if I have missings on independent variables, are there any theoretical or rational limitations where I should NOT use maximum likelihood estimation? In my special case I have two time points were data was either collected via telephone or via mail if not reached by phone. If someone participated at only one time point, there are missings at all variables of the second time point. If I wanted to estimate all missing values, I wondered if I even could use maximum likelihood estimation to estimate the contact modus (telephone or a mail).
I know this is a more global question not specifically about Mplus. However, I would be glad about some help or some related reference!
Missing data theory does not apply to covariates. I would use FIML and mention the variances of the covariates in the MODEL command. They will then be treated as dependent variables and distributional assumptions will be made about them. This is asymptotically equivalent to multiple imputation.