Pushing the Limits: The Performance of Maximum Likelihood and Bayesian Estimation with Small and Unbalanced Samples in a Latent Growth Model

Abstract

Longitudinal developmental research is often focused on patterns of change or growth across different (sub)groups of individuals. Particular to some research contexts, developmental inquiries may involve one or more (sub)groups that are small in nature and therefore difficult to properly capture through statistical analysis. The current study explores the lower-bound limits of subsample sizes in a multiple group latent growth modeling by means of a simulation study. We particularly focus on how the maximum likelihood (ML) and Bayesian estimation approaches differ when (sub)sample sizes are small. The results show that Bayesian estimation resolves computational issues that occur with ML estimation and that the addition of prior information can be the key to detect a difference between groups when sample and effect sizes are expected to be limited. The acquisition of prior information with respect to the smaller group is especially influential in this context.