I am trying to learn latent class models. I don't know much about them. I'm trying to figure out how to use GSEM in stata. In particular, I can estimate the first stage analyses.

I understand these classes are based on latent (unobservable) variables. Let's say I am estimating the following simple model:

Y = b1x1 + b2x2 + e

Let's say that I want to estimate b1 and b2 for 10 different classes. So that means that I will get 10 b1 coefficients and 10 b2 coefficients (one for each class). Is there a way to identify the observations in each class? Is that question silly/unanswerable? I understand the classes are unobservable, but I am wondering if I could somehow use GSEM to identify the classes.

Ultimately, what I want to do is the following. Let's say I have 10 coefficients for b1. Let's say that there are 100 observations with each b1. I want to identify which observations in the sample have which b1 coefficients. Then, I want to estimate regressions of these b1 coefficients against other variables to see if I can find in which way other firm characteristics are related to the differences in the 10 b1 coefficients. Does that make sense?

Thanks!