I am trying to understand how the log likelihood is calculated in Latent class analysis (since this is the basis of all the other quality of fit measures).
For a single group, I have been able to calculate the Log Likelihood by assuming the (same) group part-worth for each respondent and using steps a) and b) described here: https://sawtoothsoftware.com/forum/24014/compute-rlh-for-hb
As described here: https://www.sawtoothsoftware.com/download/techpap/lclass_manual.pdf
(on p.32), the overall log likelihood is obtained by summing the logs of those probabilities, over all respondents and questions. This worked fine for the 1 group case.
However, for the two-group case, my results differed from the log likelihood reported by Sawtooth. Could it be, that I need to use the pseudo individual-level utilities for each respondent (described here: https://sawtoothsoftware.com/forum/13296/hit-rate-in-latent-class-analysis?show=13296#q13296
) instead of the group-level utility of the group, to which a respondent is most likely to belong?
If so, does this make sense with regards to the quality measures (AIC, BIC etc)? The purpose of these measures is to see, how well the groups capture the underlying preferences. However, if I use a "pseudo"-individual utility, this isn't really the same as the utility of the group, because I would use different utilities for each respondent...