Factor- and Composite-Based Structural Equation Modeling -- A New Approach to Incorporate Composites in the Traditional SEM Framework

Abstract

Structural equation modeling (SEM) is a prevalent approach for studying constructs.Traditionally, these constructs are modeled as reflectively measured latent variables - common factors that account for the variance-covariance structure of their associated indicators. Over the past two decades, there has been growing interest in an alternative way of modeling constructs: the composite, i.e., a linear combination of indicators. However, existing approaches to estimating composite models either limit researchers from fully leveraging SEM's capabilities, such as handling missing data, evaluating overall model fit, and testing group differences, or significantly increase complexity of the model specification by introducing additional variables. Against this background, this paper presents a new way of integrating both common factors and composites in the traditional SEM framework. Our presented model specification, along with its model-implied variance-covariance matrix, enables researchers to: (i) utilize well-established SEM estimators, including maximum likelihood and generalized least squares estimators, and (ii) can leverage developments from the traditional SEM framework in terms of model specification, evaluation, and handling of missing data. This way of analyzing structural equation models involving common factors and composites is referred to as factor- and composite-based SEM (FC-SEM). This advancement aims to enhance the flexibility and applicability of SEM in analyzing constructs.

Figures (3)

• Figure 1: Example of a Common Factor $\eta$ With $P$ Measures $y_1, \dots y_P$
• Figure 2: Example of a Composite $\eta$ With $P$ Indicators $y_1, \dots y_P$
• Figure 3: Population Model