I have a score of depression. I did a factor analysis for different populations in which we think the score works in a different way. I got the different matrices of factor loadings, but I am looking for a test to compare the matrices. Did you know any approach?
If you have enough items, you could do a comparison of factor loadings between pairs of your population groups using a related t-test or Wilcoxon. However this may be underpowered if your effect size is not strong or you only have a small number of item factor loadings.
You could do an analysis of the raw data based on differences you see in the factor structure. For example, if Population A loads differently than Population B for Item 1 of your scale, then you could do difference tests on the raw scores for Item 1 in an unpaired comparison of means test, such as an unrelated t-test. Or you could run correlation tests on data that would test predictions indicated by variations in your factor structure between your groups. If you did this for all of your scales - providing sample sizes are adequate within your population groups - then you should be able to identify significant effects predicted by your matrices. You just need to predict effects in your raw data from those in your factor loadings matrices.
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