I have estimated the same model using LGC and HLM models in Mplus. When the model did not include a level-2 variable, Log L was essentially the same for the two models (difference of .001) and parameter estimates were essentially the same (maximum difference of .001). When the model included a dichotomous level-2 variable, -Log L was not equal for the two models (-59311.800 vs -56107.439) but parameter estimates were esssentailly the same (maximum difference of .002). I am looking for a source that presents the expressions for the likelihood so I can determine why the behavior of -2 Log L is different in the two cases. If anyone can provide a source, I will appreciate it.