MGA for more than two groups

[dnirmala]

Hi,

I am currently trying to do MGA for three groups. I have conducted MICOM procedure and only partial measurement invariance was established as equal mean values and variances is not available.

I am bit confused about the next step. Should I run, Permutation MGA or Bootstrap MGA next?

Also, I would thank full to anyone who can direct me to literature which has done MGA for more than two groups.

Thank you.
regards
Dasun

[jmbecker]

I think this would be the perfect reference for you: https://www.sciencedirect.com/science/a ... 6322010049

Cheah, J. H., Amaro, S., & Roldán, J. L. (2023). Multigroup analysis of more than two groups in PLS-SEM: A review, illustration, and recommendations. Journal of Business Research, 156, 113539.

[dnirmala]

Dear Dr. Becker

Thank you very much for the reply.

The paper you referred Cheah et al. (2023) uses the OTG method after the MICOM procedure. However, some sources say to conduct "Pairwise comparison and familywise error correction". Also, how to decide what procedure to run in Smart PLS (MGA or permutation MGA) to conduct pairwise comparison?

Screenshot 2023-10-14 0947122.png (96.62 KiB) Viewed 1897 times

Regards
Dasun

[jmbecker]

The OTG approach does not work properly. I think they also refer to sources have have found this.
In addition, the question is also whether such an omnibus test is actually helpful. Do you want to know that your three groups are on average somehow different, or do you want to know between which groups there are difference?

The last one can only be answered by pairwise comparisons using proper correction for inflation of the error rate.

I think the paper clearly recommends the permutation-based test for pairwise difference testing (they call it the non-parametric permutation-based test (NPT)). That is also what I would generally recommend. Earlier research had some differential recommendations for the bootstrap-based and permutation-based MGA depending of the type of model and data. Latest research by Klessel et al. (2022), however, recommends the permutation-based approach univocally. Although the difference to the bootstrap-based test are usually not large. I also always do the bootstrap-based MGA as an additional robustness check. If the results agree, you can be more certain about the finding.

[dnirmala]

Dear Dr. Becker

Thank you very much. Your comments are greatly appreciated.
I like the suggestion to use bootstrap MGA as robust test.

Regards
Dasun