Abstract:
|
In an observational study, propensity scores are commonly modeled by a generalized linear model (GLM), but the standard maximum likelihood solution may suffer from unsatisfactory covariate balance. This paper proposes to use tailored loss functions- covariate balancing scoring rules (CBSR)-to estimate the propensity score. A CBSR is determined by the link function in the GLM and the estimand (some weighted average treatment effect). If the Bernoulli likelihood criterion is replaced by CBSR to fit the GLM, the resulting inverse probability weights automatically balance all predictors in the GLM. More practical and adaptive strategies are then proposed, including forward stepwise, regularized and reproducing kernel Hilbert space regressions, connecting causal inference with novel machine learning methods. This paper studies the asymptotic efficiency and bias reduction of GLMs fitted by maximizing CBPS, and uses two examples (one simulation, one real data) to study the performance of the proposed methods. Both theoretical and empirical analysis show that CBPS is a superior alternative to Bernoulli likelihood.
|