Methods for Moderation Analysis with Missing Data

In the study, I consider a simple moderated multiple regression (MMR) model, where the effect of predictor X on the outcome Y is moderated by a moderator U. My primary interest is to find ways of estimating and testing the moderation effect with the existence of missing data. I mainly focus on cases when X and/or Y are missing completely at random (MCAR), missing at random (MAR) or missing depending on auxiliary variables (missing not at random; denoted AV-MNAR). Four methods are proposed and compared: (1) Listwise deletion; (2) Normal-distribution-based maximum likelihood estimation (NML); (3) Normal-distribution-based multiple imputation (NMI); and (4) Bayesian estimation (BE). Results from simulation studies show that the proposed methods had different relative performance depending on various factors. The factors are missing data mechanisms, population moderation effect sizes, sample sizes, missing data proportions, and distributions of predictor X. Influence of adding auxiliary variables is also discussed in terms of estimation accuracy for NML and NMI.