CB-SEM Multigroup Analysis (MGA)
Multigroup analysis (MGA) in covariance-based SEM (CB-SEM) tests whether a specified model holds equivalently across different groups, such as male vs. female or experimental vs. control. It allows researchers to assess the stability of relationships between constructs and to compare parameter estimates across subpopulations (Hair et al., 2018). SmartPLS extends its CB-SEM functionality by estimating 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 as follows.
| Constraint type | Purpose |
|---|---|
| Fix values | E.g., fix a loading to 1 for scale identification. |
| Equality constraints | Force two or more parameters to share the same value (e.g., equal loadings or paths). |
| Across-group constraints | Constrain parameters to be equal across all groups for invariance testing. |
Measurement Invariance Testing
Ensuring measurement invariance is a requirement for multigroup analysis. SmartPLS provides a structured framework for assessing measurement invariance by comparing nested models with increasingly strict equality constraints; see the linked page for the full set of invariance levels and testing sequences.
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.
Frequently Asked Questions
What does multigroup analysis in CB-SEM test?
CB-SEM MGA tests whether a specified model holds equivalently across different groups, such as male vs. female or experimental vs. control. It lets researchers assess the stability of relationships between constructs and compare parameter estimates across subpopulations.
What kinds of constraints can I apply in CB-SEM MGA?
You can fix specific values (e.g., fixing a loading to 1 for scale identification), apply equality constraints that force two or more parameters to share the same value, or apply across-group constraints that require parameters to be equal across all groups for invariance testing.
Do I need to establish measurement invariance before running MGA?
Yes. Ensuring measurement invariance is a requirement for multigroup analysis. SmartPLS provides a structured framework for this on its dedicated measurement invariance assessment page.
What happens if I don't specify cross-group constraints?
SmartPLS estimates the same model separately for each group without imposing cross-group constraints, unless you specify them.
Related SmartPLS Methods
- CB-SEM Measurement Invariance Assessment
- CB-SEM Moderation
- CB-SEM Bootstrapping
- CB-SEM Model Comparison (LRT)
- CB-SEM
References
- Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2018). Multivariate data analysis (8th ed.). Cengage Learning.
- 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
