Abstract:
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We propose a flexible Bayesian semi-parametric approach for estimating heterogeneous treatment effects from observational data. Specifically, we model the Transformed Response Variable (TRV) proposed by Dudik et al. (2011) and Beygelzimer and Langford (2009) as the conditional average treatment effect (CATE) with Bayesian Additive Regression Trees (BART) plus a residual which is a mixture of two Gaussian distributions resulting from the response under treatment and response under control. We therefore flexibly adapt to effect heterogeneity by simultaneously accounting for the response independent of treatment status. Importantly, our method allows us to estimate the treatment effect directly without the need to model two response surfaces for the groups assigned to treatment and control. Moreover, due to the improved model specification in our method, we are able to substantially reduce the error in the CATE relative to competing methods using the TRV while simultaneously reducing the variance of our estimators.
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