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

Abstract

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 c`ontext 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.

How can the transition from office to telework be managed? The impact of tasks and workplace suitability on collaboration and work performance

“…In our study, we deal with two types of concepts: formed concepts and behavioral concepts (Edwards, 2001 ; Henseler, 2017 ; Schuberth et al, 2018 ; Benitez et al, 2020 ; Henseler and Schuberth, 2020a ; Hubona et al, 2021 ; Schuberth, 2021 ) 1 . In brief, formed concepts are the abstractions of design science, defined by a set of components and can be operationalized with help of a composite model (Henseler et al, 2015 ; Hubona et al, 2021 ; Yu et al, 2021 ), in which the concept is represented by an emergent variable (Henseler and Schuberth, 2020b ).…”

A model and its fit lie in the eye of the beholder: Long live the sum score

“…For example, instead of the construct influencing its indicators, for some constructs it might be more reasonable to assume the other causal pathway, that it, the construct being influenced by its indicators. The indicators educational background and salary raise my socio-economic status, instead of my socio-economic status raising my education and salary (Schuberth, in press ). Another possibility is that there is no unifying latent construct; instead, the indicators might directly influence one another.…”

“…From a logical perspective, this is a converse error (“affirming the consequent”; see e.g., Martinsen, 2022 ): given that a constrained version of factor analysis implies a sum score, McNeish and Wolf assume that a sum score must imply factor analysis, overlooking that other models could also imply sum scores. Specifically, it can be shown mathematically that data patterns implied by factor analysis are also implied by multiple other kinds of models (e.g., Schuberth, in press ). For example, a latent class analysis, modeling two classes of individuals through a categorical rather than a continuous latent variable, will generally imply the same means and variance-covariance matrix as a unidimensional factor analysis applied to the same data (Molenaar and von Eye, 1994 ).…”

“…In addition, it has been shown that psychometric network models can produce data that are in accordance with factor analysis (van der Maas et al, 2006 ). Another kind of model implying equivalent data is a composite, which conceptualizes a formative rather than a reflective construct (Schuberth, in press ). It stands to debate why exactly factor analysis should be applied to data to see whether it fits data and to extract factor sores, given that these alternative models, particularly if they are in better accordance with theoretical assumptions, might better capture the data-generating process.…”

Confirmatory composite analysis in human development research

“…Against this background, this article presents confirmatory composite analysis (CCA; Schuberth et al, 2018), a novel technique that is devoted to the analysis of composites. Using a recently proposed specification of composites allows to specify the models studied in CCA as a special case of structural equation models (Henseler & Schuberth, 2020a; Schuberth, 2021b). Overall, CCA shows the same benefits for assessing theoretical concepts modeled as composites as CFA shows for theoretical concepts modeled as common factors.…”