The article titled “Assessing Measurement Model Quality in PLS-SEM Using Confirmatory Composite Analysis” by Joe F. Hair Jr., Matt C. Howard, and Christian Nitzl, published in the Journal of Business Research, offers a comprehensive introduction to Confirmatory Composite Analysis (CCA) as an innovative alternative to Confirmatory Factor Analysis (CFA) for assessing measurement model quality within Partial Least Squares Structural Equation Modeling (PLS-SEM). The authors aim to familiarize readers with the concept, process, and advantages of CCA, especially when dealing with both reflective and formative measurement models, as well as when adapting existing scales or developing new ones.
The article begins by tracing the historical evolution of measurement model quality, linking it to early psychometric developments such as Guilford’s (1936) item analysis and Spearman’s (1904) classical test theory. It outlines how Exploratory Factor Analysis (EFA), Covariance-Based SEM (CB-SEM), and the CFA technique emerged in the 1980s, followed by the development of PLS-SEM by Wold (1982) as a prediction-oriented alternative.
A detailed comparison of EFA, CFA, and CCA is provided. While EFA is primarily exploratory, aiming at data reduction, both CFA and CCA serve confirmatory purposes. However, a key distinction is that CFA is grounded in common variance and typically does not yield determinant construct scores, whereas CCA, based on total variance (similar to Principal Component Analysis), does provide these scores. Moreover, CCA is also more accommodating of formative models, unlike CFA which is largely restricted to reflective constructs.
Among the advantages of CCA highlighted in the paper are its ability to retain more items for measuring constructs—thereby improving content validity—and its capacity to compute composite scores. Additionally, when prediction is a primary goal, CCA offers superior utility within the PLS-SEM framework. The authors note that the conventional reliance on Goodness-of-Fit (GOF) indices in CFA does not translate well to CCA because the objectives and statistical logic underlying PLS-SEM differ; namely, the emphasis in PLS-SEM is on prediction rather than model fit.
The article outlines step-by-step guidelines for implementing CCA. For reflective models, researchers are advised to assess indicator loadings (≥ 0.708), indicator reliability, composite reliability (CR and Cronbach’s alpha both > 0.70), Average Variance Extracted (AVE ≥ 0.50), discriminant validity using the Heterotrait-Monotrait (HTMT) ratio (< 0.85 or < 0.90), as well as nomological and predictive validity. For formative models, the key steps include evaluating convergent validity through redundancy analysis (path coefficient ≥ 0.70), checking multicollinearity among indicators (VIF ≤ 3.0), analyzing the size and significance of indicator weights (p ≤ 0.05), assessing indicator contributions (outer loading ≥ 0.50), and determining predictive validity.
Once measurement models are confirmed, structural model assessment follows. This includes testing for collinearity among constructs, estimating the size and significance of path coefficients, and evaluating predictive capabilities using R² (for in-sample prediction), f² effect sizes, Q² values (predictive relevance), and PLSpredict (for out-of-sample prediction). The PLSpredict procedure involves k-fold cross-validation and compares prediction errors such as MAE and RMSE with those from a naïve linear model to determine the level of predictive power (high, medium, low, or none).
In conclusion, the authors assert that while both CCA and CFA have merit, researchers must clearly understand their distinctions and apply them based on the research objective. CCA is deemed particularly advantageous when content validity and prediction are emphasized, and when working with complex models or smaller samples. The article advocates for continual engagement with emerging literature on PLS-SEM to ensure best practices in measurement model evaluation.
| Category | Step | Description | Threshold/Criteria |
|---|---|---|---|
| 1. Reflective Measurement Model Assessment | Estimate of Loadings & Significance | Assess standardized indicator loadings and significance using bootstrapping. | Loadings ≥ 0.708; t ≥ ±1.96 (p < 0.05) |
| Indicator Reliability | Reflects shared variance between indicator and construct. | Squared loading (≥ 0.50 ideal) | |
| Composite Reliability | Internal consistency of construct using CR and Cronbach’s alpha. | CR & α ≥ 0.70; CR > α; CR > 0.95 indicates redundancy | |
| Average Variance Extracted (AVE) | Convergent validity, calculated as average of squared loadings. | AVE ≥ 0.50 | |
| Discriminant Validity (HTMT) | Measures construct distinctiveness. | HTMT < 0.85 (strict); < 0.90 (liberal) | |
| Nomological Validity | Correlation with theoretically related constructs in nomological network. | Direction, significance, and size consistent with theory | |
| Predictive Validity | Ability of construct to predict future criteria. | Longitudinal or external criterion correlation | |
| 2. Formative Measurement Model Assessment | Convergent Validity (Redundancy) | Correlation of formative construct with reflective measure of same construct. | Path coefficient ≥ 0.70 |
| Indicator Multicollinearity | Checks for redundancy and instability in weights. | VIF ≤ 3.0; bivariate correlations < 0.50 | |
| Significance of Indicator Weights | Contribution of indicator (like regression coefficient). | p ≤ 0.05 via bootstrapping | |
| Contribution of Indicators (Loadings) | Importance based on correlation with construct. | Outer loading ≥ 0.50; significance desirable | |
| Predictive Validity | Predictive strength of formative construct over future criterion. | Correlation with external criteria (e.g., later behavior) | |
| 3. Structural Model Assessment | Structural Collinearity | Checks multicollinearity among constructs. | VIF < 3.0; bivariate r < 0.50 |
| Path Coefficients | Estimates hypothesized relationships. | β between −1 and +1; significance via bootstrapping | |
| R² of Endogenous Variables | Variance explained in dependent constructs. | Higher values indicate better in-sample prediction | |
| f² Effect Size | Effect size of individual predictors. | Small: > 0.02; Medium: > 0.15; Large: > 0.35 | |
| Q² (Blindfolding) | In-sample predictive relevance. | Q² > 0: meaningful; > 0.25: medium; > 0.50: high | |
| PLSpredict (Out-of-Sample) | Predictive accuracy using cross-validation. | MAE/RMSE < Naïve LM = High; equal/mixed = Medium; majority > LM = Low; all > LM = None | |
| Advanced Robustness Checks | Supports validity through further analysis. | Mediation, moderation, MGA, endogeneity, heterogeneity |
Reference: Hair, J. F., Jr., 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
