Confirmatory Composite Analysis (CCA): Four Steps for Testing Composite Models, and Why Its Developers Do Not Regard It as the Primary Choice

CCA plays a role similar to confirmatory factor analysis (CFA), but for composite models in PLS-SEM and GSCA. The procedure has four clear steps. However, limitations concerning fit-index cutoffs mean that even its developers do not recommend CCA as the primary approach to measurement model assessment.

PLS-SEM & SMARTPLSPrepared by Lê Minh6 min

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Composite assessment needs appropriate evidence

Concept
Clarify the composite’s role
Specification
Justify how it is formed
Assessment
Examine the relevant evidence
Limitations
State the scope of the approach

Conceptual diagram. Do not automatically interchange common-factor and composite criteria.

Source: Lê Minh · Conceptual illustration, not software output.

1. What Is CCA, and How Is Its Role Similar to CFA?

Confirmatory Composite Analysis (CCA) is a confirmatory measurement model testing procedure for composite models, applicable to both reflective and formative measurement models. Schuberth, Henseler, and Dijkstra (2018) developed CCA using the same four-step logic as CFA in CB-SEM, while replacing the common factor model with a composite model.

CCA suits component-based estimation methods such as PLS-SEM and GSCA, where latent variables are constructed as weighted combinations of indicators rather than common factors underlying them.

2. Step 1: Specify the Composite Model

Each research construct is modeled as a composite: a weighted combination of its observed indicators, with each indicator belonging to exactly one composite. Covariances among indicators within the same block are freely estimated, while covariances between different blocks follow rank-one constraints, meaning all information between two blocks must pass through their corresponding composites.

3. Step 2: Check Identification

Each weight vector is normalized so that its composite has unit variance. Every composite must connect to at least one other composite or variable in the model to ensure theoretical identification. Model degrees of freedom equal the number of nonredundant covariance elements minus the number of free parameters, plus the number of indicator blocks. Positive degrees of freedom, or overidentification, are required to test overall fit.

4. Step 3: Estimate the Model

Weights and correlations between composites are estimated using generalized canonical correlation analysis, with the maxvar option under unit-variance constraints. Maxvar maximizes the largest eigenvalue of the correlation matrix between composites. Other estimation options, including sumcor, ssqcor, minvar, genvar, PCA, and PLS-PM, are mentioned in the original article but are not the primary recommended choice for this step.

5. Step 4: Assess the Model

Assessment has two parts: a bootstrap-based test of overall fit and heuristic fit indices.

5.1. Bootstrap-based test of overall fit

This test specifies the null hypothesis that the population covariance matrix equals the model-implied covariance matrix. The data are transformed so that the sample covariance matrix equals the model-implied matrix. A reference distribution of discrepancies is then constructed by bootstrapping the transformed data, following the Bollen-Stine bootstrap logic (Bollen & Stine, 1992; based on Beran & Srivastava, 1985). The null hypothesis is rejected if the observed discrepancy exceeds a critical value, usually the 95% or 99% quantile.

Three common discrepancy measures are squared Euclidean distance (dL), geodesic distance (dG, based on Swain, 1975), and SRMR (based on Hu & Bentler, 1999). For standardized data, dL and SRMR give identical results.

5.2. Heuristic fit indices

Table 1
Index	Origin	Interpretation
SRMR	Hu & Bentler (1998)	Values below 0,10, or more conservatively below 0,08, are often cited. However, these thresholds were originally proposed for common factor models and have not been specifically validated for composite models.
NFI	Bentler & Bonett (1980)	Compares the estimated model with a baseline model in which indicators are uncorrelated; values close to one indicate good fit.
RMStheta	Lohmöller (1989)	The root mean square of residual correlations between blocks, excluding within-block residuals; values close to zero indicate good fit.

Composite model cutoffs are not firmly established

Schuberth, Henseler, and Dijkstra (2018) explicitly state that cutoffs for fit indices need to be established for CCA, implying that thresholds borrowed from common factor models may not suit composite models. Mechanically transferring the familiar CFA threshold of SRMR below 0,08 to CCA lacks a firm basis.

