A comparative evaluation of factor‐ and component‐based structural equation modelling approaches under (in)correct construct representations

Abstract

Structural equation modelling (SEM) has evolved into two domains, factor‐based and component‐based, dependent on whether constructs are statistically represented as common factors or components. The two SEM domains are conceptually distinct, each assuming their own population models with either of the statistical construct proxies, and statistical SEM approaches should be used for estimating models whose construct representations correspond to what they assume. However, SEM approaches have often been evaluated and compared only under population factor models, providing misleading conclusions about their relative performance. This is partly because population component models and their relationships have not been clearly formulated. Also, it is of fundamental importance to examine how robust SEM approaches can be to potential misrepresentation of constructs because researchers may often lack clear theories to determine whether a factor or component is more representative of a given construct. Addressing these issues, this study begins by clarifying several population component models and their relationships and then provides a comprehensive evaluation of four SEM approaches – the maximum likelihood approach and factor score regression for factor‐based SEM as well as generalized structured component analysis (GSCA) and partial least squares path modelling (PLSPM) for component‐based SEM – under various experimental conditions. We confirm that the factor‐based SEM approaches should be preferred for estimating factor models, whereas the component‐based SEM approaches should be chosen for component models. Importantly, the component‐based approaches are generally more robust to construct misrepresentation than the factor‐based ones. Of the component‐based approaches, GSCA should be chosen over PLSPM, regardless of whether or not constructs are misrepresented.

A primer on integrated generalized structured component analysis

“…A key assumption concerns which statistical representation to use for constructs in the model. Notes: SE = standard error; CI = 95% percentile bootstrap confidence interval While using factors as statistical proxies for constructs is standard in marketing research, researchers increasingly question the reflex-like assumption of their universal applicability (Cho et al, 2022a;Rhemtulla et al, 2020;Rigdon and Sarstedt, 2022). Many research situations call for the specification of components, especially when the constructs are conceptually rather close to an aggregation of their indicators.…”

“…In many situations, however, the decision is not clear-cut, and both approaches are defensible from a measurement-theoretic perspective (Cho et al , 2022a). This particularly holds as most constructs are not inherently best represented by factors or components.…”

“…To estimate a structural equation model like the one on Mntande et al (2023), researchers can draw on two types of SEM methods, which differ in terms of how they statistically approximate constructs (Cho et al , 2022a; Rigdon et al , 2017). One is factor-based SEM, where (common) factors are used as statistical proxies for the constructs.…”

Images of bodies in mass and social media and body dissatisfaction: The role of internalization and self-discrepancy

“…To test the impact of perceived media images on self-discrepancy and body dissatisfaction, we used partial least squares structural equation modeling (PLS-SEM). PLS is a causal-predictive approach to SEM that emphasizes prediction in estimating models derived based on theory and logic ( Hair et al, 2019 ; Cho et al, 2022 ). PLS-SEM readily incorporates formatively specified constructs where the indicators are designed to jointly form said constructs ( Sarstedt et al, 2016 ), which is the case for perceived body ideals in our model.…”

Confirmatory composite analysis in human development research

“…In a first step of CCA, a composite model has to be specified (Cho et al, 2022; Dijkstra, 2013, 2017). Considering K observed variables, the observed variables that belong to one composite η j are stored in block x j with K j observed variables, which are allowed to covary freely.…”