Estimating interaction effects with incomplete predictor variables

The existing missing data literature does not provide a clear prescription for estimating interaction effects with missing data, particularly when the interaction involves a pair of continuous variables. In this article, we describe maximum likelihood and multiple imputation procedures for this common analysis problem. We outline 3 latent variable model specifications for interaction analyses with missing data. These models apply procedures from the latent variable interaction literature to analyses with a single indicator per construct (e.g., a regression analysis with scale scores). We also discuss multiple imputation for interaction effects, emphasizing an approach that applies standard imputation procedures to the product of 2 raw score predictors. We thoroughly describe the process of probing interaction effects with maximum likelihood and multiple imputation. For both missing data handling techniques, we outline centering and transformation strategies that researchers can implement in popular software packages, and we use a series of real data analyses to illustrate these methods. Finally, we use computer simulations to evaluate the performance of the proposed techniques.