Regularized calibrated estimation of propensity scores with model misspecification and high-dimensional data

By Zhiqiang Tan. Biometrika, 2017

106 citations recorded by the source corpus.

Propensity scores are widely used with inverse probability weighting to estimate treatment effects in observational studies. We study calibrated estimation as an alternative to maximum likelihood estimation for fitting logistic propensity score models. We show that, with possible model misspecification, minimizing the expected calibration loss underlying the calibrated estimators involves reducing both the expected likelihood loss and a measure of relative errors between the limiting and true propensity scores, which governs the mean squared errors of inverse probability weighted estimators. Furthermore, we derive a regularized calibrated estimator by minimizing the calibration loss with a lasso penalty. We develop a Fisher scoring descent algorithm for computing the proposed estimator and provide a high-dimensional analysis of the resulting inverse probability weighted estimators, leveraging the control of relative errors of propensity scores for calibrated estimation. We present a simulation study and an empirical application to demonstrate the advantages of the proposed methods over maximum likelihood and its regularization. The methods are implemented in the R package RCAL.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4357237496a2e94435508bf763a0201fa42bf2ef

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Citations in the corpus

Robust Estimation of Causal Effects via High-Dimensional Covariate Balancing Propensity Score. (2018, methodology): “Most recently and independently of this paper, Tan (2017, 2018) proposed a penalized calibrated propensity score method and studied its robustness to model misspecification.”
A unifying approach for doubly-robust $\ell_1$ regularized estimation of causal contrasts (2019, unknown): “However, there exist parameters which are defined implicitly as solutions of population moment equations Eη [u (O, a, b, χ)] = 0 involving two unknown nuisances a (Z) ≡ a (Z; η) and b (Z) ≡ b (Z; η) , and such that Eη [u (O, a ′, b, χ)] = Eη [u (O, a, b ′, χ)] = 0 for any a′ (Z) ≡ a (Z; η′) and b′ (”
The Balancing Act in Causal Inference (2021, methodology): “In their dual form, these weights have been proposed independently as an estimator of the propensity score using a log-linear model that is calibrated in the sense that it achieves balance even if misspecified (Tan, 2020).”
Model-assisted inference for treatment effects using regularized calibrated estimation with high-dimensional data (2018, methodology): “The estimator γ̂ 1RCAL is a regularized calibrated estimator of γ from Tan (2017) as in Section 3.3.”