I attended a presentation where the Auxiliary feature in Mplus was discussed. A main part of the presentation was that auxiliary variables (Z) can contribute information to the relationship estimation between the dependent (Y) and independent (X) variables -- even in the presence of missingness of Y or X.
It was stated though, that -- if an observation is missing Y *and* X, but contains Z -- this observation is not removed and still contributes to the model estimates. Could you please provide an answer or reference about how this is done? I am new to Mplus. Thanks much.
It does contribute to the model estimates – here is a simple example – suppose that Z is a perfect indicator for Y (i.e. when Y and Z are both observed Y=Z) – then adding the auxiliary Z will make Y always observed (essentially) and thus the mean of Y will depend on Z and those observations where Z is the only observed value.