What is Confirmatory Composite Analysis?
Confirmatory Composite Analysis (CCA) is a subtype of composite-based structural equation modeling (SEM) that aims at assessing composite models of emergent variables. It was originally sketched 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) elaborate on CCA and provide the first full description. CCA was designed in analogy to confirmatory factor analysis. The only difference between the two is that CFA helps to assess common factor models, whereas CCA helps to assess composite models (Henseler and Schuberth, 2020). In contrast to reflective measurement models which represent instantiations of classical measurement theory, composite models represent 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 of these 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), approaches to generalized canonical correlation analysis (Schuberth et al., 2018) and the maximum-likelihood estimator (Schuberth, 2022; Yu et al., 2023). Consequently, the composite model can be tested by both parametric and non-parametric approaches. In doing so, 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.
Explanation video:
References:
Henseler, J., Dijkstra, T. K., Sarstedt, M., Ringle, C. M., Diamantopoulos, A., Straub, D. W., Ketchen, D. J., Hair, J. F., Hult, G. T. M., & Calantone, R. J. (2014). Common beliefs and reality about PLS: Comments on Rönkkö and Evermann (2013). Organizational Research Methods, 17(2), 182–209. https://doi.org/10.1177/1094428114526928
Henseler, J., & Schuberth, F. (2020). Using confirmatory composite analysis to assess emergent variables in business research. Journal of Business Research, 120, 147–156. https://doi.org/10.1016/j.jbusres.2020.07.026
Henseler, J. & Schuberth, F. (2021). Confirmatory composite analysis. In: Henseler, J., Composite-Based Structural Equation Modeling: Analyzing Latent and Emergent Variables, New York: Guilford Press, pp. 179-201.
Schuberth, F., Henseler, J., & Dijkstra, T. K. (2018). Confirmatory Composite Analysis. Frontiers in Psychology, 9(2541). https://doi.org/10.3389/fpsyg.2018.02541
Schuberth, F. (2023). The Henseler–Ogasawara specification of composites in structural equation modeling: A tutorial. Psychological Methods, 28(4), 843-859. https://doi.org/10.1037/met0000432
Yu, X., Schuberth, F., Henseler, J. (2023). Specifying composites in structural equation modeling: A refinement of the Henseler-Ogasawara specification. Statistical Analysis and Data Mining, 16(4), 348–357. https://doi.org/10.1002/sam.11608