Measurement invariance hypotheses verify:
- configural variance
- construct-level metric invariance
- item-level metric invariance
- residual variance invariance
- intercept invariance
- equivalence of construct variance
- equivalence of construct covariance
- equivalence of latent means
Sarstedt et al. (2011) state: Construct measures are invariant among groups
Moderator variable effect is restricted to the path coefficient
If, variance among group not same, used SST method by Chin (2000), modified Nitzl (2010).
Chin W.W. 2000. Frequently Asked Questions – Partial Least Squares & PLS-Graph. URL http://disc-nt.cba.uh.edu/chin/plsfac/plsfac.html
Chin, W.W., Mills, A.M., Steel, D.J., and Schwarz, A. 2012. “Multi-Group Invariance Testing: An Illustrative Comparison of PLS Permutation and Covariance-Based SEM Invariance Analysis,” Proceedings: 7th International Conference on Partial Least Squares and Related Methods, Houston, Texas USA, pp. 1-11.
Sarstedt, M., Henseler, J., and Ringle, C.M. 2011. “Multigroup Analysis in Partial Least Squares (PLS) Path Modeling: Alternative Methods and Empirical Result,” Advances in International Merketing (22:1), 195-218.
Visinescu, L. 2012. PLS Group Comparison: A Proposal for Relaxing Measurement Invariance Assumptions. Proceedings: 7th International Conference on Partial Least Squares and Related Methods, Houston, Texas USA.