6. Scholarly Debate and a Cautious Recommendation

Crittenden, Sarstedt, Astrachan, Hair, and Lourenco (2020) note continuing scholarly debate over CCA implementation and the relationship between different perspectives on the method. Reflecting this lack of agreement, official SmartPLS guidance explicitly states that the authors do not recommend CCA as the primary approach to measurement model assessment.

CCA is a supplementary tool rather than the default choice

Given this position, CCA is best treated as a supplementary or comparative analysis alongside more familiar PLS-SEM measurement assessment criteria, such as reliability, AVE, and HTMT, rather than replacing them with a single overall fit test.

Nevertheless, CCA has published practical applications. Ciavolino et al. (2022) used CCA to validate an Italian version of a psychological scale, the Interactions Anxiousness Scale. This illustrates its value in specific research situations, provided the limitations concerning cutoffs are clearly reported.

7. Common Mistakes

Table 2
Weak wording	Why it is inappropriate	Recommended wording
"SRMR is below 0,08, so the composite model fits well, just as in CFA."	The 0,08 threshold was originally proposed for common factor models and has not been established specifically for composite models.	Report SRMR with a note that composite model cutoffs are not firmly established.
"CCA has been run, so reliability, AVE, and HTMT no longer need assessment."	SmartPLS does not recommend CCA as the primary measurement model assessment method, so it should not completely replace familiar criteria.	Present CCA as a supplementary analysis alongside standard PLS-SEM measurement model assessment criteria.
"An overall fit test can still be run when the model has negative degrees of freedom."	The model must have positive degrees of freedom, or be overidentified, for overall fit testing to be meaningful.	Check degrees of freedom before interpreting the overall fit test.

8. Checklist before Reporting

Have you clearly described the composite model specification, including rank-one constraints between blocks?
Have you checked degrees of freedom and confirmed overidentification?
Have you reported the estimation method used, such as maxvar?
Have you reported the bootstrap-based overall fit test and the discrepancy measure used: dL, dG, or SRMR?
Have you explained the limitations of composite model cutoffs when reporting heuristic indices?
Have you presented CCA as supplementary to standard measurement model assessment criteria?

Conclusion

CCA provides a clearly structured framework for testing composite models, following four steps familiar from CFA and including a bootstrap-based overall fit test. Its practical value has an important limitation: fit-index cutoffs for composite models are not as firmly established as those in CFA.

Because of this limitation, CCA should supplement the familiar PLS-SEM measurement assessment criteria rather than replace them entirely. SmartPLS guidance explicitly states this position.

References

Schuberth, F., Henseler, J., & Dijkstra, T. K. (2018). Confirmatory composite analysis. Frontiers in Psychology, 9, Article 2541. https://doi.org/10.3389/fpsyg.2018.02541
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
Hair, J. F., Howard, M. C., & Nitzl, C. (2020). Assessing measurement model quality in PLS-SEM using confirmatory composite analysis. Journal of Business Research, 109, 101-110. https://doi.org/10.1016/j.jbusres.2019.11.069
Crittenden, V., Sarstedt, M., Astrachan, C., Hair, J., & Lourenco, C. E. (2020). Guest editorial: Measurement and scaling methodologies. Journal of Product & Brand Management, 29(4), 409-414. https://doi.org/10.1108/JPBM-07-2020-009
Ciavolino, E., Ferrante, L., Sternativo, G. A., Cheah, J.-H., Rollo, S., Marinaci, T., & Venuleo, C. (2022). A confirmatory composite analysis for the Italian validation of the Interactions Anxiousness Scale: A higher-order version. Behaviormetrika, 49(1), 23-46. https://doi.org/10.1007/s41237-021-00151-x

Academic note: This article presents the four-step CCA procedure of Schuberth, Henseler, and Dijkstra (2018), together with the cautious position stated publicly in SmartPLS guidance. Readers applying CCA to a specific model should consult the cited sources directly, especially concerning the lack of firmly established cutoffs for composite models.