Comparison of Nested Models for Multiply Imputed Data

The multiple imputation (MI) is one of the most popular and efficient methods to deal with missing data. For MI, the estimated parameters from imputed data sets are combined based on the Rubin’s rule; however, there are no general suggestions on how to combine the log-likelihood functions. The log-likelihood is a key component for model fit statistics. This study compares different ways to combine likelihood functions when MI is used for hierarchically nested models. Specifically, three ways for pooling likelihoods and four weights for combined log-likelihood value suggested by Kientoff are compared. Simulation studies are conducted to investigate the performance of these methods under six conditions, such as different sample sizes, different missing rates, and different numbers of parameters. We imputed missing data using the multiple imputation by chained equations for MI.