Mplus has several options for the estimation of models with missing data. Mplus provides maximum likelihood (ML) estimation under MCAR (missing completely at random) and MAR (missing at random; Little & Rubin, 2002) for continuous, censored, binary, ordered categorical (ordinal), unordered categorical (nominal), counts, or combinations of these variable types. MAR means that missingness can be a function of observed covariates and observed outcomes. For censored and categorical outcomes using the weighted least squares estimators, missingness is allowed to be a function of the observed covariates but not the observed outcomes. Non-ignorable missing data modeling is possible using maximum likelihood where categorical outcomes represent indicators of missingness and where missingness may be influenced by continuous and categorical latent variables (Muthén et al., 2003).
Multiple data sets generated using multiple imputation (Schafer, 1997) can be analyzed using a special feature of Mplus. Parameter estimates are averaged over the set of analyses, and standard errors are computed using the average of the standard errors over the set of analyses and the between analysis parameter estimate variation.
In all models, missingness is not allowed for the observed covariates because they are not part of the model. The outcomes are modeled conditional on the covariates and the covariates have no distributional assumption. Covariate missingness can be modeled if the covariates are explicitly brought into the model and given a distributional assumption. With missing data, the standard errors for the parameter estimates are computed using the observed rather than the expected information matrix (Kenward & Molenberghs, 1998). Bootstrap standard errors and confidence intervals are also available with missing data.