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 Ismail S posted on Tuesday, March 15, 2016 - 4:55 am

I was wondering if you could help me with something:

When I run single-group analyses for Trading firms and Tourism firms, the relationship between TQM and customer results is significant for Tourism firms but nonsignificant for Trading firms. However, a multiple group analysis involving these two types of firms suggests that this relationship is invariant across the two groups (based on the Lagrange Mutiplier Test). When I check the output for each group, this relationship now appears to be significant for BOTH. So how does this relationship go from being nonsignificant to being significant for Trading firms? When I explain my findings, what should I say about the bottomline significance of this relationship for Trading firms?

As well, when I do another multiple group analysis involving Trading firms and Manufacturing firms, this same relationship is now nonsignificant for Trading firms. Can you please explain? Thanks.
 Bengt O. Muthen posted on Tuesday, March 15, 2016 - 12:22 pm
In multiple-group analysis several parameters are typically held equal across groups and these parameters benefit from the sample being larger than in either group so that their SEs are smaller. Because parameter estimates are correlated, this can influence SEs for all parameter estimates - that's probably what happens in your case.

Also, testing that each effect is significant is different than testing that they are equal. For instance, if the estimates are 0.25 and 0.35, it can happen that the 0.25 estimate is not be sig. different from zero, the second is, and their difference is not.
 Ismail S posted on Tuesday, March 15, 2016 - 1:00 pm
so how would you handle the situation with the SEs?

I am using multiple group analysis to see if model fit and individual parameters are different across groups. However, I also want to explain why,say, TQM affects customer results positively in Tourism firms but not in Trading firms. If multiple group analysis says they are equal, can I still use the single group analysis results which says this relationship is significant for one group while it's not for the other one?
 Bengt O. Muthen posted on Tuesday, March 15, 2016 - 5:31 pm
I would report the multiple-group analysis results assuming this model fits well.
 Ismail S posted on Tuesday, March 15, 2016 - 5:55 pm
So should I just say that some of the model parameters are invariant and some noninvariant without getting into the specifics about their group-level significance? Thanks.
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