Dear Sabina, in my opinion you can test the factorial structure using statistical invariance between groups by SEM. In this way you can find if two group have the same factorial structure or, alternatively, if there are differences.

thank you so much I will definitely try these techniques .

but is it possible to compare PCAs for Ordinal data (variables) using chi-square as well

?

thank you. but i am using SAS software for computation i will try to figure out how can we compute the suggested polychoric correlations or t-test on PCAs

one more thing i just want to compare performance of two groups using PCAs or factors extracted from Factor analysis and Canonical correlations later on.

Hi Sabina,

Maybe you should have a look at some multivariate analysis techniques that are specifically designed for comparing groups such as "Discriminant analysis". They can provide you the components that discriminate best your two groups.

Another rather similar option (I've not exactly figured out the precise difference up to now) couldbe to use a "Redundancy analysis" techniques (usually abbreviated RDA) using the group as an explanatory factor.

Hope it helps!

thank you All for your kind suggestions.