Hello, I am trying to perform a “LCA with a second-order factor (twin analysis)” according to example 7.18 in the ‘version 7’ manual. According to a preliminary LCA I did with all the twins in a long format, the best model is one with 4 classes in the latent variable C, and that is what I asked in the current example.
I would like to ask three questions regarding the analysis: 1) I am wondering why there is no constraint in the example, so that the relation between the indicators and the classes will be equal for both twins? Is there a theoretical reason to believe that one set of kids will have different set of indicators’ probabilities than their co-twins?
2) I couldn’t find the meaning of the ‘minus one’ that was added in the LCA commands (e.g., “[u11$1-u13$1*-1];”). How should I refer to it if I have four classes instead of two?
3)Finally, the next step I am planning is to examine the ACE model on the latent variable C. Should I: a) use the knownclass command on example 7.18; b) download the most probable class for each participant(i.e., use savedata) and then follow example 7.28-“TWO-GROUP TWIN MODEL FOR CATEGORICAL OUTCOMES USING MAXIMUM LIKELIHOOD AND PARAMETER CONSTRAINTS”, with the most probable category as an observed categorical variable?; or c) do something completly different I haven't thought of?
UG ex 7.18 is intended mainly for a binary latent class variable so that the f->c (c on f) relationship is logistic regression - although with a latent DV. You have 4 classes which means that the c on f regression is a multinomial logistic regression where the DV is nominal. This means that you don't have a single slope but several slopes for c on f. That means that a standard ACE decomposition is not available.
If you believe that your latent classes are ordered you could first classify subjects and then enter their class membership as an observed variable that you can then declare as categorical in which case an ordinal logistic regression is used with a single slope. That should make it possible to do an ACE decomposition in the usual way for ordinal observed DVs. For that, however, you have to consult the twin literature.
Mplus estimates the model in 7.18 by ML in a single step.
Note also that you can look at twin congruence of classification across nominal classes and how that differs between twin types - but I don't think that is standard twin methodology.
So as you see this modeling approach is at the research frontier.