (small, moderate, large), number of clusters (10, 25, 50, 100), cluster size (10, 20, 40), class proportions (equal, unequal), and intraclass correlation coefficient (ICC, .05, .15). Data were generated in Mplus 8.8 (Muthén & Muthén, 1998-2017) for the two model types separately. Simulation outcomes were correct class enumeration rate (for AIC, BIC, saBIC, Lo-Mendell-Rubin or LMR test, and the adjusted LMR test) and parameter recovery including relative bias, Type I error rate, and statistical power of growth factors. A subset of results (for ML GMM-L1 conditions under moderate class separation, two classes, and equal proportions) showed that 50 or 100 clusters paired with cluster size of 40 were needed for BIC and saBIC to identify the 2-class model when there were eight time points; otherwise, under-extraction of classes occurred. LMR and aLMR performed well in supporting the 2-class model across sample sizes, except for 50 or 100 clusters paired with cluster sizes of 20 or 40.
This study contributes to the literature of finite mixture modeling by providing sample size recommendations regarding two types of ML GMM. Ultimately, we aim to promote the use of ML GMMs and further our understanding of the distinction and choices between the two types of ML GMMs from the perspective of sample size requirements.

Authors

• Alexandria P. Winstead, University of Massachusetts - Lowell
  Presenting Author

• Rose Holder
  Presenting Author

• Yan Wang, University of Massachusetts - Lowell
  Presenting Author

• Jiabin Shen
  Presenting Author