I'd like to know your opinion on the applicability of the discussion regarding formative versus reflective indicators from the Factor Analysis world to the Latent Class world. In the FA world there is a good discussion on making sure that the measurement is modeled correctly: arrows pointing to or from the indicators, based on substantive theory; you cannot have a latent variable determining, say, your gender, therefore you should not model a FA with gender as indicator (at most it can be a predictor).
However, it seems to me that in LCA this fact does not apply the same way; class membership does not necessarily cause an indicator. For example: obviously the latent class I (more likely) belong to does not cause my race, but can I use race as an indicator for LCA instead of using it as predictor? (the question does not refer to the technicality component of modeling such an analysis, but more to the theoretical one) To give a common example, is it reasonable to model, using LCA, the classic socio-economic status, using education, income, and job prestige as class indicators? What are your opinions on this issue?
It's an interesting question. In both FA and LCA do you have a latent variable that is thought to influence the observed indicators. This is why one believes in conditional independence (or uncorrelatedness) among the indicators given the latent variable status, which is the essence of both FA and LCA. For FA, I don't believe a latent SES continuum influences education, income and job prestige - although some might argue that a person has a latent SES "need" that gets fulfilled by certain values of those indicators. More practically, the SES indicators are probably not conditionally independent - for example, education would correlate directly (have a "residual correlation") with income even within narrow SES strata. The formative as opposed to reflective approach is therefore more suited to this situation. Same for LCA - I don't think a well-fitting LCA with a small number of latent classes is likely to be found for a set of SES indicators, but there will be "residual correlations". On the other hand, it seems like change in a continuous latent variable influencing indicators implies a stronger statement about the direction of influence than with a change in a categorical latent variable. A categorical latent variable can be seen just as a cluster analysis device - finding groups of people. In other words, I would feel theoretically more comfortable with a LCA attempt for SES indicators. Well, this was a longwinded way of saying I don't know. Others may have opinions as well. - Welcome back to Mplus discussion.