Hi; I have a couple of quick questions concerning single indicators in LCA. The reason I want a single indicator is I'm testing multiple variable models, in some the indicator is specified on a variable with others, in some it's by itself (unfortunately, it would be nice to have more indicators).
In covariance structure models, there are a number of ways to include a single-indicator latent variable. One of these is to fix the factor loading to one and error variance at 0, the other is to fix the residual variance to account for reliability.
If I'm correct, the analogue to the first solution to this in LCA in MPLUS is to fix the logit at some high value (say 15) for one class, thus producing a probability on one class of 1. The first question I have is, can I just enter the indicator into the model in this case as I would in SEM and produce the same result as if I created a 2 class latent variable w/the constraint?
My second question is how to produce an anlogue to the second solution, fixing the probability (in this case the logit) to some lower threshold to account for imperfect measurement, making some assumption about how imperfect. Is this a valid technique?
You can accomplish this by having a latent class variable take the role of an error-free counterpart to the categorical outcome. This is discussed in our handout for "Day 4" of our 5-day course. - See pages 10 and 11.