The bias of a weighted regression estimate due to an omitted confounder is exactly a function of two weighted partial R-squared values, yielding simple sensitivity statistics for IPW, matching, and balancing weights.
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Sensitivity of weighted least squares estimators to omitted variables
The bias of a weighted regression estimate due to an omitted confounder is exactly a function of two weighted partial R-squared values, yielding simple sensitivity statistics for IPW, matching, and balancing weights.