Multiple Imputation of Missing Data in Moderated Factor Analysis

In moderated factor analysis, the parameters of the traditional common factor model are a function of an external continuous moderator variable. Handling missing values on the observed indicator variables of the common factors is straightforward as the parameters can be estimated using full information maximum likelihood. However, for cases with missing values on the moderator variable the likelihood function cannot be evaluated. Consequently, in practical applications of the moderated factor model, these cases are omitted from the analysis by listwise deletion. As listwise deletion is known to potentially affect the consistency and precision of the results, we propose a moderated factor model based multiple imputation procedure for handling missing values on the moderator variable in the presence of missing values on the indicator variables. We compare this new procedure with listwise deletion and predictive mean matching. The results show that both listwise deletion and predictive mean matching have less power and produce more bias in parameter estimates than multiple imputation under the moderated factor model.