The Henseler-Ogasawara specification of composites in structural equation modeling: A tutorial

Structural equation modeling (SEM) is a versatile statistical method that should theoretically be able to emulate all other methods that are based on the general linear model. In practice, however, researchers using SEM encounter problems incorporating composites into their models. In this tutorial article, I present a specification for SEM that was recently sketched by Henseler (2021) to incorporate composites in structural models. It draws from the same idea that was proposed in the còntext of canonical correlation analysis to express a set of observed variables forming a composite by a set of synthetic variables (Ogasawara, 2007), which were labeled by Henseler (2021) as emergent and excrescent variables. An emergent variable is a linear combination of variables that is related to other variables in the structural model, whereas an excrescent variable is a linear combination of variables that is unrelated to all other variables in the structural model. This approach is advantageous over existing approaches, as it allows drawing on all existing developments in SEM, such as testing parameter estimates, testing for overall model fit and dealing with missing values. To demonstrate the presented approach, I conduct a small scenario analysis. Moreover, SEM applying the presented specification is used to reestimate an empirical example from Hwang et al. (2021). Finally, this article discusses avenues for future research opened by this approach for SEM to study composites.