Multigroup Analysis (MGA)
Multigroup analysis (MGA) tests whether predefined data groups differ significantly in their group-specific parameter estimates, such as outer weights, outer loadings, and path coefficients. Researchers use it to check whether a PLS-SEM model's relationships hold equally across groups, for example different countries, customer segments, or demographic categories, or whether they differ in a statistically meaningful way. SmartPLS provides outcomes from three different approaches, all based on bootstrapping results computed separately for every group.
How Multigroup Analysis Works
SmartPLS offers the permutation MGA (Chin & Dibbern, 2010) and the bootstrap MGA (Sarstedt et al., 2011). Hair et al. (2024) and Matthews (2017) describe these MGA methods for PLS-SEM (i.e., the PLS-MGA) in detail.
Based on the permutation procedure, SmartPLS provides MGA results that allow you to test whether predefined data groups have statistically significant differences in their group-specific parameter estimates (e.g., outer weights, outer loadings, and path coefficients). The permutation procedure also supports the MICOM procedure for analyzing measurement invariance.
Bootstrap MGA Results
The bootstrap MGA provides the following results:
| Method | What it tests |
|---|---|
| (1) Confidence intervals (bias corrected) | Computes bias-corrected confidence intervals for the group-specific parameter estimates in the PLS path model. The group-specific results of a path coefficient are significantly different if the bias-corrected confidence intervals do not overlap. |
| (2) Partial least squares multigroup analysis (PLS-MGA) | A non-parametric significance test for the difference of group-specific results that builds on PLS-SEM bootstrapping results. A result is significant at the 5% probability of error level if the p-value is smaller than 0.05 or larger than 0.95 for a given difference of group-specific path coefficients. The PLS-MGA method (Henseler et al., 2009), as implemented in SmartPLS, is an extension of the bootstrap-based MGA approach originally proposed for PLS-SEM (as described, for example, by Sarstedt et al., 2011). |
| (3) Parametric test | A parametric significance test for the difference of group-specific PLS-SEM results that assumes equal variances across groups. |
| (4) Welch-Satterthwaite test | A parametric significance test for the difference of group-specific PLS-SEM results that assumes unequal variances across groups. |
MGA Settings in SmartPLS
Select Groups: The selected groups will be assessed for significant differences in the parameter estimates (e.g., outer weights, outer loadings, and path coefficients). All data groups selected under Group A will be compared against all data groups selected under Group B.
Frequently Asked Questions
What is multigroup analysis (MGA) in PLS-SEM?
MGA tests whether predefined data groups, such as different countries or customer segments, have statistically significant differences in group-specific parameter estimates like outer weights, outer loadings, or path coefficients.
Which MGA methods does SmartPLS provide?
SmartPLS provides the permutation MGA and the bootstrap MGA. The bootstrap MGA in turn reports four sets of results: bias-corrected confidence intervals, the non-parametric PLS-MGA significance test, a parametric test assuming equal variances, and a Welch-Satterthwaite test assuming unequal variances.
How do I know if a path coefficient differs significantly between two groups?
Using bias-corrected confidence intervals, the group-specific results for a path coefficient are significantly different if the confidence intervals of the two groups do not overlap. Alternatively, the PLS-MGA test flags a significant difference at the 5% probability of error level when the p-value is smaller than 0.05 or larger than 0.95.
Should I use the parametric test or the Welch-Satterthwaite test?
That depends on whether the variances of the parameter estimates are equal across groups. The parametric test assumes equal variances across groups, while the Welch-Satterthwaite test assumes unequal variances.
Do I need to check measurement invariance before running an MGA?
Yes. Group comparisons are only meaningful once measurement invariance has been established. The permutation procedure that underlies MGA in SmartPLS also supports the MICOM procedure for analyzing measurement invariance.
Related SmartPLS Methods
References
- Chin, W. W., & Dibbern, J. (2010). A permutation based procedure for multi-group PLS analysis: Results of tests of differences on simulated data and a cross cultural analysis of the sourcing of information system services between Germany and the USA. In V. Esposito Vinzi, W. W. Chin, J. Henseler, & H. Wang (Eds.), Handbook of partial least squares: Concepts, methods and applications (Springer Handbooks of Computational Statistics Series, Vol. II) (pp. 171–193). Springer.
- 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.). Sage.
- Henseler, J., Ringle, C. M., & Sinkovics, R. R. (2009). The use of partial least squares path modeling in international marketing. Advances in International Marketing, 20, 277–320.
- Matthews, L. (2017). Applying multi-group analysis in PLS-SEM: A step-by-step process. In H. Latan & R. Noonan (Eds.), Partial least squares structural equation modeling: Basic concepts, methodological issues and applications (pp. 219–243). Springer.
- Sarstedt, M., Henseler, J., & Ringle, C. M. (2011). Multi-group analysis in partial least squares (PLS) path modeling: Alternative methods and empirical results. Advances in International Marketing, 22, 195–218.
- More literature ...
Cite correctly
Please always cite the use of SmartPLS!
Ringle, Christian M., Wende, Sven, & Becker, Jan-Michael. (2024). SmartPLS 4. Bönningstedt: SmartPLS. Retrieved from https://www.smartpls.com
