My LCA model is like the example 7.20 in User's Guide Examples. I have two second-order factors and i am studying the the effect of first second-order factor (data measured in the year 2003) to the other second order factor (data for the year 2006). Factor loading are set equal at the two time points. There is 3 first order factors and 4 items for each first order factor. I have also created a simulated data set to study this kind of modelling.
The second order factor model (without LCA) runs OK and i get right parameter values (for the simulated data set). Then when i try to study with LCA, if there are latent classes or subpopulations (CLASSES = c(2)), where the regression parameter between the two second order factors might be different, tho model does not converge (non-positive definite fisher information matrix).
Problem involves the first parameter of the alpha-vector (in my case first first-level factor intercept).
My question is how to setup these intercepts or factor means -parameters in this kind of second-order factor model?
There are 2 versions of the modeling that you can consider (see also my "latent variable hybrid" overview paper on the web site). One has the measurement intercepts of your factor indicators held equal across classes. This makes it possible to identify your factor means in one class (while the other has means fixed at zero). The other version - which usually fits much better - has the measurement intercepts unequal across classes. In this case, it is not possible to also identify factor means and they should therefore be fixed at zero in the overall part of the model.