Checking for associations after a latent class analysis

[George Gregory]

I have preformed a latent class analysis on my data to understand how different types of abuse relate to each other. Now I have a four class model.
I want to check of association with different independent variables such as age, sex, education and income (all as categorical variables). Thus, I want to treat the latent classes as the outcome and the other variables as exposure. Questions:

1. Would it make sense to preform a multinomial logistic regression?
2. I am unsure what group to make the reference group since I believe it makes the results difficult to interpret. I was thinking that potentially I could manually create a different class which would be those that are not abused and then used that group as the reference. It would make the interpretation more straighforward and in line with the goal of the research but I am not sure if it makes sense statistically speaking or if I am mixing two methods. What do you think?

Thanks!

[Erik Ruzek]

The main problem you have with this approach is that you are taking a latent categorical variable that has a fair degree of uncertainty and giving it absolute certainty by predicting its value for each individual in the dataset. Unless the model is doing a very good job putting individuals into the latent classes (you need to calculate and check the entropy of your model to help determine this), this introduces a lot of noise and can lead to problems. If the entropy of the model is >= 0.8, then you probably can be fairly confident in the classification of individuals to the classes. Absent that, then you need to employ other methods for doing this. See this presentation by Tompsett & DeStavola (2022) for a guide to using R and Stata to do it appropriately.

The other option is to include the covariates in your LCA. See this cross-validated Q&A on this idea. You can do this in Stata very easily (see Kristin MacDonald's presentation here).