Misspecifications in structural equation modeling: The choice of latent variables, causal-formative constructs or composites

Abstract

Empirical research in many social disciplines involves constructs that are not directly observable, such as behaviors. To model them, constructs must be operationalized using their relations with indicators. Structural equation modeling (SEM) is the primary approach for this purpose. In SEM, three types of constructs are distinguished: latent variables, causal-formative constructs, and composites. To estimate the parameters of the different models, various estimators have been developed. Many Monte Carlo studies have examined the estimation performances of different estimators for the construct types. One aspect evaluated is the consequences of construct misspecification - when the true construct type differs from the modeling choice - on parameter estimates and model fit. For example, parameter bias in models that misspecify latent variables as composites is often attributed to the chosen estimator, although model parameters depend on different estimators, making it impossible to examine the factors individually. This article aims to disentangle the issues of construct misspecification and parameter estimation by a comprehensive Monte Carlo study of all combinations between true and assumed construct types. To focus on misspecification, we used the same estimator for all models, namely the maximum likelihood (ML) estimator. To generalize beyond ML, we replicated the simulation using another estimator. We aim to examine the role of construct misspecification, not estimator choice, on the estimation performance and show that misspecification leads indeed to biased path coefficient estimates. Further, we evaluate whether fit measures can distinguish models with correct from those with misspecified constructs. We find that none of the criteria considered is suited for this. These findings stress the importance of thoughtful construct specification and the need for further research.