I have a model that has data from two different groups. As per the suggestion from Beaujean (2014) I run measurementInvariance and find that even the strong fit has good fit indices.
chisq df pvalue cfi rmsea srmr 47.992 57 0.797 1.0 0.0 0.047
This suggests that I could merge the data and run a joint model, right? When I run the model jointly (constraining loading and intercepts), one particular loading is significant (p < 0.05). However when I run the two groups separately (unconstrained loading and intercept), that loading becomes significant in one group (p <0.1) and insignificant in another (p>0.1). I understand that the significant / insignificant issue is because of the arbitrary significance level (p = 0.1). But, assuming that I can't fight the arbitrariness, how should I look at and report this issue? Should I run the constrained model only and ignore the difference between the two groups? Or should I run the unconstrained model and claim that for this loading, the two groups are different?