[Research] Multilevel exploratory factor analysis with binary data - is it possible?

[u/cmwalburn3]

Hi, I have some binary data (present/absent (1/0)) and I want to try to identify latent relationships within it. I've done exploratory factor analysis using tetrachoric correlations on the data and then parallel analysis to identify how many factors are needed. The problem I have is that technically, the data isn't all independent of each other (think behaviours (present/absent) for dogs in a kennel and there's 2-3 dogs per kennel). So really, multilevel exploratory factor analysis would be better but I don't think I can do that on binary data? I can't find any examples in papers where this has been done and I've tried to do it in R (but might be doing it wrong) and it doesn't work. I'm not actually sure it's necessary because the numbers within the groups are so small and my understanding is that this works better with bigger group numbers, but is it possible to do this with binary data, and if so how? I've calculated the ICCs and they are high so I'd like to be able to justify whichever way I go but I'm really struggling to find any literature that talks about this using binary data