A FINITE MIXTURE MULTILEVEL STRUCTURAL EQUATION MODEL FOR UNOBSERVED HETEROGENEITY IN RANDOM VARIABILITY

Abstract

Variability is often of key interest in various research and applied settings. Important research questions about intraindividual variability (e.g., consistency across repeated measurements) or intragroup variability (e.g., cohesiveness among members within a team) are piquing the interest of researchers from a variety of disciplines. To address the research needs in modeling random variability as the key construct, Feng and Hancock (2020, 2022) proposed a multilevel SEM-based modeling approach where variability can be modeled as a random variable. This modeling framework is a highly flexible analytical tool that can model variability in observed measures or latent constructs, variability as the predictor or the outcome, as well as the between-subject comparison of variability across observed groups. A huge challenge still remains, however, when it comes to modeling the unobserved heterogeneity in random variability. Given that no existing research addresses the methodological considerations of uncovering the unobserved sub-populations that differ in intraindividual variability or intragroup variability, or sub-populations that differ in the various processes and mechanisms involving intraindividual variability or intragroup variability, the current dissertation study aims to fill this gap in literature. In the current study, a finite-mixture MSEM for modeling unobserved heterogeneity in random variability (MMSEM-RV) is introduced. Bayesian estimation via MCMC is proposed for model estimation. The performance of MMSEM-RV with Bayesian estimation is systematically evaluated in a simulation study across varying conditions. An illustrative example with empirical PISA data is also provided to demonstrate the practical application of MMSEM-RV.