Abstract:
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Examples of "doubly robust" (DR) estimators for missing data include augmented inverse probability weighting (AIPWT; Robins et al., 1994) and penalized splines of propensity prediction (PSPP; Zhang and Little, 2009). DR estimators have the property that, if either the response propensity or the mean is modeled correctly, a consistent estimator of the population mean is obtained. However, DR 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 and mean model estimation. We term these "robust-squared" in the sense that the propensity score, the means, or both can be estimated with minimal model misspecification, and applied to the DR estimator. We consider their behavior via simulations where propensities and/or mean models are misspecified. We also apply our proposed method to impute missing instantaneous velocity (delta-v) values from the 2014 National Automotive Sampling System Crashworthiness Data System dataset.
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