Dear all,
I am conducting a multiple-group path analysis (with observed variables) using AMOS. The unconstrained model reveals that several paths coefficient were different according to p values.
When I compare the fully constrained model to the unconstrained model, chi-square differences were insignificant. However, when I compare the models by constraining only one path at a time, I have various variant path coefficients (significant chi-square change).
Should I assume that the model is invariant based on the comparison between fully unconstrained and fully constrained models? Or, should I use the "one path at a time approach" to decide and freely estimate all variant paths? So, I would like to have your opinion on the best approach.
Ps: Although the chi-square did not change, the CFI decreased in the constrained model. Could it be a reason to examine specific path variances?
Thanks
Best
Pinar
Unless you have a priori hypotheses about specific paths that would be expected to be non-invariant, I would think that the omnibus chi-square difference approach (comparing the fully constrained vs. unconstrained models globally) is the more appropriate approach. This is somewhat similar to what you would do in ANOVA. You look at the omnibus F test first. You run post hoc tests (pairwise comparisons) only if you obtain a significant F statistic. Otherwise you run into the risk of type-1 error inflation.
In your case with a non-significant overall chi-square difference, you would not compare individual paths.
Dear Christian Geiser thank you so much for your help.
Edit: Although the chi-square did not change, the CFI decreased in the constrained model. Could it be a reason to examine specific path variances?
Best
Pinar
You can go through my paper titled, "Moderating Variables in Business Research".
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