Hello, I ran a LCA with 4 classes and 12 binary indicators (u1-u12) (n=1264; with missing data). The model fits the data well except for the presence of residual variance between 2 indicators, namelly between level 2 of u1 and level 2 of u2. I can see this by looking at the bivariate model fit information.
I want to correct this using a LCA with random effect. I am using ex 7.16 as a guide to write my model.
1) How do I know if the conditional independence is violated in one, two, three or all four classes? If I can't find out, do I just write my model like this:
MODEL: %overall% f by u2-u3;
2) If I have residual variance between another set of indicators, say u3 and u4, how do I model it? I could not find an exemple for this.
3) Do I have to use numerical integration here or can I just leave it at type = mixture? I read chapter 13 re: numerical integration but (sorry if this is basic) I do not understand what you mean by "...posterior distribution does not have a CLOSED FORM".
1. If you specify the residual variance for one class, the program will find the class for which that fits best. Given that each residual covariance is one dimension of integration, I would do it one at a time as shown in Example 7.16.
2. You would specify another factor.
3. Yes, numerical integration is required when the outcomes are categorical.