## Invariance Testing

Frequently asked questions about PLS path modeling.
jkelley
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### Invariance Testing

Is there a particular method for testing construct invariance in a cross-country study? I am concerned that reviews will take issue with the lack of invariance testing.

James Kelley, PhD.
Saint Joseph's University
James B. Kelley, Ph.D.

Hengkov
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Hi James,

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).

References:
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.

Best Regards,
Hengky

jkelley
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Thank you. I should have been more specific. I understand what invariance, however, I am not clear how to do in SmartPls. I am a convert to PLS, but predominately do international research.

So, based on your suggestions, Should I follow the suggested articles in your post to test for invariance?

Regards,
James
James B. Kelley, Ph.D.

Hengkov
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Hi James,

Yes, please check two paper Symposium Houston by Chin et al. (2012) and Visinescu (2012) for how to test invariance in PLS-SEM OK.
I cannot detail explain it very long.

Best Regards,
Hengky

Hosam
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unfortunately I couldn't find the full papers of of Chin et al. (2012) or Visinescu (2012), the last one is available online in a form of presentation only through this link

http://www.plsconference.com/Slides/PLS ... arison.pdf

I could find this one very useful
(Chin & Dibbern, 2010)

Chin, W. W., & Dibbern, J. (2010). An introduction to a permutation based procedure for multi-group PLS analysis: Results of tests of differences on simulated data and a cross cultural analysis of the sourcing of information system services between Germany and the USA Handbook of Partial Least Squares (pp. 171-193): Springer.

any other suggestion regarding this subject?

Thanks in advance.