I am testing measurement invariance with a bifactor model where every item loads on the main factor and one of two item group factors (binary indicators). Along the lines of the section on partial measurement invariance in chapter 13 of the Userís Guide, if I find that the loading for an item on one of the two factors is not invariant, would you recommend that I relax the equality constraint on the other factor in addition to relaxing the equality constraint for the threshold to test for partial invariance? Thank you very much for your assistance.
Hello, in a multigroup configural invariant model with categorical indicators, latent means are zero in all groups. In a multigroup measurement invariant model with categorical indicators, latent means are freely estimated in the non-reference groups.
What about the scenario of partial measurement invariance (where some loadings and thresholds are constrained across groups and others not)? Should the latent means be set at zero or freely estimated in the second and third groups (the non-reference groups)? It seems that setting the means to be zero in the non-reference groups creates a linear dependency (possibly through the thresholds)?