I am running a series of path analyses in Mplus in order to account for my missing data (which is MAR). I noticed that when I use ML estimation with a continuous dependent variable, the model includes all of my subjects who have some data somewhere. However, when I use ML or MLR with the categorical dependent variable, the model limits the sample a lot. I understand that this is because ML estimation is not robust when the dependent variable is not multivariate normal.
Is there another estimation method or modeling approach to retain some of these subjects with missing data while modeling a categorical (binary) dependent measure?
It seems you are using a version prior to version 6. The differences you are seeing are because in one case the model is estimated conditioned on the observed exogenous covariates and in the other case they are part of the model. A full explanation of this can be found on the website under Version History for Version 6.1.