Triply Robust Information Criterion for Propensity Score Analysis

Abstract

When the Akaike Information Criterion (AIC) is derived based on its original definition,there is a setting in which the penalty term deviates significantly from twice the number of parameters: propensity score analysis, which is the basis of causal inference. Although a semi-parametric approach based on propensity scores is considered, the formal use of AIC for the problem of selecting the marginal structure in a marginal structure model leads to a large over-fitting. In recent years, a semi-parametric approach that has been widely used is called doubly robust estimation, which is robust against model mis-specification. In this paper, we adopt the idea of covariate balancing for the doubly robust estimation, and change the loss function from ordinary log-likelihood to one that is robust against outliers. Then, we derive a penalty term while maintaining the robustness, and propose a triply robust criterion as an information criterion with validity. In numerical experiments, we first show that the triply robust criterion clearly outperforms the formal criterion with a penalty term twice the number of parameters in terms of predictive performance in the case without model mis-specification or outliers. Next,we deal with the cases of model mis-specification or outliers, and confirm that the triply robust criterion is less sensitive to them.