Conducting a three-step Latent Class Analysis in R I'm trying to conduct a Latent Class Analysis in R using the poLCA package, and I have now become stuck on two aspects of the process.


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*I have conducted Latent Class Analysis separately for males and females, as it looks as though the variables behave differently in each. However, I am aware journals tend to want a significance test to assert that this separation was necessary - does anyone have any idea how to code this with poLCA objects?

*I am trying to use the three-step method to assign people to classes, based on that described by Asparouhov and Muthen (https://www.tandfonline.com/doi/pdf/10.1080/10705511.2014.915181?needAccess=true). Yet, again, I can't work out how to do it. I thought this reddit thread might help (https://www.reddit.com/r/statistics/comments/2dh5h5/hey_all_i_need_help_converting_between_logits_and/), but I still don't understand (a) how to convert between the tables described, nor (b) how this data would then be used to assign each individual to a class.
Sorry that my descriptions of the issues are slightly vague; can anyone shed any light on either of them?
 A: I can only comment on #1 for now. You are talking about fitting a multiple-group latent class model (link goes to UCLA website with a worked example in MPlus. This is a bit like differential item function in item response theory. In the latent class case, you would fit a multiple group model, then use Wald tests for the parameter estimates. You can obviously do this in MPlus, and I typed up the Stata syntax here.
Unfortunately, it appears that poLCA can't fit a multiple-group LCA. You can obviously fit the models separately, but I don't see a way to test if the parameters differ. I am not that conversant on the capabilities of other R packages, so I can't advise.
On #2, as I understand the article, you're talking about a method to estimate the relationship between latent classes and a distal (unrelated) outcome. We recently had a discussion about that and there is likely to be a simpler method than what Muthén and Asparaouhov proposed above, although I believe they critique the paper I was referencing in the link.
I've read the Muthén/Asparouhov article you linked, and right now, it is not making sense to me (not because I think they're wrong, but because I can't understand it). I may alter this answer if I read it and finally get it.
A: Re question 1, why would you need to fit a LC model for each group separately? An alternative (and presumably easier - or at least more conceptually straightforward) would be to analyse all the data at same time and then use gender as predictor of class membership - This will tell you whether gender has a significant effect on variability in your data (and you can compute the magnitude of the gender effect - eg "male are on average +25% more likely to belong to class #1 than reference class").
Re question 2, I haven't read the cited article yet, but "simple" post-estimation following the Bayesian rule should do the job (as nicely explained in https://www.sciencedirect.com/science/article/pii/S0191261502000462) [Not sure this approach has already been implemented in R/Matlab though].
A: For question 1, you can use GLCA to do a grouped LCA. There is a detailed vignette explaining how to test for model invariance.
(In fact, I think this package has now surpassed poLCA as the best LCA package in R).
