A Structural Equation Modeling Approach for Modeling Variability as a Latent Variable

Translational Abstract In many research and applied settings across the social, behavioral, and health sciences, it is variability, rather than averages, that is of key interest. Examples include consistency/stability of an individual over multiple measurements (intraindividual variability), and cohesiveness among members within a group or team (intragroup variability). Drawing upon recent developments in structural equation modeling, the current study presents an analytical framework for addressing research questions that focus on intraindividual, or intragroup, variability. Beyond merely serving as an alternative to existing multilevel modeling approaches, this framework allows for extensions to accommodate a variety of complex research scenarios by parameterizing variability as a latent variable, which can be studied as the outcome, predictor, and/or mediators simultaneously in relation to other observed and/or latent variables. This study delineates the latent random variability models and offers a discussion of model estimation as well as parameter interpretation. To demonstrate the versatility of the proposed methods, the latent random variability models are fit to empirical data and parameter estimates are obtained via Bayesian estimation. The Mplus, BUGS, and Stan model syntax for the illustrative examples are supplied for applied researchers' reference. Drawing upon recent developments in structural equation modeling, the current study presents an analytical framework for addressing research questions in which, rather than focusing on means, it is intraindividual (or intragroup) variability that is of direct research interest. Beyond merely serving as an alternative to existing multilevel modeling approaches, this framework allows for extensions to accommodate a variety of complex research scenarios by parameterizing variability as a latent variable that can in turn be embedded within a broader covariance and mean structure involving other observed and/or latent variables. The estimation procedures and parameter interpretation for the latent random variability models are discussed. The versatility of the proposed methods is demonstrated through four empirical examples. The Mplus, BUGS, and Stan model syntax for the illustrative examples are supplied to facilitate the application of the methods.

Automated summary

This study presents an analytical framework based on recent developments in structural equation modeling to address research questions focusing on intraindividual or intragroup variability. The framework allows for extensions to accommodate complex research scenarios by parameterizing variability as a latent variable, simultaneously considering other observed and/or latent variables. The proposed methods are demonstrated through empirical examples and their syntax is provided for applied researchers.