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Dear everyone,

I am a newbie and trying to conduct MICOM and MGA analysis. However, result of Stage 2 (MICOM) showed 'no' compositional invarience (compositional invarience not established). What are the optimal solution for dealing with this?

I have found an article from Henseler 2016 told that "The analysis of Situation 6 shows that the lack of compositional invariance implies that the scores obtained through group-specific model estimations differ from the scores resulting from the pooled data (no measurement invariance established). Researchers should only analyze and interpret the group-specific model estimations separately."
The link of article: https://www.emerald.com/insight/content ... /full/html

Would anyone tell me in more details what and how can I do with :"analyze and interpret the group-specific model estimations separately" ?

I would like to express thankful attitude for your help,

I wish you all a good working ahead,

Best regard,
Hung

If compositional invarience not established, you cannot compare the groups (the group-specific estimates such as path coefficients), because it is not assured that the construct are measured in the same way. Therefore, differences in the path coefficients, for example, could be the reason of measuring different concepts instead of different strength of the same relationship.

Thank you for your answer.
"...you cannot compare the groups (the group-specific estimates such as path coefficients), because it is not assured that the construct are measured in the same way...."
Would you please explain more on measured in the same way? Here, I understand that we use the same questionnaires for different groups = measure in the same way -> Is it true?
I wish you a good day

What you refer to is more configural invariance, that you have identical indicators (e.g., the same questions), construct orientation (e.g., reflective vs. formative), data treatment, etc. This is a prerequisite for all later stages of invariance.

Compositional invariance should establish that there are no discrepancies of what is intended to be measured and what is actually measured in terms of the compositional structure of the indicators of the construct. Groups of individuals may interpret a measure in a conceptually different manner and respond to the indicators (your measures) in systematically different ways. If this is the case, you can actually not conclude that you have measured the same concept in both groups. And if you cannot assure that you have measured the same concept you cannot say that the influence of concept A is stronger/weaker in group 1 vs. 2, because the one is the effect of A1 and the other the effect of A2.

Thank you so much for your detailed answer. I think that I can understand much about that

Compositional invariance exists when the composite scores are the same across the groups, despite possible differences in the group- specific weights used to compute the scores.