Specifying composites in structural equation modeling: A refinement of the Henseler–Ogasawara specification

Structural equation modeling (SEM) plays an important role in business and social science and so do composites, that is, linear combinations of variables. However, existing approaches to integrate composites into structural equation models still have limitations. A major leap forward has been the Henseler–Ogasawara (H–O) specification, which for the first time allows for seamlessly integrating composites into structural equation models. In doing so, it relies on emergent variables, that is, the composite of interest, and one or more orthogonal excrescent variables, that is, composites that have no surplus meaning but just span the remaining space of the emergent variable's components. Although the H–O specification enables researchers to flexibly model composites in SEM, it comes along with several practical problems: (i) The H–O specification is difficult to visualize graphically; (ii) its complexity could create difficulties for analysts, and (iii) at times SEM software packages seem to encounter convergence issues with it. In this paper, we present a refinement of the original H–O specification that addresses these three problems. In this new specification, only two components load on each excrescent variable, whereas the excrescent variables are allowed to covary among themselves. This results in a simpler graphical visualization. Additionally, researchers facing convergence issues of the original H–O specification are provided with an alternative specification. Finally, we illustrate the new specification's application by means of an empirical example and provide guidance on how (standardized) weights including their standard errors can be calculated in the R package lavaan. The corresponding Mplus model syntax is provided in the Supplementary Material.