adjusted_critical_value function

Bias-adjusted critical values

These functions compute bias adjusted critical values for a given postulated strength of omitted variable with the dependent and independent variables of an OLS regression.

Researchers can thus easily perform sensitivity analysis by simply substituting traditional thresholds with bias-adjusted thresholds, when testing a particular null hypothesis, or when constructing confidence intervals.

adjusted_critical_value(r2dz.x, r2yz.dx, dof, alpha = 0.05, max = T)

Arguments

• r2dz.x: hypothetical partial R2 of unobserved confounder Z with treatment D, given covariates X.
• r2yz.dx: hypothetical partial R2 of unobserved confounder Z with outcome Y, given covariates X and treatment D.
• dof: residual degrees of freedom of the regression.
• alpha: significance level. Default is 0.05.
• max: if TRUE (default) it computes the worst possible adjusted critical threshold for an omitted variable with strength limited by r2dz.x and r2yz.dx.

Returns

Numeric vector with bias-adjusted critical values.

Examples

# traditional critical threshold (no confounding) is 1.96 (dof = 1e4)
adjusted_critical_value(r2dz.x = 0, r2yz.dx = 0, dof = 1e4, alpha = 0.05)

# adjusted critical threshold, r2 = 1% is 2.96 (dof = 1e4)
adjusted_critical_value(r2dz.x = 0.01, r2yz.dx = 0.01, dof = 1e4, alpha = 0.05)

References

Cinelli, C. and Hazlett, C. (2020), "Making Sense of Sensitivity: Extending Omitted Variable Bias." Journal of the Royal Statistical Society, Series B (Statistical Methodology).

Cinelli, C. and Hazlett, C. (2023), "An Omitted Variable Bias Framework for Sensitivity Analysis of Instrumental Variables."