Abstract:
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Example of "doubly robust" estimators for missing data include augmented inverse probability weighting (AIPWT) models (Bang and Robins 2005) and penalized spline of propensity prediction (PSPP) models (Zhang and Little 2009). Under missing at random (MAR) mechanisms, consistent estimation of a population mean can be obtained by weighting by the inverse of the probability of response conditional on observed covariates, or by prediction from those covariates. Double robustness refers to models in which if either the response propensity or the mean is modeled correctly, a consistent estimator of a population mean is obtained. Doubly robust estimators can perform poorly when modest misspecification is present in both models (Kang and Schafer 2007). Here we consider extensions of the AIPWT and PSPP models that use Bayesian Additive Regression Trees (BART; Chipman et al. 2010) to provide highly robust propensity estimation. We consider their behavior via simulations where propensities and/or mean models are misspecified, and show that BART applied to PSPP provides efficient and robust estimation. We also consider an application to the National Automotive Sampling System (NASS).
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