# AIC and BIC in Latent class analysis

I am using the Latent Class Analysis feature available in Stata 15. The two statistical criterions gave me different indications: $AIC$ suggests me to use 6 classes, instead $BIC$ suggests to use 5 classes. Is this discordance unusual or not? Which is more relaible? Another thing that surprised me is that, according to the values of $AIC$ and $BIC$, the model with 2 classes is preferable to the 3-classes model..but the 4-classes model is preferable to the 2-classes and 3-classes model. I would expect that, if the 4-classes model is the best one, the 3-classes model should be preferable to the 2-classes model. Again, are these results unuasual or not? Thank you for your attention

Apologies that this answer is late, but hopefully it will help someone if not the OP.

Nylund, Asparouhov, and Muthén attempted to shed some light on this question via a simulation study some time ago. They simulated some latent class data with various structures. This is detailed on page 546 and subsequent, but basically they simulated data where the true number of latent classes was 4 or 3. Their table 7 gives their results for AIC, BIC, and one variant of each.