CB-SEM Measurement Invariance Assessment
Abstract
A requirement for the CB-SEM multigroup analysis (MGA) is measurement model assessment (Vandenberg, 2000), which SmartPLS also supports for CB-SEM. More specifically, SmartPLS extends its CB-SEM functionality by providing a systematic procedure to evaluate whether constructs are measured equivalently across groups by imposing progressively stricter equality constraints.
Measurement Invariance Testing
SmartPLS provides a structured framework for assessing measurement invariance by comparing nested models with increasing constraints:
Invariance Test Setup
Available predefined group-model constraints:
- 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:
Basic Sequence
- Configural model
- Weak (loading) invariance
- Strong (loading + intercept) invariance
- Strong (loading + intercept + means) invariance
Strict Sequence
- Configural model
- Weak (loading) invariance
- Strong (loading + intercept) invariance
- Strict (loading + intercept + residual variance) invariance
- 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).
References
- Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2018). Multivariate Data Analysis (8 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
