# 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.

1. 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?

2. 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?

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.

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].

• Imagine you think that the probability of responding to each item or the mean of each item differs between two observed groups. This is conceptually distinct from just using observed groups to predict latent class membership. It's more akin to differential item function in IRT. This was already alluded to in my answer. – Weiwen Ng Mar 25 '19 at 21:00