Variable Selection for Causal Effect Estimation: Nonparametric Conditional Independence Testing With Random Forests

Abstract

Widespread availability of rich educational databases facilitates the use of conditioning strategies to estimate causal effects with nonexperimental data. With dozens, hundreds, or more potential predictors, variable selection can be useful for practical reasons related to communicating results and for statistical reasons related to improving the efficiency of estimators. Background knowledge should take precedence in deciding which variables to retain. However, with many potential predictors, theory may be weak, such that functional form relationships are likely to be unknown. In this article, I propose a nonparametric method for data-driven variable selection based on permutation testing with conditional random forest variable importance. The algorithm automatically handles nonlinear relationships and interactions in its naive implementation. Through a series of Monte Carlo simulation studies and a case study with Early Childhood Longitudinal Study–K data, I find that the method performs well across a variety of scenarios where other methods fail.