CB-SEM Measurement Invariance Assessment
Measurement invariance testing examines whether a construct is measured equivalently across groups before those groups are compared substantively. It is a requirement for a meaningful CB-SEM multigroup analysis (MGA): if indicators do not relate to their construct the same way across groups, differences found in a group comparison may reflect measurement artifacts rather than genuine differences in the underlying construct (Vandenberg, 2000). SmartPLS supports this assessment for CB-SEM by imposing progressively stricter equality constraints across groups and comparing the resulting nested models.
Measurement Invariance Testing
SmartPLS provides a structured framework for assessing measurement invariance by comparing nested models with increasing constraints.
Invariance Test Setup
The following predefined group-model constraints are available:
| Invariance level | Constraints applied |
|---|---|
| Configural invariance | No across-group constraints; same model structure in each group, freely estimated. |
| Weak (loading) invariance | All loadings constrained equal across groups. |
| Strong (intercept) invariance | Loadings and intercepts constrained equal. Construct means fixed to zero in the first group, freely estimated in others. |
| Strong (intercept + means) invariance | Loadings, intercepts, and construct means constrained equal across groups. |
| Strict (residual) invariance | Loadings, intercepts, and indicator residual variances constrained equal across groups. Construct means fixed to zero in the first group, freely estimated in others. |
| Strict (residual + means) invariance | Loadings, intercepts, residual variances, and construct means constrained equal across groups. |
By default, MGA in SmartPLS uses the configural model without cross-group equality constraints, unless specified by the user.
Strict vs. Basic Invariance Testing
SmartPLS implements two standard invariance testing sequences, which differ in how many equality constraints are imposed before groups are compared.
| Step | Basic sequence | Strict sequence |
|---|---|---|
| 1 | Configural model | Configural model |
| 2 | Weak (loading) invariance | Weak (loading) invariance |
| 3 | Strong (loading + intercept) invariance | Strong (loading + intercept) invariance |
| 4 | Strong (loading + intercept + means) invariance | Strict (loading + intercept + residual variance) invariance |
| 5 | — | Strict (loading + intercept + residual variance + means) invariance |
In the strict sequence, the model using strong (loading + intercept + means) invariance is skipped, as comparisons are made directly between the model using strong (loading + intercept) invariance and the model using strict (loading + intercept + residual variance) invariance.
CB-SEM Examples in SmartPLS
SmartPLS provides directly computable CB-SEM measurement invariance assessment examples from leading textbooks (e.g., Hair et al., 2018). The results in SmartPLS replicate the textbook outcomes exactly. Try out the CB-SEM example projects in SmartPLS. Thereafter, you can run a CB-SEM multigroup analysis (MGA).
Frequently Asked Questions
Why is measurement invariance a prerequisite for CB-SEM multigroup analysis?
If indicators do not relate to their construct the same way across groups, differences observed in a group comparison may reflect measurement artifacts rather than genuine differences in the construct itself. Measurement invariance testing rules this out before groups are compared substantively.
What is the difference between weak, strong, and strict invariance?
Weak (loading) invariance constrains only the loadings to be equal across groups. Strong (intercept) invariance additionally constrains the intercepts. Strict (residual) invariance goes furthest by also constraining the indicator residual variances to be equal across groups. Each level can optionally also constrain construct means.
Should I use the basic or the strict invariance testing sequence?
Both sequences start with the configural model and weak (loading) invariance, then add strong (loading + intercept) invariance. The basic sequence proceeds to strong (loading + intercept + means) invariance, while the strict sequence proceeds to strict (residual) invariance and then strict (residual + means) invariance, skipping the strong (loading + intercept + means) step. The choice depends on how strict a test of invariance the research question requires.
What happens if I don't specify any invariance constraints?
By default, SmartPLS uses the configural model, which imposes no across-group constraints and freely estimates the same model structure in each group.
Related SmartPLS Methods
References
- Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2018). Multivariate data analysis (8th ed.). Cengage Learning.
- Vandenberg, R. J., & Lance, C. E. (2000). A review and synthesis of the measurement invariance literature. Organizational Research Methods, 3(1), 4–70.
- 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
