Confirmatory Composite Analysis (CCA)

Abstract

Confirmatory factor analysis (CFA) has historically been used to develop and improve reflectively measured constructs based on the domain sampling model. Compared to CFA, confirmatory composite analysis (CCA; Hair et al. 2018, Chapter 13; Hair et al., 2020) is a recently proposed alternative approach applied to confirm measurement models when using partial least squares structural equation modeling (PLS-SEM). CCA is a series of steps executed with PLS-SEM to confirm both reflective and formative measurement models of established measures that are being updated or adapted to a different context. CCA is also useful for developing new measures. Finally, CCA offers several advantages over other approaches for confirming measurement models consisting of linear composites.

CCA in PLS-SEM Steps

CCA is a systematic methodological process for confirming measurement models in PLS-SEM. To perform a CCA in the PLS-SEM, researchers must follow specific steps for the reflective measurement models, the formative measurement models, and the structural model (Hair et al. 2018, Chapter 13; Hair et al., 2020). Note that in their alternative approach to CCA, Schuberth et al. (2018) require a measure of fit to confirm PLS-SEM measurements and structural models. Hair et al. (2020) do not consider fit to be a requirement for confirming PLS-SEM models, including the CCA approach advocated by them.

Reflective Measurement Models

  1. Estimate of Loadings and Significance
  2. Indicator Reliability (items)
  3. Composite Reliability (construct)
  4. Average Variance Extracted (AVE)
  5. Discriminant Validity – HTMT
  6. Nomological Validity
  7. Predictive Validity

Formative Measurement Models

  1. Convergent Validity – redundancy
  2. Indicator Multicollinearity
  3. Size and Significance of Indicator Weights
  4. Contribution of Indicators (size & significance of loadings)
  5. Assess Predictive Validity

Structural Model

  1. Evaluate structural model collinearity
  2. Examine size and Significance of Path Coefficients
  3. R² of Endogenous Variables (in-sample prediction)
  4. f² Effect Size (in-sample prediction)
  5. Predictive Relevance Q² (primarily in-sample prediction)
  6. PLSpredict (out-of-sample prediction)

Summary

CCA is becoming increasingly important as an alternative to the use of CFA in the development, adaptation and confirmation of measurement scales (Hair et al. 2018, Chapter 13; Hair et al., 2020). SmartPLS fully supports the CCA in PLS-SEM. Thereby, social science scholars obtain the statistical methods they need to explore and better understand the phenomena they are researching.

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