Fitting models in latent profile analysis comes with several problems and pitfalls. One is that some models can not be fitted due to singualarities in covariance matrix (see Fraley & Raftery, 2007). In these cases, I do not get fit indices but warnings in R ( I'm using R packages tidyLPA and mclust). Literature suggests Bayesian Regularization to avoid this (= function priorControl () ). Indeed, models can be fitted afterwards but the fit indices (especially BIC) look kind of suspicious. There is now a huge bump in BIC for the models that could not be fitted beforehand. Does anyone have a guess what is going on here? And does anybody have a recommendation how to deal with that? Any thoughts are appreciated. I hope the plots attached can illustrate the issue.

Many thanks!!