CB-SEM Multigroup Analysis (MGA)

Abstract

Multigroup analysis (MGA) in covariance-based SEM (CB-SEM) is used to test whether a specified model holds equivalently across different groups (e.g., male vs. female, experimental vs. control). It allows researchers to assess the stability of relationships between constructs and compare parameter estimates across subpopulations (Hair et al., 2018). More specifically, SmartPLS extends its CB-SEM functionality by providing the estimation of a single SEM across predefined groups with optional cross-group constraints.

Multigroup Analysis in SmartPLS

Specification of Groups

Users specify the groups for which CB-SEM MGA will be performed (e.g., gender, region, treatment). SmartPLS estimates the same model separately for each group, while allowing for cross-group constraints to be imposed.

Constraints

Parameter constraints can be specified to:

Fix values: e.g., fix a loading to 1 for scale identification.
Apply equality constraints: force two or more parameters to share the same value (e.g., equal loadings or paths).
Apply across-group constraints: constrain parameters to be equal across all groups for invariance testing.

Measurement Invariance Testing

Ensuring measurement invariance is a requirement for the multigroup analysis. SmartPLS provides a structured framework for assessing measurement invariance by comparing nested models with increasing constraints:

CB-SEM Examples in SmartPLS

SmartPLS provides directly computable CB-SEM multigroup analysis examples from leading textbooks (e.g., Hair et al., 2018). The results in SmartPLS replicate the textbook examples exactly. Try out the CB-SEM example projects in SmartPLS. Alternatively, you can run a CB-SEM moderator analysis.

References

Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2018). Multivariate Data Analysis (8 ed.). Cengage Learning.
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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