Abstract

When using PLS-SEM, group comparisons can be misleading unless researchers establish the invariance of their measures. A three-step procedure allows analyzing measurement invariance of composite models (MICOM) before undertaking multigroup analyses in PLS-SEM.

Brief Description

Measurement invariance is an important issue when conducting PLS-SEM multigroup analyses. The research by Henseler et al. (2016) introduces a procedure to assess measurement invariance of composite models (MICOM) when using PLS-SEM. In a three-step approach, MICOM requires analyzing following elements: (1) configural invariance, (2) compositional invariance, and (3) the equality of composite mean values and variances. The article by Henseler et al. (2016) explains in detail each step, shows simulation study results, and the outcomes of an empirical example (also see Hair et al., 2024).

MICOM in SmartPLS

The results report of the permutation algorithm in SmartPLS also returns the MICOM outcomes of Step 2 (compositional invariance) and Step 3 (the equality of composite mean values and variances).

• The results of Step 1 cannot be included in SmartPLS since the configural invariance assessment requires an inspection of the model set-up, the selected settings and other things that do not involve a statistical test. Running MICOM in SmartPLS usually automatically establishes configural invariance (Step 1).
• In Step 2, SmartPLS returns permutation-based confidence intervals that allow determining if a composite has a correlations in Group A and Group B that is significantly lower than one. If this is not the case, the composite does not differ much in both groups and compositional invariance has been established.
• Finally, in Step 3, permutation-based confidence intervals for the mean values and the variances allow assessing if a composite's mean value and its variance differs across groups. These results are important to reveal if partial or full measurement invariance has been established.

The article by Henseler et al. (2016) explains in detail how to interpret the results tables provided by SmartPLS in accordance with the three-step MICOM procedure (also see Hair et al., 2018).

Please note that MICOM builds on permutation-based confidence intervals. For this reason, the sentence on page 416 in the article by Henseler et al. (2016), "If the confidence intervals of differences in mean values and logarithms of variances between the construct scores of the first and second group include zero, the researcher can assume that the composite mean values and variances are equal.", needs to be changed. The more precise and corrected version of this sentence is as follows: “If the permutation-based confidence intervals of differences in mean values and logarithms of variances between the construct scores of the first and second group include the obtained difference, the researcher can assume that the composite mean values and variances are equal.”

References

• Hair, J. F., Sarstedt, M., Ringle, C. M., & Gudergan, S. P. (2024). Advanced Issues in Partial Least Squares Structural Equation Modeling (PLS-SEM), 2nd Ed., Thousand Oaks, CA: Sage.

• Henseler, J., Ringle, C. M., and Sarstedt, M. 2016. Testing Measurement Invariance of Composites Using Partial Least Squares. International Marketing Review, 33(3), 405-431.

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