How to Impute Interactions, Squares, and other Transformed Variables

Researchers often carry out regression analysis using data that have missing values. Missing values can be filled in using multiple imputation, but imputation is tricky if the regression includes interactions, squares, or other transformations of the regressors. In this paper, we examine different approaches to imputing transformed variables; and we find one simple method that works well across a variety of circumstances. Our recommendation is to transform, then impute—i.e., calculate the interactions or squares in the incomplete data and then impute these transformations like any other variable. The transform-then-impute method yields good regression estimates, even though the imputed values are often inconsistent with one another. It is tempting to try and “fix” the inconsistencies in the imputed values, but methods that do so lead to biased regression estimates. Such biased methods include the passive imputation strategy implemented by the popular ice command for Stata.