I have four, four-item subscales that I'd like to use in a mixture model. Currently the subscales are continuous and thus I want to conduct a latent profile analysis (LPA). However, given that this LPA would only have the four indicators (one of each subscale), I can only extract up to 3 latent classes before my degrees of freedom become negative.
Could I embed a CFA into the mixture model, so that each subscale's items indicate a latent factor for that subscale, and those latent factors are used as indicators in the LPA?
Is this A. feasible and B. something that would overcome my negative df issue, so that I can extract more possible classes?
It is possible in principle to extract latent classes based on latent factors (in programs like Mplus) but difficult in practice. Another (simpler) idea would be to analyze item-level data using classical LCA for categorical/ordinal data. That way, you could increase your number of latent class indicators to a maximum of 4 x 4 = 16. (Or perhaps you could select only the two or three best items from each subscale.)
Thanks Christian Geiser ! I've also been reading up on factor mixture modeling--using the item-level indicators both to confirm the factor structure as well as to inform class membership.
Factor mixture modeling is definitely another option that you could try.
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