I have conducted a Latent Profile Analysis to form clusters of 'organizational commitment' based on 8 items (x1-x8) and clusters of 'union commitment' based on 12 items (u1-u12). I have obtained 3 clusters for organizational commitment and 2 clusters for union commitment (using LCA with Mplus). Then, I did a LCA with a second order factor. I obtained 3 x 2=6 clusters. I would like to test the influence of this second order factor (let’s say it is ‘dual commitment’) on an outcome (a continuous and/ or a categorical variable y). How can I do that? I can’t use the ‘auxiliary’ function with a second order factor. Moreover, there are theoretical arguments that another variable (m1) might moderate the relationship between ‘dual commitment’ and y. m1 is a binary moderator (actually, m1 is another cluster with 2 classes based on 10 items). How can I test this moderation?
Any help and guidance would be appreciated. Thanks in advance.
I have already tried y ON f and it did not lead to the kind of results I would like (or maybe I did not find the right results in the output). Actually, I would like the equivalent of an equality test of means across classes of f (3*2 =6 classes here)using posterior-based multiple imputation. I can do it for C1 and C2 but not for f which is the second order factor.