Moderated mediation with composites: The composite moderated structural equations approach

Moderated mediation models are crucial in many disciplines, particularly the social sciences. Researchers use them to analyze the conditions under which different variables are related. Structural equation modeling (SEM) is an eminently suitable framework for this endeavor. In fact, several approaches have been proposed and extended to model moderated mediation effects involving reflectively measured latent variables. However, approaches to modeling moderated mediation involving unknown-weight composites (i.e., weighted linear combinations of variables whose weights are estimated freely) are limited in either model specification or model assessment. Unknown-weight composites are used, for example, to model formative constructs or collections of heterogeneous causes. In this study, we propose composite moderated structural equations (CMS), a new approach that combines latent moderated structural equations (LMS), the standard SEM approach for estimating moderation effects among latent variables, with the H-O specification, a recently introduced specification for flexibly modeling composites. A Monte Carlo simulation demonstrates the performance of CMS and confirms that CMS enables researchers to flexibly model and estimate moderated mediation effects involving unknown-weight composites.