# Multigroup Analysis (MGA

## Abstract

The multigroup analysis (MGA) allows to test if pre-defined data groups have significant differences in their group-specific parameter estimates (e.g., outer weights, outer loadings and path coefficients). SmartPLS provides outcomes of three different approaches that are based on bootstrapping results from every group.

## Description

The MGA allows to test if pre-defined data groups have significant differences in their group-specific parameter estimates (e.g., outer weights, outer loadings and path coefficients). SmartPLS provides outcomes of three different approaches that are based on bootstrapping results from every group. More specifically, 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 resutls that allow to test if pre-defined 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.

The bootstrap MGA provides the following results:

## (1) Confidence Intervals (Bias Corrected)

This method computes the bias-corrected confidence intervals for the group specific estimations of parameters 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)

This method is 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 certain difference of group-specific path coefficients. Please note: 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

This method is a parametric significance test for the difference of group-specific PLS-SEM results that assumes equal variances across groups.

### (4) Welch-Satterthwait Test

This method is 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.

## 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., Thousand Oaks, CA: Sage. - Henseler, J., Ringle, C. M., and 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., and 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. BÃ¶nningstedt: SmartPLS. Retrieved from https://www.smartpls.com