📈 Data ScientistID:
ds-propensity-score-matching-doubly-robustPSM Matching & Doubly Robust Estimator
倾向得分 PSM 与双重稳健估计器
🎯Core Definition
Propensity Score Matching (PSM), Inverse Probability Weighting (IPW) & Doubly Robust Estimators (AIPW, Robins et al.) eliminate confounding and selection bias from high-dimensional observational data; Core theory: the Propensity Score is the conditional treatment assignment probability (modeled via Logistic Regression or GBDT); Rosenbaum-Rubin Theorem: under unconfoundedness, conditioning on the 1D scalar propensity score $e(X)$ is mathematically sufficient to balance all multi-dimensional covariates $X$; Matching Algorithms include Nearest Neighbor, Caliper thresholding, and Common Support trimming; The Doubly Robust (AIPW) estimator unifies the propensity score weighting model with an outcome regression model: if either the propensity model OR the outcome model is correctly specified, the causal estimate remains asymptotically unbiased and consistent.
💡Use Cases
Measuring non-randomized feature adoption (e.g. true causal lift of VIP subscription purchasing) and retention campaign attribution.
⚡Key Problems Solved
Active users naturally retain higher (selection bias), inflating perceived feature value; PSM/AIPW constructs synthetic twin control users to estimate genuine causal increments.
🎯5 High-Frequency Exam Points
1
Prove the Rosenbaum-Rubin dimension reduction theorem establishing conditional independence given 1D propensity score ?
2
Derive Inverse Probability Weighting (IPW) estimator and explain extreme variance explosions when propensity scores approach 0 or 1?
3
Derive the AIPW estimator formula and prove why misspecification in either the propensity score or outcome model preserves unbiasedness?
4
How to audit propensity score overlap histograms and enforce common support trimming to prevent dangerous extrapolation?
5
Why is Standardized Mean Difference (SMD ) preferred over -values to evaluate post-matching covariate balance?
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Updated 2026-08-14🎯
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