Obtaining Predictions from Models Fit to Multiply Imputed Data

Obtaining predictions from regression models fit to multiply imputed data can be challenging because treatments of multiple imputation seldom give clear guidance on how predictions can be calculated, and because available software often does not have built-in routines for performing the necessary calculations. This research note reviews how predictions can be obtained using Rubin's rules, that is, by being estimated separately in each imputed data set and then combined. It then demonstrates that predictions can also be calculated directly from the final analysis model. Both approaches yield identical results when predictions rely solely on linear transformations of the coefficients and calculate standard errors using the delta method and diverge only slightly when using nonlinear transformations. However, calculation from the final model is faster, easier to implement, and generates predictions with a clearer relationship to model coefficients. These principles are illustrated using data from the General Social Survey and with a simulation.