Multilevel Analysis of Mediation, Moderation, and Nonlinear Effects in Small Samples, Using Expected a Posteriori Estimates of Factor Scores

ABSTRACT

In the analysis of hierarchical data, multilevel structural equation modeling (multilevel SEM) has become the standard in the social sciences. To estimate these models, maximum likelihood (ML) approaches have been applied because they are the default in latent variable software. However, one drawback of ML is that it tends to suffer from estimation problems such as nonconvergence when the sample size is small to moderate, and the results that come from nonconverged solutions are useless in research practice. Nonconvergence is a particularly serious problem when more complex multilevel SEMs are estimated. Therefore, in this article, we show how factor score regression (FSR) can be used to obtain estimates of multilevel mediation, moderation, and nonlinear effects. We conducted two simulation studies to validate our approaches. Our findings were generally promising, which renders FSR an attractive alternative to ML.

KEYWORDS:

• Factor score regression
• maximum likelihood
• structural equation modeling
• multilevel modeling

Notes

¹ We make this assumption to facilitate presentation and later computation.

² As an indication of nonconvergence, we used Mplus’ error message “ESTIMATION DID NOT TERMINATE NORMALLY.”