Confirmatory Factor Analysis (CFA), Exploratory Structural Equation Modeling (ESEM), and Set-ESEM: Optimal Balance Between Goodness of Fit and Parsimony

Abstract

Herbert W. Marsha* , Jiesi Guoa , Theresa Dickea , Philip D. Parkera & Rhonda G. Cravena a Institute of Positive Psychology and Education, ‎Australian Catholic University, Sydney, AustraliaSupplemental data for this article can be accessed at https://doi.org/10.1080/00273171.2019.1602503CONTACT Herbert W. Marsh Herb.Marsh@acu.edu.au Institute for Positive Psychology and Education (IPPE), Australian Catholic University, North Sydney NSW 20160 2135, Australia.AbstractCFAs of multidimensional constructs often fail to meet standards of good measurement (e.g., goodness-of-fit, measurement invariance, and well-differentiated factors). Exploratory structural equation modeling (ESEM) represents a compromise between exploratory factor analysis’ (EFA) flexibility, and CFA/SEM’s rigor and parsimony, but lacks parsimony (particularly in large models) and might confound constructs that need to be kept separate. In Set-ESEM, two or more a priori sets of constructs are modeled within a single model such that cross-loadings are permissible within the same set of factors (as in Full-ESEM) but are constrained to be zero for factors in different sets (as in CFA). The different sets can reflect the same set of constructs on multiple occasions, and/or different constructs measured within the same wave. Hence, Set-ESEM that represents a middle-ground between the flexibility of traditional-ESEM (hereafter referred to as Full-ESEM) and the rigor and parsimony of CFA/SEM. Thus, the purposes of this article are to provide an overview tutorial on Set-ESEM, juxtapose it with Full-ESEM, and to illustrate its application with simulated data and diverse “real” data applications with accessible, heuristic explanations of best practice.