What is Confirmatory Composite Analysis?
Confirmatory Composite Analysis (CCA) is a subtype of structural equation modeling (SEM) that aims to evaluate composite models of emergent variables. It was originally outlined by Jörg Henseler and Theo K. Dijkstra in the context of partial least squares path modeling (Henseler et al., 2014). In 2018, Schuberth et al. (2018) elaborated on CCA and provided the first full description. CCA is analogous to confirmatory factor analysis (CFA). The only difference between the two is that CFA helps to evaluate common factor models, whereas CCA helps to evaluate composite models (Henseler and Schuberth, 2020). In contrast to reflective measurement models, which are instantiations of classical measurement theory, composite models are instantiations of synthesis theory as introduced by Henseler and Schuberth (2021). Composite models assume that all information between blocks of observed variables is conveyed solely by the emergent variables formed from those observed variables. As shown in the tutorial section, various estimators can be employed in CCA, such as partial least squares path modeling (Henseler & Schuberth, 2020), generalized canonical correlation analysis approaches (Schuberth et al., 2018), and the maximum likelihood estimator (Schamberger et al., 2023; Schuberth, 2023; Yu et al., 2023). Thus, the composite model can be tested by both parametric and nonparametric approaches. The discrepancy between the empirical and the model-implied variance-covariance matrix of the observed variables is assessed. An unacceptable model fit provides empirical evidence against the synthesis theory.
See what Wikipedia says about CCA: https://en.wikipedia.org/wiki/Confirmatory_composite_analysis
Check the QuantFish workshop on CCA: https://www.goquantfish.com/courses/composite-models-in-mplus
Listen to the Quantitude podcast on CCA: https://quantitudepod.org/s5e08-confirmatory-composite-analysis/