Primary Submission Category: Omitted Variable Bias
Multiple Regression Analysis of Unmeasured Confounding: Bounding Causal Effects by Reasoning about Randomness
Authors: R. Mitchell Hughes, Brian Knaeble,
Presenting Author: R. Mitchell Hughes*
By reasoning about randomness, we can bound the uncertainty of a causal effect of interest due to omitted variable bias in a multiple regression setting. In previous work, we introduced a methodology for computing confounding intervals, enabling assessment of uncertainty due to unmeasured attributes. We have since generalized that methodology to multiple regression and developed an algorithm to partially identify a causal effect of interest in a multiple regression model when subject matter knowledge is available. Alternatively, the algorithm supports sensitivity analysis when such knowledge is absent. The strength of our approach lies in its use of coefficients of determination which allow us to calculate bounds by intuitively reasoning about randomness. We demonstrate our methodology in two example applications which highlight how the algorithm quantifies the robustness of the causal effect against omitted variable bias.