I'm testing two groups in an SEM. I went through measurement invariance testing and the measures look equivalent across groups. I'd like to test for invariance in path coefficients. My MODEL was:
MODEL: SATAQ by SATAQP1 SATAQP2 SATAQP3; Surv by SurvP1 SurvP2 SurvP3; Shame by SHAMEP1 SHAMEP2 SHAMEP3; Accept by AcceptP1 (1) AcceptP2 (1); Control by ControlP1 (2) ControlP2 (2); CUSE by sexmech sexobtain sexdissassert;
Int4 on CUSE (3); CUSE on Accept (4) Control (5); Accept on Shame (6); Control on Shame (7); Shame on SATAQ (8) Surv (9); Surv on SATAQ (10);
I thought the (x) numbers would constrain across groups, and show MIs for paths to free, but it doesn't. The model df drops by only 2, so I think I'm doing the constraints wrong. I want to test for differences among all the paths, between the two groups.
Accept and Control have constraints per Kenny on latent variables with two indicators (http://davidakenny.net/cm/identify_formal.htm, cond. B.2.b.). Is this is messing up the multigroup model (by constraining each pair to equality across both models)? I don't know how to fix this (add a Model Yes: and free those between groups? I'm not sure that's right)
If I am only interested in examining pathway differences (rather than mean differences in the latent variables) between groups, is it necessary to establish factor mean invariance? Can I terminate the analysis at the factor variance-covariance stage?