# Sensitivity Analysis with the $R^2$-Calculus

### Abstract

To estimate causal effects from observational data, assumptions that cannot be verified with the given data are an unavoidable obstacle. For instance, Linear Regression requires that all confounders are observed and Instrumental Variables is only valid if the instruments do not have a direct effect on the outcome. Therefore, researchers are in need of methods that allow them to reason about the bias introduced by the violation of assumptions. We apply the algebraic rules of partial correlations and $R^2$-values (coefficients of determination) to express the bias and variance of different estimators in terms of few interpretable quantities. Thus, we can give a recommendation on what estimator to use given certain beliefs on the strength of confounding and provide interpretable sensitivity analysis for commonly used estimators.

Date
2021-11-24 14:45 — 14:50
Event
Cantab Capital Institute for the Mathematics of Information - Industry Engagement