Identifying When Effect Restoration Will Improve Estimates of Causal Effect

Several methods have been developed that combine multiple models learned on different data sets and then use that combination to reach conclusions that would not have been possible with any one of the models alone. We examine one such method—effect restoration—which was originally developed to mitigate the effects of poorly measured confounding variables in a causal model. We show how effect restoration can be used to combine results from different machine learning models and how the combined model can be used to estimate causal effects that are not identifiable from either of the original studies alone. We characterize the performance of effect restoration by using both theoretical analysis and simulation studies. Specifically, we show how conditional independence tests and common assumptions can help distinguish when effect restoration should and should not be applied, and we use empirical analysis to show the limited range of conditions under which effect restoration should be applied in prac-