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...

If I understand you right:

1. "logit estimation is done for each group": so in case of two groups, I would twice use the steps a to b described here (https://sawtoothsoftware.com/forum/24014/compute-rlh-for-hb) once to calculate L_xji_1 for each respondent "i" and task "j", assuming utilities of group "1", and the second time to calculate L_xji_2 for each respondent "i" and task "j", assuming utilities of group "2"?

2. "each respondent is weighted by the likelihood of belonging in each group... LLs are summed across the multiple groups": so I would calculate the total LL as sum of probability weighted root likelihoods over all respondents "i" and all tasks "j":

Sum[log(L_xji_1) * wi_1 + log(L_xji_2) * wi_2]

where wi_1 is the likelihood of respondent i belonging to group 1?

Is that what you mean, or did I get you wrong?

edited May 6, 2020