Is there a way of using the penalized likelihood estimator when running a complex model in Mplus?
We are working with rare events data with binary outcome variable (suicide plan or attempt) with 10-15 independent variables, 5 of which are binary. The cell sizes are unequal, some of our cell sizes are as small as 1-5 and there is one empty cell, some are as large as 300.
From your description however I am not sure what methods you have tried and how they failed - I think ML should be fine as well without penalty. Also note that no statistical methodology can "fix" the data. If the events are rare, statistical methodology is not a substitute for the lack of information.